High Performance Computation for Engineered Systems (HPCES)
https://hdl.handle.net/1721.1/3652
2024-09-19T06:43:57ZShock Capturing with Discontinuous Galerkin Method
https://hdl.handle.net/1721.1/30375
Shock Capturing with Discontinuous Galerkin Method
Nguyen, Vinh Tan; Khoo, Boo Cheong; Peraire, Jaime; Persson, Per-Olof
Shock capturing has been a challenge for computational fluid dynamicists over the years. This article deals with discontinuous Galerkin method to solve the hyperbolic equations in which solutions may develop discontinuities in finite time. The high order discontinuous Galerkin method combining the basis of finite volume and finite element methods has shown a lot of attractive features for a wide range of applications. Various techniques proposed in the literature to deal with discontinuities basically reduce the order of interpolation in the region around these discontinuities. The accuracy of the scheme therefore may be degraded in the vicinity of the shock. The proposed method resolves the discontinuities presented in the solution by applying viscosity into the shock-containing elements. The discontinuity is spread over a distance and is well approximated in the space of interpolation functions. The technique of adding viscosity to the system and the indicator based on the expansion coefficients of the solution are presented. A number of numerical examples in one and two dimensions is carried out to show the capability of the scheme for shock capturing.
2006-01-01T00:00:00ZReal-Time Reliable Prediction of Linear-Elastic Mode-I Stress Intensity Factors for Failure Analysis
https://hdl.handle.net/1721.1/30374
Real-Time Reliable Prediction of Linear-Elastic Mode-I Stress Intensity Factors for Failure Analysis
Huynh, Dinh Bao Phuong; Peraire, Jaime; Patera, Anthony T.; Liu, Guirong
Modern engineering analysis requires accurate, reliable and efficient evaluation of outputs of interest. These outputs are functions of "input" parameter that serve to describe a particular configuration of the system, typical input geometry, material properties, or boundary conditions and loads. In many cases, the input-output relationship is a functional of the field variable - which is the solution to an input-parametrized partial differential equations (PDE). The reduced-basis approximation, adopting off-line/on-line computational procedures, allows us to compute accurate and reliable functional outputs of PDEs with rigorous error estimations. The operation count for the on-line stage depends only on a small number N and the parametric complexity of the problem, which make the reduced-basis approximation especially suitable for complex analysis such as optimizations and designs. In this work we focus on the development of finite-element and reduced-basis methodology for the accurate, fast, and reliable prediction of the stress intensity factors or strain-energy release rate of a mode-I linear elastic fracture problem. With the use of off-line/on-line computational strategy, the stress intensity factor for a particular problem can be obtained in miliseconds. The method opens a new promising prospect: not only are the numerical results obtained only in miliseconds with great savings in computational time; the results are also reliable - thanks to the rigorous and sharp a posteriori error bounds. The practical uses of our prediction are presented through several example problems.
2006-01-01T00:00:00ZA Precorrected-FFT Method for Coupled Electrostatic-Stokes Flow Problem
https://hdl.handle.net/1721.1/30373
A Precorrected-FFT Method for Coupled Electrostatic-Stokes Flow Problem
Nguyen, Ngoc Son; Lim, Kian-Meng; White, Jacob K.
We present the application of the boundary integral equation method for solving the motion of biological cell or particle under Stokes flow in the presence of electrostatic field. The huge dense matrix-vector product from the boundary integral method poses a computationally challenging problem for solving the large system of equations generated. In our work, we used the precorrected-FFT (pFFT) method to reduce the computational time and memory usage drastically, so that large scale simulations can be performed quickly on a personal computer. Results on the force field acting on the particle, as well as the behavior of the particle through cell trap are presented.
2006-01-01T00:00:00ZNumerical Study of the Poisson-Boltzmann Equation for Biomolecular Electrostatics
https://hdl.handle.net/1721.1/30372
Numerical Study of the Poisson-Boltzmann Equation for Biomolecular Electrostatics
Tan, Lian Hing; Lim, Kian Meng; White, Jacob K.
Electrostatics interaction plays a very important role in almost all biomolecular systems. The Poisson-Boltzmann equation is widely used to treat this electrostatic effect in an ionic solution. In this work, a simple mixed discrete-continuum model is considered and boundary element method is used to solve for the solution.
2006-01-01T00:00:00ZModel Order Reduction for Determining Bubble Parameters to Attain a Desired Fluid Surface Shape
https://hdl.handle.net/1721.1/7535
Model Order Reduction for Determining Bubble Parameters to Attain a Desired Fluid Surface Shape
My-Ha, D.; Lim, K. M.; Khoo, Boo Cheong; Willcox, Karen E.
In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained is close to a desired shape. Predictions of the free surface in two-dimensions and three-dimensions are presented.
2005-01-01T00:00:00ZNumerical comparison between Maxwell stress method and equivalent multipole approach for calculation of the dielectrophoretic force in octupolar cell traps
https://hdl.handle.net/1721.1/7534
Numerical comparison between Maxwell stress method and equivalent multipole approach for calculation of the dielectrophoretic force in octupolar cell traps
Rosales, C.; Lim, K. M.; Khoo, Boo Cheong
This work presents detailed numerical calculations of the dielectrophoretic force in octupolar traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using an indirect implementation of the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that the full MST calculation is only required in the study of non-spherical particles.
2005-01-01T00:00:00ZPreconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming
https://hdl.handle.net/1721.1/7410
Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming
Chai, Joo-Siong; Toh, Kim Chuan
We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a two-phase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interior-point method. Numerical experiments have been performed on some LP test problems in the NETLIB suite to demonstrate the potential of the preconditioning method discussed.
2005-01-01T00:00:00ZFastAero – A Precorrected FFT – Fast Multipole Tree Steady and Unsteady Potential Flow Solver
https://hdl.handle.net/1721.1/7378
FastAero – A Precorrected FFT – Fast Multipole Tree Steady and Unsteady Potential Flow Solver
Willis, David; Peraire, Jaime; White, Jacob K.
In this paper a precorrected FFT-Fast Multipole Tree (pFFT-FMT) method for solving the potential flow around arbitrary three dimensional bodies is presented. The method takes advantage of the efficiency of the pFFT and FMT algorithms to facilitate more demanding computations such as automatic wake generation and hands-off steady and unsteady aerodynamic simulations. The velocity potential on the body surfaces and in the domain is determined using a pFFT Boundary Element Method (BEM) approach based on the Green’s Theorem Boundary Integral Equation. The vorticity trailing all lifting surfaces in the domain is represented using a Fast Multipole Tree, time advected, vortex participle method. Some simple steady state flow solutions are performed to demonstrate the basic capabilities of the solver. Although this paper focuses primarily on steady state solutions, it should be noted that this approach is designed to be a robust and efficient unsteady potential flow simulation tool, useful for rapid computational prototyping.
2005-01-01T00:00:00ZAn Immersed Interface Method for the Incompressible Navier-Stokes Equations in Irregular Domains
https://hdl.handle.net/1721.1/7377
An Immersed Interface Method for the Incompressible Navier-Stokes Equations in Irregular Domains
Le, Duc-Vinh; Khoo, Boo Cheong; Peraire, Jaime
We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity.
2005-01-01T00:00:00ZA Conservative Front Tracking Algorithm
https://hdl.handle.net/1721.1/7376
A Conservative Front Tracking Algorithm
Nguyen, Vinh Tan; Khoo, Boo Cheong; Peraire, Jaime
The discontinuities in the solutions of systems of conservation laws are widely considered as one of the difficulties in numerical simulation. A numerical method is proposed for solving these partial differential equations with discontinuities in the solution. The method is able to track these sharp discontinuities or interfaces while still fully maintain the conservation property. The motion of the front is obtained by solving a Riemann problem based on the state values at its both sides which are reconstructed by using weighted essentially non oscillatory (WENO) scheme. The propagation of the front is coupled with the evaluation of "dynamic" numerical fluxes. Some numerical tests in 1D and preliminary results in 2D are presented.
2005-01-01T00:00:00ZCertified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation
https://hdl.handle.net/1721.1/7375
Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation
Nguyen, N. C.; Liu, Guirong; Patera, Anthony T.
We present a technique for the rapid and reliable
evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation
process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse
computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and
error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense)
system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is
decreased.
2005-01-01T00:00:00ZViscoelastic Mobility Problem Using A Boundary Element Method
https://hdl.handle.net/1721.1/4021
Viscoelastic Mobility Problem Using A Boundary Element Method
Nhan, Phan-Thien; Fan, Xi-Jun
In this paper, the complete double layer boundary integral equation formulation for Stokes flows is extended to viscoelastic fluids to solve the mobility problem for a system of particles, where the non-linearity is handled by particular solutions of the Stokes inhomogeneous equation. Some techniques of the meshless method are employed and a point-wise solver is used to solve the viscoelastic constitutive equation. Hence volume meshing is avoided. The method is tested against the numerical solution for a sphere settling in the Odroyd-B fluid and some results on a prolate motion in shear flow of the Oldroyd-B fluid are reported and compared with some theoretical and experimental results.
2002-01-01T00:00:00ZA Trajectory Piecewise-Linear Approach to Model Order Reduction and Fast Simulation of Nonlinear Circuits and Micromachined Devices
https://hdl.handle.net/1721.1/4020
A Trajectory Piecewise-Linear Approach to Model Order Reduction and Fast Simulation of Nonlinear Circuits and Micromachined Devices
RewieÅ ski, MichaÅ
In this paper we present an approach to the nonlinear model reduction based on representing the nonlinear system with a piecewise-linear system and then reducing each of the pieces with a Krylov projection. However, rather than approximating the individual components to make a system with exponentially many different linear regions, we instead generate a small set of linearizations about the state trajectory which is the response to a 'training input'. Computational results and performance data are presented for a nonlinear circuit and a micromachined fixed-fixed beam example. These examples demonstrate that the macromodels obtained with the proposed reduction algorithm are significantly more accurate than models obtained with linear or the recently developed quadratic reduction techniques. Finally, it is shown tat the proposed technique is computationally inexpensive, and that the models can be constructed 'on-the-fly', to accelerate simulation of the system response.
2002-01-01T00:00:00ZOptimal Design of Transonic Fan Blade Leading Edge Shape Using CFD and Simultaneous Perturbation Stochastic Approximation Method
https://hdl.handle.net/1721.1/4019
Optimal Design of Transonic Fan Blade Leading Edge Shape Using CFD and Simultaneous Perturbation Stochastic Approximation Method
Xing, X.Q.; Damodaran, Murali
Simultaneous Perturbation Stochastic Approximation method has attracted considerable application in many different areas such as statistical parameter estimation, feedback control, simulation-based optimization, signal & image processing, and experimental design. In this paper, its performance as a viable optimization tool is demonstrated by applying it first to a simple wing geometry design problem for which the objective function is described by an empirical formula from aircraft design practice and then it is used in a transonic fan blade design problem in which the objective function is not represented by any explicit function but is estimated at each design iteration by a computational fluid dynamics algorithm for solving the Navier-Stokes equations
2002-01-01T00:00:00ZStochastic Transportation-Inventory Network Design Problem
https://hdl.handle.net/1721.1/4018
Stochastic Transportation-Inventory Network Design Problem
Shu, Jia; Teo, Chung Piaw; Shen, Zuo-Jun Max
In this paper, we study the stochastic transportation-inventory network design problem involving one supplier and multiple retailers. Each retailer faces some uncertain demand. Due to this uncertainty, some amount of safety stock must be maintained to achieve suitable service levels. However, risk-pooling benefits may be achieved by allowing some retailers to serve as distribution centers (and therefore inventory storage locations) for other retailers. The problem is to determine which retailers should serve as distribution centers and how to allocate the other retailers to the distribution centers. Shen et al. (2000) and Daskin et al. (2001) formulated this problem as a set-covering integer-programming model. The pricing subproblem that arises from the column generation algorithm gives rise to a new class of submodular function minimization problem. They only provided efficient algorithms for two special cases, and assort to ellipsoid method to solve the general pricing problem, which run in O(n⁷ log(n)) time, where n is the number of retailers. In this paper, we show that by exploiting the special structures of the pricing problem, we can solve it in O(n² log n) time. Our approach implicitly utilizes the fact that the set of all lines in 2-D plane has low VC-dimension. Computational results show that moderate size transportation-inventory network design problem can be solved efficiently via this approach.
2002-01-01T00:00:00ZStatistical Error in Particle Simulations of Low Mach Number Flows
https://hdl.handle.net/1721.1/4017
Statistical Error in Particle Simulations of Low Mach Number Flows
Hadjiconstantinou, Nicolas G.; Garcia, Alejandro L.
We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Expressions for the fluid velocity, density and temperature are derived using equilibrium statistical mechanics. The results show that the number of samples needed to adequately resolve the flow-field scales as the inverse square of the Mach number. The theoretical results are verified for a dilute gas using direct Monte Carlo simulations. The agreement between theory and simulation verifies that the use of equilibrium theory is justified.
2002-01-01T00:00:00ZSolving symmetric indefinite systems in an interior-point method for second order cone programming
https://hdl.handle.net/1721.1/4016
Solving symmetric indefinite systems in an interior-point method for second order cone programming
Toh, Kim Chuan; Cai, Zhi; Freund, Robert M.
Many optimization problems can be formulated as second order cone programming (SOCP) problems. Theoretical results show that applying interior-point method (IPM) to SOCP has global polynomial convergence. However, various stability issues arise in the implementation of IPM. The standard normal equation based implementation of IPM encounters stability problems in the computation of search direction. In this paper, an augmented system approach is proposed to overcome the stability problems. Numerical experiments show that the new approach can improve the stability.
2002-01-01T00:00:00ZSolution Methodologies for the Smallest Enclosing Circle Problem
https://hdl.handle.net/1721.1/4015
Solution Methodologies for the Smallest Enclosing Circle Problem
Xu, Sheng; Freund, Robert M.; Sun, Jie
Given a set of circles C = {c₁, ..., cn}on the Euclidean plane with centers {(a₁, b₁), ..., (an, b<sub>n</sub>)}and radii {r₁..., r<n},the smallest enclosing circle (of fixed circles) problem is to ï¬nd the circle of minimum radius that encloses all circles in C. We survey four known approaches for this problem, including a second order cone reformulation, a subgradient approach, a quadratic programming scheme, and a randomized incremental algorithm. For the last algorithm we also give some implementation details. It turns out the quadratic programming scheme outperforms the other three in our computational experiment.
2002-01-01T00:00:00ZSimulation Study of a Semi-Dynamic AGV-Container Unit Job Deployment Scheme
https://hdl.handle.net/1721.1/4014
Simulation Study of a Semi-Dynamic AGV-Container Unit Job Deployment Scheme
Cheng, Yong Leong
Automated Guided Vehicle (AGV) Container-Job deployment is essentially a vehicle-dispatching problem. In this problem, the impact of vehicle dispatching polices on the ship makespan for discharging and/or loading operations is analyzed. In particular, given a storage location for each container to be discharged from the ship and given the current location of each container to be loaded onto the ship, the problem is to propose an efficient deployment scheme to dispatch vehicles to containers so as to minimize the makespan of the ship so as to increase the throughput. The makespan of the ship refers to the time a ship spends at the port for loading and unloading operations. In this paper, we will compare the performance of current deployment scheme used with the new proposed deployment scheme, both with deadlock prediction & avoidance algorithm done in previous study [1]. The prediction & avoidance algorithm predicts and avoids cyclic deadlock. The current deployment scheme, namely pmds makes use of a greedy heuristics which dispatches the available vehicle that will reach the quay with the minimum amount of time the vehicle has to spend waiting for the crane to discharge/load the container from/onto the ship. The new deployment scheme, namely mcf aims to formulate the problem as a minimum cost flow problem, which will then be solved by network simplex code. The two simulation models are implemented using discrete-event simulation software, AutoMod, and the performances of both deployment schemes are analyzed. The simulation results show that the new deployment scheme will result in a higher throughput and lower ship makespan than the current deployment scheme.
2002-01-01T00:00:00ZA Simulation Method for Calculating the Path Travel Time in Dynamic Transportation Network
https://hdl.handle.net/1721.1/4013
A Simulation Method for Calculating the Path Travel Time in Dynamic Transportation Network
Lin, G.C.; Peraire, Jaime; Khoo, Boo Cheong; Perakis, Georgia
The calculation of path travel times is an essential component for the dynamic traffic assignment and equilibrium problems. This paper presents a simulation method for calculating actual path travel times for the traffic network with dynamic demands. The method is based on a path-based macroscopic simulation model of network traffic dynamics. There is no need to explicitly model intersection delays in this method. Discontinuity in the travel time caused by traffic light control can be captured by this method. It's flexible in terms that the model is not limited to a specific velocity-density relationship. Some numerical results for signalized and unsignalized networks are reported.
2002-01-01T00:00:00ZA Simple But Effective Evolutionary Algorithm for Complicated Optimization Problems
https://hdl.handle.net/1721.1/4012
A Simple But Effective Evolutionary Algorithm for Complicated Optimization Problems
Xu, Y.G.; Liu, Guirong
A simple but effective evolutionary algorithm is proposed in this paper for solving complicated optimization problems. The new algorithm presents two hybridization operations incorporated with the conventional genetic algorithm. It takes only 4.1% ~ 4.7% number of function evaluations required by the conventional genetic algorithm to obtain global optima for the benchmark functions tested. Application example is also provided to demonstrate its effectiveness.
2002-01-01T00:00:00ZSecond-Order Fluid Dynamics Models for Travel Times in Dynamic Transportation Networks
https://hdl.handle.net/1721.1/4011
Second-Order Fluid Dynamics Models for Travel Times in Dynamic Transportation Networks
Kachani, Soulaymane; Perakis, Georgia
In recent years, traffic congestion in transportation networks has grown rapidly and has become an acute problem. The impetus for studying this problem has been further strengthened due to the fast growing field of Intelligent Vehicle Highway Systems (IVHS). Therefore, it is critical to investigate and understand its nature and address questions of the type: how are traffic patterns formed? and how can traffic congestion be alleviated? Understanding drivers' travel times is key behind this problem. In this paper, we present macroscopic models for determining analytical forms for travel times. We take a fluid dynamics approach by noticing that traffic macroscopically behaves like a fluid. Our contributions in this work are the following: (i) We propose two second-order non-separable macroscopic models for analytically estimating travel time functions: the Polynomial Travel Time (PTT) Model and the Exponential Travel Time (ETT) Model. These models generalize the models proposed by Kachani and Perakis as they incorporate second-order effects such as reaction of drivers to upstream and downstream congestion as well as second-order link interaction effects. (ii) Based on piecewise linear and piecewise quadratic approximations of the departure flow rates, we propose different classes of travel time functions for the first-order separable PTT and ETT models, and present the relationship between these functions. (iii) We show how the analysis of the first-order separable PTT Model extends to the second-order model with non-separable velocity functions for acyclic networks. (iv) Finally, we analyze the second-order separable ETT model where the queue propagation term - corresponding to the reaction of drivers to upstream congestion or decongestion - is not neglected. We are able to reduce the analysis to a Burgers equation and then to the more tractable heat equation.
2002-01-01T00:00:00ZResearch and Tutorial Exposition
https://hdl.handle.net/1721.1/4010
Research and Tutorial Exposition
Strang, Gilbert
My research is concentrated on applications of linear algebra in engineering, including wavelet analysis and structured matrices and (currently) approximation of large dense matrices by a mosaic of low rank blocks.
2002-01-01T00:00:00ZReliable Real-Time Solution of Parametrized Elliptic Partial Differential Equations: Application to Elasticity
https://hdl.handle.net/1721.1/4009
Reliable Real-Time Solution of Parametrized Elliptic Partial Differential Equations: Application to Elasticity
Veroy, K.; Leurent, T.; Prud'homme, C.; Rovas, D.V.; Patera, Anthony T.
The optimization, control, and characterization of engineering components or systems require fast, repeated, and accurate evaluation of a partial-differential-equation-induced input-output relationship. We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic partial differential equations with affine parameter dependence. The method has three components: (i) rapidly convergent reduced{basis approximations; (ii) a posteriori error estimation; and (iii) off-line/on-line computational procedures. These components -- integrated within a special network architecture -- render partial differential equation solutions truly "useful": essentially real{time as regards operation count; "blackbox" as regards reliability; and directly relevant as regards the (limited) input-output data required.
2002-01-01T00:00:00ZReduced-Basis Output Bound Methods for Parametrized Partial Differential Equations
https://hdl.handle.net/1721.1/4008
Reduced-Basis Output Bound Methods for Parametrized Partial Differential Equations
Prud'homme, C.; Rovas, D.V.; Veroy, K.; Machiels, L.; Maday, Y.; Patera, Anthony T.; Turinici, G.
We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations -- Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation -- relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures -- methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage -- in which, given a new parameter value, we calculate the output of interest and associated error bound -- depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.
2002-01-01T00:00:00ZPup Matching: Model Formulations and Solution Approaches
https://hdl.handle.net/1721.1/4007
Pup Matching: Model Formulations and Solution Approaches
Bossert, J.M.; Magnanti, Thomas L.
We model Pup Matching, the logistics problem of matching or pairing semitrailers known as pups to cabs able to tow one or two pups simultaneously, as an NP-complete version of the Network Loading Problem (NLP). We examine a branch and bound solution approach tailored to the NLP formulation through the use of three families of cutting planes and four heuristic procedures. Theoretically, we specify facet defining conditions for a cut family that we refer to as odd flow inequalities and show that each heuristic yields a 2-approximation. Computationally, the cheapest of the four heuristic values achieved an average error of 1.3% among solved test problems randomly generated from realistic data. The branch and bound method solved to optimality 67% of these problems. Application of the cutting plane families reduced the average relative difference between upper and lower bounds prior to branching from 18.8% to 6.4%.
2002-01-01T00:00:00ZOptimal Bidding in Online Auctions
https://hdl.handle.net/1721.1/4006
Optimal Bidding in Online Auctions
Bertsimas, Dimitris J.; Hawkins, Jeff; Perakis, Georgia
Online auctions are arguably one of the most important and distinctly new applications of the internet. The predominant player in online auctions, eBay, has over 18.9 milllion users, and it was the host of over $5 billion worth of goods sold in the year 2000. Using methods from approximate dynamic programming and integer programming, we design algorithms for optimally bidding for a single item online auction, and simultaneous or overlapping multiple online auctions. We report computational evidence using data from eBay's web site from 1772 completed auctions for personal digital assistants and from 4208 completed auctions for stamp collections that show that (a) the optimal dynamic strategy outperforms simple but widely used static heuristic rules for a single auction, and (b) a new approach combining the value functions of single auctions found by dynamic programming using an integer programming framework produces high quality solutions fast and reliably.
2002-01-01T00:00:00ZModeling generalized stacking fault in Au using tight-binding potential combined with a simulated annealing method
https://hdl.handle.net/1721.1/4005
Modeling generalized stacking fault in Au using tight-binding potential combined with a simulated annealing method
Cai, Jun; Wang, Jian-Sheng
Tight-binding potential combined with a simulated annealing method is used to study the generalized stacking fault structure and energy of gold. The potential is chosen to fit band structures and total energies from a set of first-principles calculations (Phys. Rev. B54, 4519 (1996)). It is found that the relaxed stacking fault energy (SFE) and anti-SFE are equal to 46 and 102 mJ/m², respectively, and in good agreement with the first principles calculations and experiment. In addition, the potential predicts that the c/a of hcp-like stacking fault structure in Au is slightly smaller than the ideal one.
2002-01-01T00:00:00ZIdentification of Convection Constants for Electronic Packages Using Modified Genetic Algorithm and Reduced-Basis Method
https://hdl.handle.net/1721.1/4004
Identification of Convection Constants for Electronic Packages Using Modified Genetic Algorithm and Reduced-Basis Method
Yang, Zhenglin; Lee, Jung Hong; Liu, Guirong; Patera, Anthony T.; Lam, Khin Yong
A new inverse analysis method is presented to identify parameters of heat convection in microelectronic packages. This approach adopts a modified Micro Genetic Algorithm (µGA) in finding the global optimum of parameters. A reduced-basis approach is introduced in the forward heat transfer analysis so as to significantly improve the efficiency in the calculation. Different identification procedures are employed to identify heat convection coefficients of a typical microelectronic package. Comparisons between different algorithms are performed. Results show that the use of the reduced-basis method together with the modified µGA outperforms the conventional GAs significantly. The presented method of coefficient identification is ideal for practical applications. It is efficient enough even for online analysis of both forward and inverse problem.
2002-01-01T00:00:00ZFinite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow
https://hdl.handle.net/1721.1/4003
Finite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow
Peraire, Jaime; Budge, Alexander M.
We introduce a new method for computing a posteriori bounds on engineering outputs from finite element discretizations of the incompressible Stokes equations. The method results from recasting the output problem as a minimization statement without resorting to an error formulation. The minimization statement engenders a duality relationship which we solve approximately by Lagrangian relaxation. We demonstrate the method for a stabilized equal-order approximation of Stokes flow, a problem to which previous output bounding methods do not apply. The conceptual framework for the method is quite general and shows promise for application to stabilized nonlinear problems, such as Burger's equation and the incompressible Navier-Stokes equations, as well as potential for compressible flow problems.
2002-01-01T00:00:00ZFast Analysis of Scattering by Arbitrarily Shaped Three-Dimensional Objects Using the Precorrected-FFT Method
https://hdl.handle.net/1721.1/4002
Fast Analysis of Scattering by Arbitrarily Shaped Three-Dimensional Objects Using the Precorrected-FFT Method
Nie, Xiaochun; Li, Le-Wei
This paper presents an accurate and efficient method-of-moments solution of the electrical-field integral equation (EFIE) for large, three-dimensional, arbitrarily shaped objects. In this method, the generalized conjugate residual method (GCR) is used to solve the matrix equation iteratively and the precorrected-FFT technique is then employed to accelerate the matrix-vector multiplication in iterations. The precorrected-FFT method eliminates the need to generate and store the usual square impedance matrix, thus leading to a great reduction in memory requirement and execution time. It is at best an O(N log N) algorithm and can be modified to fit a wide variety of systems with different Green’s functions without excessive effort. Numerical results are presented to demonstrate the accuracy and computational efficiency of the technique.
2002-01-01T00:00:00ZElectromagnetic Scattering by Open-Ended Cavities: An Analysis Using Precorrected-FFT Approach
https://hdl.handle.net/1721.1/4001
Electromagnetic Scattering by Open-Ended Cavities: An Analysis Using Precorrected-FFT Approach
Nie, Xiaochun; Li, Le-Wei
In this paper, the precorrected-FFT method is used to solve the electromagnetic scattering from two-dimensional cavities of arbitrary shape. The integral equation is discretized by the method of moments and the resultant matrix equation is solved iteratively by the generalized conjugate residual method. Instead of directly computing the matrix-vector multiplication, which requires N² operations, this approach reduces the computation complexity to O(N log N) as well as avoids the storage of large matrices. At the same time, a technique known as the complexifying k is applied to accelerate the convergence of the iterative method in solving this resonance problem. Some examples are considered and excellent agreements of radar cross sections between these computed using the present method and those from the direct solution are observed, demonstrating the feasibility and efficiency of the present method.
2002-01-01T00:00:00ZThe Efficient Computation of Bounds for Functionals of Finite Element Solutions in Large Strain Elasticity
https://hdl.handle.net/1721.1/4000
The Efficient Computation of Bounds for Functionals of Finite Element Solutions in Large Strain Elasticity
Bonet, J.; Huerta, A.; Peraire, Jaime
We present an implicit a-posteriori finite element procedure to compute bounds for functional outputs of finite element solutions in large strain elasticity. The method proposed relies on the existence of a potential energy functional whose local minima, over a space of suitably chosen continuous functions, corresponds to the problem solution. The output of interest is cast as a constrained minimization problem over an enlarged discontinuous finite element space. A Lagrangian is formed were the multipliers are an adjoint solution, which enforces equilibrium, and hybrid fluxes, which constrain the solution to be continuous. By computing approximate values for the multipliers on a coarse mesh, strict upper and lower bounds for the output of interest on a suitably refined mesh, are obtained. This requires a minimization over a discontinuous space, which can be carried out locally at low cost. The computed bounds are uniformly valid regardless of the size of the underlying coarse discretization. The method is demonstrated with two applications involving large strain plane stress incompressible neo-hookean hyperelasticity.
2002-01-01T00:00:00ZDynamic Pricing in a Competitive Environment
https://hdl.handle.net/1721.1/3999
Dynamic Pricing in a Competitive Environment
Perakis, Georgia; Sood, Anshul
We present a dynamic optimization approach for perishable products in a competitive and dynamically changing market. We build a general optimization framework that ties together the competetive and the dynamic nature of pricing. This approach also allows differential pricing for large customers as well as demand learning for the seller. We analyze special cases of the model and illustrate the policies numerically.
2002-01-01T00:00:00ZDynamic AGV-Container Job Deployment Strategy
https://hdl.handle.net/1721.1/3998
Dynamic AGV-Container Job Deployment Strategy
Sen, Hock Chan
Automated Guided Vehicles (AGVs) are now becoming popular in container-handling applications at seaport. Efficacy of the dispatching strategy adopted to deploy AGVs is a prime factor affecting the performance of the entire system. The objective of this project is thus to develop an efficient dispatching strategy to deploy AGVs in a container terminal.
The scenario considered was a container terminal where containers are uploaded to and discharged from ships. Discharged containers are stored at specific storage locations in the terminal yard. Containers are moved between dock and yard by a dedicated fleet of AGVs. At any point of time, each AGV carries at most two containers. This two-container load may comprise of any plausible permutation of containers for discharge or upload. To reduce congestion and increase utility level, an efficient dispatching strategy for AGVs is paramount.
At present, a variety of heuristic methods for dispatching AGVs are available, but these methods were primarily developed to work in a manufacturing context where the network structure is uncomplicated and only a small number of AGVs are required. The situation under consideration entails greater network complexity and also a large fleet of close to 80 AGVs.
In this study, the problem was modeled via network flows with constraints, which describe the disparate instances when the AGV carries one container and when it carries two. Heuristic algorithms based on this model are proposed and their performance investigated.
2002-01-01T00:00:00ZDesign and Optimization of Complex Systems
https://hdl.handle.net/1721.1/3997
Design and Optimization of Complex Systems
Willcox, Karen E.
Truely optimal solutions to system design can only be obtained if the entire system is considered. In this research we consider design of commercial aircraft, but we expand the system to include a family of planes. A multidisciplinary design optimization framework is developed in which multiple aircraft, each with different missions, can be optimized simultaneously. Results are presented for a two-member family whose individual missions differ significantly. We show that both missions can be satisfied with common designs, and that by optimizing both planes simultaneously rather than following the traditional baseline plus derivative approach, the common solution is vastly improved. The new framework is also used to gain insight to the effect of design variable scaling on the optimization algorithm.
2002-01-01T00:00:00ZDesign and Analysis of Printed Circuit Boards Using FDTD Method for The 20-H Rule
https://hdl.handle.net/1721.1/3996
Design and Analysis of Printed Circuit Boards Using FDTD Method for The 20-H Rule
Jiang, Yi; Li, Le-Wei; Li, Er-Ping
With the increasing demand of higher operating frequencies for electronic circuits, the printed circuit board designers face more electromagnetic radiation problems than ever. Some “rules-of-thumb” are employed to help the designers to reduce the radiation problems. The 20H rule is one of printed circuit design rules, which intends to minimize the electromagnetic radiation. This project focuses on analysis and simulation of 20H rule’s signal propagation mechanisms. The model used in the project is a 2D planar structure. The numerical electromagnetic method, Finite Difference Time Domain (FDTD) method, is used for the field computation and analysis. Simulation is based on various structures of model and different distributions of excitation sources. Analysis focuses on the signal propagation models. Field distributions and radiation patterns are visualized by mathematical software. Meanwhile, Poynting vectors are calculated to give quantitative expression. The simulation results indicate three factors, namely, operating frequency, size of PCB and separation distance that will affect the function of 20H rule. The effects of three factors are shown by comparison of specific cases in this thesis.
2002-01-01T00:00:00ZBounds on Linear PDEs via Semidefinite Optimization
https://hdl.handle.net/1721.1/3995
Bounds on Linear PDEs via Semidefinite Optimization
Bertsimas, Dimitris J.; Caramanis, Constantine
Using recent progress on moment problems, and their connections with semidefinite optimization, we present in this paper a new methodology based on semidefinite optimization, to obtain a hierarchy of upper and lower bounds on both linear and certain nonlinear functionals defined on solutions of linear partial differential equations. We apply the proposed methods to examples of PDEs in one and two dimensions with very encouraging results. We also provide computation evidence that the semidefinite constraints are critically important in improving the quality of the bounds, that is without them the bounds are weak.
2002-01-01T00:00:00ZApplications of Semidefinite Optimization in Stochastic Project Scheduling
https://hdl.handle.net/1721.1/3994
Applications of Semidefinite Optimization in Stochastic Project Scheduling
Bertsimas, Dimitris J.; Natarajan, Karthik; Teo, Chung Piaw
We propose a new method, based on semidefinite optimization, to find tight upper bounds on the expected project completion time and expected project tardiness in a stochastic project scheduling environment, when only limited information in the form of first and second (joint) moments of the durations of individual activities in the project is available. Our computational experiments suggest that the bounds provided by the new method are stronger and often significant compared to the bounds found by alternative methods.
2002-01-01T00:00:00ZAcceleration of Gas Bubble-Free Surface Interaction Computation Using Basis Preconditioners
https://hdl.handle.net/1721.1/3993
Acceleration of Gas Bubble-Free Surface Interaction Computation Using Basis Preconditioners
Tan, Kiok Lim; Khoo, Boo Cheong; White, Jacob K.
The computation of gas bubble-free surface interaction entails a time-stepping algorithm whereby a linear system is solved at each time-iteration. In our investigation, the linear systems are derived from a desingularized boundary integral formulation and are poorly conditioned. This leads to poor convergence rates when Krylov subspace methods are used to solve these systems. The convergence rates may however be improved with proper preconditioning.
We limit our investigation to gas bubbles initiated at depths sufficiently small such that a spike forms on the free surface during the later stages of evolution. Bubble dynamics dictate that for gas bubbles initiated at such depths, the stages through which the gas bubble and free surface evolve are similar. Based on this fact, we propose to perform one computation run for a gas bubble initiated at one particular depth, obtain a judicious set of a priori basis preconditioners from this run and thereafter, use this set of preconditioners on computation runs for gas bubble initiated at different depths.
The computation time taken by the proposed method is, in general, 50% and 20% of the time taken by the present method (without preconditioning) with terminating criteria of 1.0e-5 and 1.0e-7 in the infinity-norm respectively using the Bi-conjugate Gradient Stabilized solver. The present method further enables computation to an infinity-norm terminating criterion of 1.0e-10 in a shorter time compared to the present method with a criterion of 1.0e-5.
2002-01-01T00:00:00ZSubstrate Resistance Extraction Using a Multi-Domain Surface Integral Formulation
https://hdl.handle.net/1721.1/3923
Substrate Resistance Extraction Using a Multi-Domain Surface Integral Formulation
Vithayathil, Anne; Hu, Xin; White, Jacob K.
In order to assess and optimize layout strategies for minimizing substrate noise, it is necessary to have fast and accurate techniques for computing contact coupling resistances associated with the substrate. In this talk, we describe an extraction method capable of full-chip analysis which combines modest geometric approximations, a novel integral formulation, and an FFT-accelerated preconditioned iterative method.
2004-01-01T00:00:00ZUnsteady Flow Sensing and Estimation via the Gappy Proper Orthogonal Decomposition
https://hdl.handle.net/1721.1/3897
Unsteady Flow Sensing and Estimation via the Gappy Proper Orthogonal Decomposition
Willcox, Karen E.
The proper orthogonal decomposition (POD) has been widely used in fluid dynamic applications for extracting dominant flow features. The “gappy” POD is an extension to this method that allows the consideration of incomplete data sets. In this paper, the gappy POD is extended to handle unsteady flow reconstruction problems, such as those encountered when limited flow measurement data is available. In addition, a systematic approach for effective sensor placement is formulated within the gappy framework. Two applications are considered. The first aims to reconstruct the unsteady flow field using a small number of surface pressure measurements for a subsonic airfoil undergoing plunging motion. The second considers estimation of POD modal content of a cylinder wake flow for active control purposes. In both cases, using the dominant POD basis vectors and a small number of sensor signals, the gappy approach is found to yield accurate flow reconstruction results.
2004-01-01T00:00:00ZSummary Conclusions: Computation of Minimum Volume Covering Ellipsoids*
https://hdl.handle.net/1721.1/3896
Summary Conclusions: Computation of Minimum Volume Covering Ellipsoids*
Sun, Peng; Freund, Robert M.
We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points a₁,..., am âˆˆ Rn. This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structure makes it particularly amenable to solution by interior-point methods, and it has been the subject of much theoretical complexity analysis. Here we focus on computation. We present a combined interior-point and active-set method for solving this problem. Our computational results demonstrate that our method solves very large problem instances (m = 30,000 and n = 30) to a high degree of accuracy in under 30 seconds on a personal computer.
2004-01-01T00:00:00ZSimulation of Flow Field and Particle Trajectories in Hard Disk Drive Enclosures
https://hdl.handle.net/1721.1/3895
Simulation of Flow Field and Particle Trajectories in Hard Disk Drive Enclosures
Song, H.; Damodaran, Murali; Ng, Quock Y.
The airflow field and particle trajectories inside hard disk drive (HDD) are investigated in this study using commercial software Fluent and Gambit. Three-dimensional grids inside the HDD configuration are built using Gambit taking into account all the components and their geometric details. The airflow field inside HDD is simulated using three incompressible Navier-Stokes equations for various disk rotational speeds. The effects of using the various turbulence models inside the Fluent software such as the standard k - Îµ , RNG k - Îµ and Reynolds Stress Method on the computed airflow characteristics are also assessed. Steady flow fields and the effects of rotational speeds are assessed. Based on the computed steady airflow patterns, particle trajectories are computed using routines available in Fluent as well as special particle trajectory functions defined by the user via the user-defined functions. Particles of different sizes and materials are injected at various locations in the computed flow field and the corresponding particle trajectories are studied. Based on the investigation, the trajectory tends to be different according to sizes and materials. The present work forms a basis for further investigation of heat transfer processes inside the HDD to address thermal management issues and also the computation of unsteady flow fields in the HDD due to the movement of the actuator arm during data storage and retrieval
2004-01-01T00:00:00ZA Robust Optimization Approach to Supply Chain Management
https://hdl.handle.net/1721.1/3893
A Robust Optimization Approach to Supply Chain Management
Bertsimas, Dimitris J.; Thiele, Aurélie
We propose a general methodology based on robust optimization to address the problem of optimally controlling a supply chain subject to stochastic demand in discrete time. The attractive features of the proposed approach are: (a) It incorporates a wide variety of phenomena, including demands that are not identically distributed over time and capacity on the echelons and links; (b) it uses very little information on the demand distributions; (c) it leads to qualititatively similar optimal policies (basestock policies) as in dynamic programming; (d) it is numerically tractable for large scale supply chain problems even in networks, where dynamic programming methods face serious dimensionality problems; (e) in preliminary computation experiments, it often outperforms dynamic programming based solutions for a wide range of parameters.
2004-01-01T00:00:00ZReduced-order, trajectory piecewise-linear models for nonlinear computational fluid dynamics
https://hdl.handle.net/1721.1/3892
Reduced-order, trajectory piecewise-linear models for nonlinear computational fluid dynamics
Gratton, David; Willcox, Karen E.
A trajectory piecewise-linear (TPWL) approach is developed for a computational fluid dynamics (CFD) model of the two-dimensional Euler equations. The approach uses a weighted combination of linearized models to represent the nonlinear CFD system. The proper orthogonal decomposition (POD) is then used to create a reduced-space basis, onto which the TPWL model is projected. This projection yields an efficient reduced-order model of the nonlinear system, which does not require the evaluation of any full-order system residuals. The method is applied to the case of flow through an actively controlled supersonic diffuser. With an appropriate choice of linearization points and POD basis vectors, the method is found to yield accurate results, including cases with significant shock motion.
2004-01-01T00:00:00ZReduced-Basis Methods for Inverse Problems in Partial Differential Equations
https://hdl.handle.net/1721.1/3891
Reduced-Basis Methods for Inverse Problems in Partial Differential Equations
Nguyen, C.N.; Liu, Guirong; Patera, Anthony T.
We present a technique for the rapid, reliable, and accurate evaluation of functional outputs of parametrized elliptic partial differential equations. The essential ingredients are (i) rapidly globally convergent reduced-basis approximations – Galerkin projection onto a space WN spanned by the solutions of the governing partial differential equations at N selected points in parameter space; (ii) a posteriori error estimation - relaxations of the error-residual equation that provide sharp and inexpensive bounds for the error in the output of interest; and (iii) off-line/online computational procedures – methods that decouple the generation and projection stages of the approximation process. The operation count for the online stage – in which, given a new parameter, we calculate the output of interest and associated error bounds – depends only on N (typically very small) and the parametric dependencies of the problem.
In this study, we first develop rigorous a posteriori error estimators for (affine in the parameter) noncoercive problems such as the Helmholtz (reduced-wave) equation. The critical ingredients are the residual, an appropriate bound conditioner, and a piecewise-constant lower bound for the inf-sup stability factor. In addition, globally nonaffine (and nonlinear) problems are also considered: in particular, through appropriate sampling and interpolation procedures, these more difficult problems can be reduced (with very high accuracy) to the more tractable affine case.
Finally, we propose a real-time - procedure for inverse problems associated with parametrized partial differential equations based on our reduced-basis approximations and error bounds. In general practice, many inverse problems are formulated as an error minimization statement relating the calculated and measured outputs. This optimization procedure requires many evaluations of the output: the reduced-basis method --- with extremely low marginal cost --- is thus very efficient for this class of problems. As an illustrative example, we consider a very important application in nondestructive evaluation: crack identification (by harmonic excitation) in a laminated plate of composite material. The numerical results demonstrate the efficiency and accuracy of the method in detecting the location and length of the crack.
2004-01-01T00:00:00ZReduced-Basis Approximation of the Viscosity-Parametrized Incompressible Navier-Stokes Equation: Rigorous A Posteriori Error Bounds
https://hdl.handle.net/1721.1/3890
Reduced-Basis Approximation of the Viscosity-Parametrized Incompressible Navier-Stokes Equation: Rigorous A Posteriori Error Bounds
Veroy, K.; Patera, Anthony T.
We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic partial differential equations with affine (or approximately affine) parameter dependence. The essential components are (i) rapidly uniformly convergent global reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) offline/online computational procedures — stratagems which decouple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output of interest and associated error bound — depends only on N (typically very small) and the parametric complexity of the problem.
In this paper we extend our methodology to the viscosity-parametrized incompressible Navier-Stokes equations. There are two critical new ingredients: first, the now-classical Brezzi-Rappaz-Raviart framework for (here, a posteriori) error analysis of approximations of nonlinear elliptic partial differential equations; and second, offline/online computational procedures for efficient calculation of the "constants" required by the Brezzi-Rappaz-Raviart theory — in particular, rigorous lower and upper bounds for the BabuÅ¡ka inf-sup stability and Sobolev "L⁴-H¹" continuity factors, respectively. Numerical results for a simple square-cavity model problem confirm the rapid convergence of the reduced-basis approximation and the good effectivity of the associated a posteriori error bounds.
2004-01-01T00:00:00ZPerformance Analysis of Metamaterials With Two-dimensional Isotropy
https://hdl.handle.net/1721.1/3889
Performance Analysis of Metamaterials With Two-dimensional Isotropy
Yao, Hai-Ying; Li, Le-Wei
A two-dimensional isotropic metamaterials formed by crossed split-ring resonators (CSRRs) are studied in this paper. The effective characteristic parameters of this media are determined by quasi-static Lorentz theory. The induced current distributions of a single CSRR at the resonant frequency are presented. Moreover, the dependence of the resonant frequency on the dimensions of single CSRR and the spaces of the array are also discussed.
2004-01-01T00:00:00ZPartitioned Conduction Modes in Surface Integral Equation-Based Impedance Extraction
https://hdl.handle.net/1721.1/3888
Partitioned Conduction Modes in Surface Integral Equation-Based Impedance Extraction
Hu, Xin; Daniel, Luca; White, Jacob K.
As integrated circuits operate at increasingly higher speed, methods are needed to handle wideband quasi-static and full wave EM analysis of distributed RLC impedances for package and on-chip interconnects. One particular solver that is capable of this type of analysis is a surface-based integral solver called FastImp. This talk will present a method that addresses many issues currently plaguing FastImp. A significant shortcoming of FastImp is its lack of a single uniform approach to model contact current over a wide range of frequencies. In addition, FastImp's handling of contact current at high frequencies cannot optimally and efficiently capture skin effects and proximity effects while its handling of contact current at low frequencies lacks accuracy due to its use of a centroid-collocation scheme.
The method discussed in this talk addresses the above difficulties by offering a unified mean of computing contact current over a wide range of frequencies. It will be shown that the electric field on the conductor contact surfaces can be modeled accurately and efficiently by only a few “partitioned” surface-based conduction modes as basis functions. The electric field on the non-contact surface of the conductor is modeled by a set of standard piecewise constant basis functions. The conduction mode basis functions, used in a Galerkin technique, and the piecewise constant basis functions, used in a collocation scheme, are utilized for the discretization of the integral formulation in FastImp. Examples will demonstrate the improvements on accuracy, efficiency and consistency of our method.
2004-01-01T00:00:00ZA Meshfree Weak- Strong-form (MWS) method for solid and fluid mechanics
https://hdl.handle.net/1721.1/3887
A Meshfree Weak- Strong-form (MWS) method for solid and fluid mechanics
Liu, Guirong; Gua, Y.T.
Mesh free methods can be largely categorized into two main categories: mesh free methods based on strong forms (e.g. collocation methods) and mesh free methods based on the weak forms (EFG, MLPG, PIM, etc.; see Mesh Free Methods, by G. R. Liu, CRC Press, 2002). The mesh free collocation method is simple to implement and computationally efficient. However, it is often found unstable and less accurate, especially for problems governed by partial differential equations with Neumann (derivative) boundary conditions, such as solid mechanics problems with stress (natural) boundary conditions. On the other hand, the mesh free methods based on the weak form exhibits very good stability and excellent accuracy. However, the numerical integration makes them computational expensive, and the background mesh (global or local) for integration is responsible for not being “truly” mesh free. In this paper, a new idea of combination of both the strong form and the local weak form is proposed to develop truly meshless method for 2-D elasto-statics.
A novel truly meshfree method, the meshfree weak-strong (MWS) form method, is originated by Liu et al. (2002) based on a combined formulation of both the strong and local weak forms. As shown in Figure 1, the problem domain and boundaries are represented by properly scattered nodes. The key idea of the MWS method is that in establishing the discrete system equations, both the strong-form and the local Petrov-Galerkin weak-form are used for the same problem, but for different nodes.
This paper details the MWS method for solid and fluid mechanics problems. In the MWS method, the problem domain and its boundary is represented by a set of points or nodes. The strong form or collocation method is used for all the internal nodes and the nodes on the essential (Dirichlet) boundaries. The local weak form (Petrov-Galerkin weak form) is used for nodes on the natural (Neumann) boundaries. There is no need for numerical integrations for all the internal nodes and the nodes on the essential boundaries. The local numerical integration is performed only for the nodes on the natural/Neumann boundaries. The natural/Neumann boundary conditions can then be easily imposed to produce stable and accurate solutions. The locally supported radial point interpolation method (RPIM) and moving least squares (MLS) approximation are used to construct the shape functions. The final system matrix will be sparse and banded for computational efficiency.
Numerical examples of solids and fluids are presented to demonstrate the efficiency, stability and accuracy of the proposed meshfree method.
2004-01-01T00:00:00ZLong range correction for wall-fluid interaction in molecular dynamic simulations
https://hdl.handle.net/1721.1/3886
Long range correction for wall-fluid interaction in molecular dynamic simulations
He, Gang; Hadjiconstantinou, Nicolas G.
A new method is proposed for correctly modeling the long range interaction between a fluid and a bounding wall in atomistic simulations. This method incorporates the molecular structure of the solid substrate while allowing for a finite interaction cutoff by making a proper estimation of long range correction for the fluid-wall interaction. The method is then applied to a molecular dynamic simulation of a spreading droplet. Conparison to simulations using several other previously used methods shows that the long range correction can be significant in some circumstances.
2004-01-01T00:00:00ZThe Interplay of Ranks of Submatrices
https://hdl.handle.net/1721.1/3885
The Interplay of Ranks of Submatrices
Strang, Gilbert; Nguyen, Tri Dung
A banded invertible matrix T has a remarkable inverse. All "upper" and "lower" submatrices of T⁻¹ have low rank (depending on the bandwidth in T). The exact rank condition is known, and it allows fast multiplication by full matrices that arise in the boundary element method.
We look for the "right" proof of this property of T⁻¹. Ultimately it reduces to a fact that deserves to be better known: Complementary submatrices of any T and T⁻¹ have the same nullity. The last figure in the paper (when T is tridiagonal) shows two submatrices with the same nullity n – 3. Then C has rank 1. On and above the diagonal of T⁻¹, all rows are proportional.
2004-01-01T00:00:00ZImproved O(N) neighbor list method using domain decomposition and data sorting
https://hdl.handle.net/1721.1/3884
Improved O(N) neighbor list method using domain decomposition and data sorting
Yao, Zhenhua; Wang, Jian-Sheng; Cheng, Min
The conventional Verlet table neighbor list algorithm is improved to reduce the number of unnecessary inter-atomic distance calculations in molecular simulations involving large amount of atoms. Both of the serial and parallelized performance of molecular dynamics simulation are evaluated using the new algorithm and compared with those using the conventional Verlet table and cell-linked list algorithm. Results show that the new algorithm significantly improved the performance of molecular dynamics simulation compared with conventional neighbor list maintaining and utilizing algorithms in serial programs as well as parallelized programs.
2004-01-01T00:00:00ZGlobal Optimization with Polynomials
https://hdl.handle.net/1721.1/3883
Global Optimization with Polynomials
Han, Deren
The class of POP (Polynomial Optimization Problems) covers a wide rang of optimization problems such as 0 - 1 integer linear and quadratic programs, nonconvex quadratic programs and bilinear matrix inequalities. In this paper, we review some methods on solving the unconstraint case: minimize a real-valued polynomial p(x) : Rn â†’ R, as well the constraint case: minimize p(x) on a semialgebraic set K, i.e., a set defined by polynomial equalities and inequalities. We also summarize some questions that we are currently considering.
2004-01-01T00:00:00ZA Constraint Handling Strategy for Bit-Array Representation GA in Structural Topology Optimization
https://hdl.handle.net/1721.1/3882
A Constraint Handling Strategy for Bit-Array Representation GA in Structural Topology Optimization
Wang, Shengyin; Tai, Kang
In this study, an improved bit-array representation method for structural topology optimization using the Genetic Algorithm (GA) is proposed. The issue of representation degeneracy is fully addressed and the importance of structural connectivity in a design is further emphasized. To evaluate the constrained objective function, Deb's constraint handling approach is further developed to ensure that feasible individuals are always better than infeasible ones in the population to improve the efficiency of the GA. A hierarchical violation penalty method is proposed to drive the GA search towards the topologies with higher structural performance, less unusable material and fewer separate objects in the design domain in a hierarchical manner. Numerical results of structural topology optimization problems of minimum weight and minimum compliance designs show the success of this novel bit-array representation method and suggest that the GA performance can be significantly improved by handling the design connectivity properly.
2004-01-01T00:00:00ZComputing Upper and Lower Bounds for the J-Integral in Two-Dimensional Linear Elasticity
https://hdl.handle.net/1721.1/3881
Computing Upper and Lower Bounds for the J-Integral in Two-Dimensional Linear Elasticity
Xuan, Z.C.; Lee, Kwok Hong; Patera, Anthony T.; Peraire, Jaime
We present an a-posteriori method for computing rigorous upper and lower bounds of the J-integral in two dimensional linear elasticity. The J-integral, which is typically expressed as a contour integral, is recast as a surface integral which yields a quadratic continuous functional of the displacement. By expanding the quadratic output about an approximate finite element solution, the output is expressed as a known computable quantity plus linear and quadratic functionals of the solution error. The quadratic component is bounded by the energy norm of the error scaled by a continuity constant, which is determined explicitly. The linear component is expressed as an inner product of the errors in the displacement and in a computed adjoint solution, and bounded using standard a-posteriori error estimation techniques. The method is illustrated with two fracture problems in plane strain elasticity.
2004-01-01T00:00:00ZCompetitive Multi-period Pricing with Fixed Inventories
https://hdl.handle.net/1721.1/3880
Competitive Multi-period Pricing with Fixed Inventories
Perakis, Georgia; Sood, Anshul
This paper studies the problem of multi-period pricing for perishable products in a competitive (oligopolistic) market. We study non cooperative Nash equilibrium policies for sellers. At the beginning of the time horizon, the total inventories are given and additional production is not an available option. The analysis for periodic production-review models, where production decisions can be made at the end of each period at some production cost after incurring holding or backorder costs, does not extend to this model. Using results from game theory and variational inequalities we study the existence and uniqueness of equilibrium policies. We also study convergence results for an algorithm that computes the equilibrium policies. The model in this paper can be used in a number of application areas including the airline, service and retail industries. We illustrate our results through some numerical examples.
2004-01-01T00:00:00ZAutomatic Generation of Geometrically Parameterized Reduced Order Models for Integrated Spiral RF-Inductors
https://hdl.handle.net/1721.1/3879
Automatic Generation of Geometrically Parameterized Reduced Order Models for Integrated Spiral RF-Inductors
Daniel, Luca; White, Jacob K.
In this paper we describe an approach to generating low-order models of spiral inductors that accurately capture the dependence on both frequency and geometry (width and spacing) parameters. The approach is based on adapting a multiparameter Krylov-subspace based moment matching method to reducing an integral equation for the three dimensional electromagnetic behavior of the spiral inductor. The approach is demonstrated on a typical on-chip rectangular inductor.
2004-01-01T00:00:00ZAn Asymptotically Optimal On-Line Algorithm for Parallel Machine Scheduling
https://hdl.handle.net/1721.1/3878
An Asymptotically Optimal On-Line Algorithm for Parallel Machine Scheduling
Chou, Mabel; Queyranne, Maurice; Simchi-Levi, David
Jobs arriving over time must be non-preemptively processed on one of m parallel machines, each of which running at its own speed, so as to minimize a weighted sum of the job completion times. In this on-line environment, the processing requirement and weight of a job are not known before the job arrives. The Weighted Shortest Processing Requirement (WSPR) on-line heuristic is a simple extension of the well known WSPT heuristic, which is optimal for the single machine problem without release dates. We prove that the WSPR heuristic is asymptotically optimal for all instances with bounded job processing requirements and weights. This implies that the WSPR algorithm generates a solution whose relative error approaches zero as the number of jobs increases. Our proof does not require any probabilistic assumption on the job parameters and relies extensively on properties of optimal solutions to a single machine relaxation of the problem.
2004-01-01T00:00:00ZAn Immersed Interface Method for the Incompressible Navier-Stokes Equations
https://hdl.handle.net/1721.1/3877
An Immersed Interface Method for the Incompressible Navier-Stokes Equations
Le, Duc-Vinh; Khoo, Boo Cheong; Peraire, Jaime
We present an immersed interface algorithm for the incompressible Navier Stokes equations. The interface is represented by cubic splines which are interpolated through a set of Lagrangian control points. The position of the control points is implicitly updated using the fluid velocity. The forces that the interface exerts on the fluid are computed from the constitutive relation of the interface and are applied to the fluid through jumps in the pressure and jumps in the derivatives of pressure and velocity. A projection method is used to time advance the Navier-Stokes equations on a uniform cartesian mesh. The Poisson-like equations required for the implicit solution of the diffusive and pressure terms are solved using a fast Fourier transform algorithm. The position of the interface is updated implicitly using a quasi-Newton method (BFGS) within each timestep. Several examples are presented to illustrate the flexibility of the presented approach.
2004-01-01T00:00:00ZAn Algorithm for Computing the Symmetry Point of a Polytope
https://hdl.handle.net/1721.1/3876
An Algorithm for Computing the Symmetry Point of a Polytope
Belloni, Alexandre; Freund, Robert M.
Given a closed convex set C and a point x in C, let sym(x,C) denote the symmetry value of x in C, which essentially measures how symmetric C is about the point x. Denote by sym(C) the largest value of sym(x,C) among all x in C, and let x* denote the most symmetric point in C. These symmetry measures are all invariant under linear transformation, change in inner product, etc., and so are of interest in the study of the geometry of convex sets and arise naturally in the evaluation of the complexity of interior-point methods in particular. Herein we show that when C is given by the intersection of halfspaces, i.e., C={x | Ax <= b}, then x* as well as the symmetry value of C can be computed by using linear programming. Furthermore, given an approximate analytic center of C, there is a strongly polynomial-time algorithm for approximating sym(C) to any given relative tolerance.
2004-01-01T00:00:00ZAerodynamic Shape Design of Nozzles Using a Hybrid Optimization Method
https://hdl.handle.net/1721.1/3875
Aerodynamic Shape Design of Nozzles Using a Hybrid Optimization Method
Xing, X.Q.; Damodaran, Murali
A hybrid design optimization method combining the stochastic method based on simultaneous perturbation stochastic approximation (SPSA) and the deterministic method of Broydon-Fletcher-Goldfarb-Shanno (BFGS) is developed in order to take advantage of the high efficiency of the gradient based methods and the global search capabilities of SPSA for applications in the optimal aerodynamic shape design of a three dimensional elliptic nozzle. The performance of this hybrid method is compared with that of SPSA, simulated annealing (SA) and gradient based BFGS method. The objective functions which are minimized are estimated by numerically solving the 3D Euler and Navier-Stokes equations using a TVD approach and a LU implicit scheme. Computed results show that the hybrid optimization method proposed in this study shows a promise of high computational efficiency and global search capabilities.
2004-01-01T00:00:00ZFluid Models for Traffic and Pricing
https://hdl.handle.net/1721.1/3734
Fluid Models for Traffic and Pricing
Kachani, Soulaymane; Perakis, Georgia
Fluid dynamics models provide a powerful deterministic technique to approximate stochasticity in a variety of application areas. In this paper, we study two classes of fluid models, investigate their relationship as well as some of their applications. This analysis allows us to provide analytical models of travel times as they arise in dynamically evolving environments, such as transportation networks as well as supply chains. In particular, using the laws of hydrodynamic theory, we first propose and examine a general second order fluid model. We consider a first-order approximation of this model and show how it is helpful in analyzing the dynamic traffic equilibrium problem. Furthermore, we present an alternate class of fluid models that are traditionally used in the context of dynamic traffic assignment. By interpreting travel times as price/inventory-sojourn-time relationships, we are also able to connect this approach with a tractable fluid model in the context of dynamic pricing and inventory management. Finally, we investigate the relationship between these two classes of fluid models.
2003-01-01T00:00:00ZOn Optimizing PSA Berth Planning System
https://hdl.handle.net/1721.1/3720
On Optimizing PSA Berth Planning System
Teo, Chung Piaw; Dai, Jim; Moorthy, Rajeeva Lochana
Competition among container ports continues to increase as the differentiation of hub ports and feeder ports progresses. Managers in many container terminals are trying to attract carriers by automating handling equipment, providing and speeding up various services, and furnishing the most current information on the flow of containers. At the same time, however, they are trying to reduce costs by utilizing resources efficiently, including human resources, berths, container yards, quay cranes, and various yard equipment. When planning berth usage, the berthing time and the exact position of each vessel at the wharf, as well as various quay side resources are usually determined in the process. Several variables must be considered, including the length overall (LOA) and arrival time of each vessel, the number of containers for discharging and loading, and the storage location of outbound/inbound containers to be loaded onto/discharged from the corresponding vessel. Furthermore, we aim to propose berthing plan that will be "robust", since the actual arrival time of each vessel can vary substantially from forecast. This is particular important for vessels from priority customers (called priority vessels hereon), who have been promised berth-on-arrival (i.e. within two hours of arriving) service guarantee in their contract with PSA. A robust plan will also helps to minimize the frequent updates (changes) to berthing plan that have repercussion in resource and sta deployment within the terminal. Thus, the problem reduces to one of finding a berthing plan, so that priority vessels can be berthed-on-arrival with high probability, and the vessels can be berthed as close to their preferred locations as possible, to reduce the cost of transporting the containers within the terminal. In this paper, we described an approach to address this problem.
2003-01-01T00:00:00ZMulti-Disciplinary Analysis in Morphing Airfoils
https://hdl.handle.net/1721.1/3718
Multi-Disciplinary Analysis in Morphing Airfoils
Natarajan, Anand
Fully morphing wings allow the active change of the wing surface contours/wing configuration in flight enabling the optimum wing design for various flight regimes. These wing shape deformations are obtained by using smart actuators, which requires that the wing structure be flexible enough to morph under applied actuator loads and at the same time be fully capable of holding the aerodynamic loads. The study of such wing surface deformation requires an aeroelastic analysis since there is an active structural deformation under an applied aerodynamic field. Herein, a 2-D wing section, that is, an airfoil is considered. Modeling a variable geometry airfoil is performed using B-spline expansions. B-spline representation is also favorable towards optimization and provides a methodology to design curves based on discrete polygon points. The energy required for deforming the airfoil contour needs to be minimized. One of the methodologies adopted to minimize this actuation energy is to use the aerodynamic load itself for wing deformation. Another approach is to treat the airfoil deformation as a Multi Disciplinary Optimization (MDO) problem wherein the actuation energy needs to be minimized subject to certain constraints. The structural analysis is performed using commercial finite element software. The aerodynamic model is initiated from viscous-inviscid interaction codes and later developed from commercial Computational Fluid Dynamics (CFD) codes. Various modeling levels are investigated to determine the design requirements on morphing airfoils for enhanced aircraft maneuverability.
2003-01-01T00:00:00ZFast Methods for Simulation of Biomolecule of Electrostatics
https://hdl.handle.net/1721.1/3717
Fast Methods for Simulation of Biomolecule of Electrostatics
Kuo, Shihhsien; Altman, Michael D.; Bardhan, Jaydeep P.; Tidor, Bruce; White, Jacob K.
Biomolecular structure and interactions in aqueous environment are determined by a complicated interplay between physical and chemical forces including solvation, electrostatics, van der Waals forces, the hydrophobic effect and covalent bonding. Among them, electrostatics has been of particular interest due to its long-range nature and the tradeoff between desolvation and interaction effects [1]. In addition, electrostatic interactions play a significant role within a biomolecule as well as between biomolecules, making the balance between the two vital to the understanding of macromolecular systems. As a result, much effort has been devoted to accurate modeling and simulation of biomolecule electrostatics. One important application of this work is to compute the structure of electrostatic interactions for a biomolecule in an electrolyte solution, as well as the potential that the molecule generates in space. There are two valuable uses for these simulations. First, it provides a full picture of the electrostatic energetics of a biomolecular system, improving our understanding of how electrostatics contributes to stability, specificity, function, and molecular interaction [2]. Second, these simulations serve as a tool for molecular design, since electrostatic complementarity is an important feature of interacting molecules. Through examination of the electrostatics and potential field generated by a protein molecule, for example, it may be possible to suggest improvements to other proteins or drug molecules that interact with it, or perhaps even design new interacting molecules de novo [3]. There are two approaches in simulating a protein macromolecule in an aqueous solution with nonzero ionic strength. Discrete/atomistic approaches based on Monte-Carlo or molecular dynamics simulations treat the macromolecule and solvent explicitly at the atomic level. Therefore, an enormous number of solvent molecules are required to provide reasonable accuracy, especially when electric fields far away from macroscopic surface are of interest, leading to computational infeasibility. In this work, we adopt instead an approach based on a continuum description of the macromolecule and solvent. Although the continuum model of biomolecule electrostatics is widely used, the numerical techniques used to evaluate the model do not exploit fast solver approaches developed for analyzing integrated circuit interconnect. I will describe the formulation used for analyzing biomolecule electrostatics, and then derive an integral formulation of the problem that can be rapidly solved with precorrected-FFT method [4].
2003-01-01T00:00:00ZSummary Conclusions on Computational Experience and the Explanatory Value of Condition Measures for Linear Optimization*
https://hdl.handle.net/1721.1/3716
Summary Conclusions on Computational Experience and the Explanatory Value of Condition Measures for Linear Optimization*
Ordóñez, Fernando; Freund, Robert M.
The modern theory of condition measures for convex optimization problems was initially developed for convex problems in conic format, and several aspects of the theory have now been extended to handle non-conic formats as well. In this theory, the (Renegar-) condition measure C(d) for a problem instance with data d=(A,b,c) has been shown to be connected to bounds on a wide variety of behavioral and computational characteristics of the problem instance, from sizes of optimal solutions to the complexity of algorithms. Herein we test the practical relevance of the condition measure theory, as applied to linear optimization problems that one might typically encounter in practice. Using the NETLIB suite of linear optimization problems as a test bed, we found that 71% of the NETLIB suite problem instances have infinite condition measure. In order to examine condition measures of the problems that are the actual input to a modern IPM solver, we also computed condition measures for the NETLIB suite problems after pre-preprocessing by CPLEX 7.1. Here we found that 19% of the post-processed problem instances in the NETLIB suite have infinite condition measure, and that log C(d) of the post-processed problems is fairly nicely distributed. Furthermore, there is a positive linear relationship between IPM iterations and log C(d) of the post-processed problem instances (significant at the 95% confidence level), and 42% of the variation in IPM iterations among the NETLIB suite problem instances is accounted for by log C(d) of the post-processed problem instances.
2003-01-01T00:00:00ZRobust Discrete Optimization
https://hdl.handle.net/1721.1/3715
Robust Discrete Optimization
Bertsimas, Dimitris J.; Sim, Melvyn
We propose an approach to address data uncertainty for discrete optimization problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. When both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty, we propose a robust integer programming problem of moderately larger size that allows to control the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation. When only the cost coefficients are subject to uncertainty and the problem is a 0 - 1 discrete optimization problem on n variables, then we solve the robust counterpart by solving n + 1 instances of the original problem. Thus, the robust counterpart of a polynomially solvable 0 -1 discrete optimization problem remains polynomially solvable. Moreover, we show that the robust counterpart of an NP-hard α-approximable 0 - 1 discrete optimization problem remains α-approximal.
2003-01-01T00:00:00ZFast Methods for Bimolecular Charge Optimization
https://hdl.handle.net/1721.1/3711
Fast Methods for Bimolecular Charge Optimization
Bardhan, Jaydeep P.; Lee, J.H.; Kuo, Shihhsien; Altman, Michael D.; Tidor, Bruce; White, Jacob K.
We report a Hessian-implicit optimization method to quickly solve the charge optimization problem over protein molecules: given a ligand and its complex with a receptor, determine the ligand charge distribution that minimizes the electrostatic free energy of binding. The new optimization couples boundary element method (BEM) and primal-dual interior point method (PDIPM); initial results suggest that the method scales much better than the previous methods. The quadratic objective function is the electrostatic free energy of binding where the Hessian matrix serves as an operator that maps the charge to the potential. The unknowns are the charge values at the charge points, and they are limited by equality and inequality constraints that model physical considerations, i.e. conservation of charge. In the previous approaches, finite-difference method is used to model the Hessian matrix, which requires significant computational effort to remove grid-based inaccuracies. In the novel approach, BEM is used instead, with precorrected FFT (pFFT) acceleration to compute the potential induced by the charges. This part will be explained in detail by Shihhsien Kuo in another talk. Even though the Hessian matrix can be calculated an order faster than the previous approaches, still it is quite expensive to find it explicitly. Instead, the KKT condition is solved by a PDIPM, and a Krylov based iterative solver is used to find the Newton direction at each step. Hence, only Hessian times a vector is necessary, which can be evaluated quickly using pFFT. The new method with proper preconditioning solves a 500 variable problem nearly 10 times faster than the techniques that must find a Hessian matrix explicitly. Furthermore, the algorithm scales nicely due to the robustness in number of IPM iterations to the size of the problem. The significant reduction in cost allows the analysis of much larger molecular system than those could be solved in a reasonable time using the previous methods.
2003-01-01T00:00:00ZAerodynamic Shape Design of Transonic Airfoils Using Hybrid Optimization Techniques and CFD
https://hdl.handle.net/1721.1/3710
Aerodynamic Shape Design of Transonic Airfoils Using Hybrid Optimization Techniques and CFD
Xing, X.Q.; Damodaran, Murali; Teo, Chung Piaw
This paper will analyze the effects of using hybrid optimization methods for optimizing objective functions that are determined by computational fluid dynamics solvers for compressible viscous flow for optimal design of airfoils. Previous studies on this topic by the authors had examined the application of deterministic optimization methods and stochastic optimization methods such as Simulated Annealing and Simultaneous Perturbation Stochastic Analysis (SPSA). The studies indicated that SPSA method has a greater or equal efficiency as compared with SA method in reaching optimal airfoil designs for the design problem in question. However, in some situations SPSA method has a tendency to demonstrate an oscillatory behavior in the vicinity of a local optima. To overcome this tendency, a hybrid method designed to take full advantage of SPSA’s high rate of reduction of the objective function at the inception of the design process to drive the design cycles towards the optimal zone at first, and then combining with other methods to perform the final stages of the convergence towards the optimal solutions is considered. SPSA method has been combined with the gradient-based Broydon-Fletcher-Goldfarb-Shanno (BFGS) method as well as Simulated Annealing method for the transonic inverse airfoil design problem that is concerned with the specification of a target airfoil surface pressure distribution and starting from an initial guess of an airfoil shape, the target airfoil shape is reached by way of minimization of a quantity that depends on the difference between the target and current airfoil surface pressure distribution. For a typical transonic flow test case, the effects of using hybrid optimization techniques such as SPSA+BFGS and SPSA+SA as opposed to using SPSA alone can be seen in Figure 1. After 800 design cycles using SPSA, the hybrid SPSA+SA method took 2521 function evaluations of SA while the SPSA+BFGS method took 271 function evaluations to reach similar values which are much better than that reached by using SPSA alone in the entire minimization process. Results indicate that both of the two hybrid methods have capability to find a global optimum more efficiently than the SPSA method. The paper will address issues related to hybridization and its impact on the optimal airfoil shape designs in various contexts.
2003-01-01T00:00:00ZStructural Topology Optimization Using a Genetic Algorithm and a Morphological Representation of Geometry
https://hdl.handle.net/1721.1/3709
Structural Topology Optimization Using a Genetic Algorithm and a Morphological Representation of Geometry
Tai, Kang; Wang, Shengyin; Akhtar, Shamim; Prasad, Jitendra
This paper describes an intuitive way of defining geometry design variables for solving structural topology optimization problems using a genetic algorithm (GA). The geometry representation scheme works by defining a skeleton that represents the underlying topology/connectivity of the continuum structure. As the effectiveness of any GA is highly dependent on the chromosome encoding of the design variables, the encoding used here is a directed graph which reflects this underlying topology so that the genetic crossover and mutation operators of the GA can recombine and preserve any desirable geometric characteristics through succeeding generations of the evolutionary process. The overall optimization procedure is tested by solving a simulated topology optimization problem in which a 'target' geometry is pre-defined with the aim of having the design solutions converge towards this target shape. The procedure is also applied to design a straight-line compliant mechanism : a large displacement flexural structure that generates a vertical straight line path at some point when given a horizontal straight line input displacement at another point.
2003-01-01T00:00:00ZStatistical Error in Particle Simulations of Fluid Flow and Heat Transfer
https://hdl.handle.net/1721.1/3708
Statistical Error in Particle Simulations of Fluid Flow and Heat Transfer
Hadjiconstantinou, Nicolas G.; Garcia, Alejandro L.; Bazant, Martin Z.; He, Gang
We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Specifically, we present predictions for the error dependence on hydrodynamic parameters and the number of samples taken. Expressions for the common hydrodynamic variables of interest such as flow velocity, temperature, density, pressure, shear stress and heat flux are derived using equilibrium statistical mechanics. Both volume-averaged and surface-averaged quantities are considered. Comparisons between theory and computations using direct simulation Monte Carlo for dilute gases, and molecular dynamics for dense fluids, show that the use of equilibrium theory provides accurate results.
2003-01-01T00:00:00ZReliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations
https://hdl.handle.net/1721.1/3707
Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations
Oliveira, I.B.; Patera, Anthony T.
The solution of a single optimization problem often requires computationally-demanding evaluations; this is especially true in optimal design of engineering components and systems described by partial differential equations. We present a technique for the rapid and reliable optimization of systems characterized by linear-functional outputs of partial differential equations with affine parameter dependence. The critical ingredients of the method are: (i) reduced-basis techniques for dimension reduction in computational requirements; (ii) an "off-line/on-line" computational decomposition for the rapid calculation of outputs of interest and respective sensitivities in the limit of many queries; (iii) a posteriori error bounds for rigorous uncertainty and feasibility control; (iv) Interior Point Methods (IPMs) for efficient solution of the optimization problem; and (v) a trust-region Sequential Quadratic Programming (SQP) interpretation of IPMs for treatment of possibly non-convex costs and constraints.
2003-01-01T00:00:00ZReal-Time Optimal Parametric Design of a Simple Infiltration-Evaporation Model Using the Assess-Predict-Optimize (APO) Strategy
https://hdl.handle.net/1721.1/3706
Real-Time Optimal Parametric Design of a Simple Infiltration-Evaporation Model Using the Assess-Predict-Optimize (APO) Strategy
Ali, S.; Damodaran, Murali; Patera, Anthony T.
Optimal parametric design of a system must be able to respond quickly to short term needs as well as long term conditions. To this end, we present an Assess-Predict-Optimize (APO) strategy which allows for easy modification of a system’s characteristics and constraints, enabling quick design adaptation. There are three components to the APO strategy: Assess - extract necessary information from given data; Predict - predict future behavior of system; and Optimize – obtain optimal system configuration based on information from the other components. The APO strategy utilizes three key mathematical ingredients to yield real-time results which would certainly conform to given constraints: dimension reduction of the model, a posteriori error estimation, and optimization methods. The resulting formulation resembles a bilevel optimization problem with an inherent nonconvexity in the inner level. Using a simple infiltration-evaporation model to simulate an irrigation system, we demonstrate the APO strategy’s ability to yield real-time optimal results. The linearized model, described by a coercive elliptic partial differential equation, is discretized by the reduced-basis output bounds method. A primal-dual interior point method is then chosen to solve the resulting APO problem.
2003-01-01T00:00:00ZOptimization of Passive Constrained Layer Damping Treatments for Vibration Control of Cylindrical Shells
https://hdl.handle.net/1721.1/3705
Optimization of Passive Constrained Layer Damping Treatments for Vibration Control of Cylindrical Shells
Zheng, H.; Pau, G.S.H.; Liu, Guirong
This paper presents the layout optimization of passive constrained layer damping (PCLD) treatment for vibration control of cylindrical shells under a broadband force excitation. The equations governing the vibration responses are derived using the energy approach and assumed-mode method. These equations provided relationship between the integrated displacement response over the whole structural volume, i.e. the structural volume displacement (SVD), of a cylindrical shell to structural parameters of base structure and multiple PCLD patches, Genetic algorithms (GAs) based penalty function method is employed to find the optimal layout of rectangular PCLD patches with minimize the maximum displacement response of PCLD-treated cylindrical shells. Optimization solutions of PCLD patches’ locations and shape are obtained under the constraint of total amount of PCLD in terms of percentage added weight to the base structure. Examination of the optimal layouts reveals that the patches tend to increase their coverage in the axial direction and distribute over the whole surface of the cylindrical shell for optimal control of the structural volume displacement.
2003-01-01T00:00:00ZNonsmooth Newton’s Method and Semidefinite Optimization
https://hdl.handle.net/1721.1/3704
Nonsmooth Newton’s Method and Semidefinite Optimization
Sun, Jie
We introduce basic ideas of a nonsmooth Newton’s method and its application in solving semidefinite optimization (SDO) problems. In particular, the method can be used to solve both linear and nonlinear semidefinite complementarity problems. We also survey recent theoretical results in matrix functions and stability of SDO that are stemed from the research on the matrix form of the nonsmooth Newton’s method.
2003-01-01T00:00:00ZMultiparameter Moment Matching Model Reduction Approach for Generating Geometrically Parameterized Interconnect Performance Models
https://hdl.handle.net/1721.1/3703
Multiparameter Moment Matching Model Reduction Approach for Generating Geometrically Parameterized Interconnect Performance Models
Daniel, Luca; Ong, Chin Siong; Low, Sok Chay; Lee, Kwok Hong; White, Jacob K.
In this paper we describe an approach for generating geometrically-parameterized integrated-circuit interconnect models that are efficient enough for use in interconnect synthesis. The model generation approach presented is automatic, and is based on a multi-parameter model-reduction algorithm. The effectiveness of the technique is tested using a multi-line bus example, where both wire spacing and wire width are considered as geometric parameters. Experimental results demonstrate that the generated models accurately predict both delay and cross-talk effects over a wide range of spacing and width variation.
2003-01-01T00:00:00ZModel reduction for active control design using multiple-point Arnoldi methods
https://hdl.handle.net/1721.1/3702
Model reduction for active control design using multiple-point Arnoldi methods
Lassaux, G.; Willcox, Karen E.
A multiple-point Arnoldi method is derived for model reduction of computational fluid dynamic systems. By choosing the number of frequency interpolation points and the number of Arnoldi vectors at each frequency point, the user can select the accuracy and range of validity of the resulting reduced-order model while balancing computational expense. The multiple-point Arnoldi approach is combined with a singular value decomposition approach similar to that used in the proper orthogonal decomposition method. This additional processing of the basis allows a further reduction in the number of states to be obtained, while retaining a significant computational cost advantage over the proper orthogonal decomposition. Results are presented for a supersonic diffuser subject to mass flow bleed at the wall and perturbations in the incoming flow. The resulting reduced-order models capture the required dynamics accurately while providing a significant reduction in the number of states. The reduced-order models are used to generate transfer function data, which are then used to design a simple feedforward controller. The controller is shown to work effectively at maintaining the average diffuser throat Mach number.
2003-01-01T00:00:00ZGeneralized Stationary Points and an Interior Point Method for MPEC
https://hdl.handle.net/1721.1/3701
Generalized Stationary Points and an Interior Point Method for MPEC
Liu, Xinwei; Sun, Jie
Mathematical program with equilibrium constraints (MPEC)has extensive applications in practical areas such as traffic control, engineering design, and economic modeling. Some generalized stationary points of MPEC are studied to better describe the limiting points produced by interior point methods for MPEC.A primal-dual interior point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced without assuming strict complementarity or linear independence constraint qualification. Under very general assumptions, the algorithm can always find some point with strong or weak stationarity. In particular, it is shown that every limiting point of the generated sequence is a piece-wise stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a certain point with weak stationarity can be obtained. Preliminary numerical results are satisfactory, which include a case analyzed by Leyffer for which the penalty interior point algorithm failed to find a stationary solution.
2003-01-01T00:00:00ZEffect of Column Inlet and Outlet Geometry on Large-scale HPLC
https://hdl.handle.net/1721.1/3700
Effect of Column Inlet and Outlet Geometry on Large-scale HPLC
Tan, S.N.; Khoo, Boo Cheong
The separating characteristics of high performance liquid chromatography (HPLC) columns, measured in terms of the height equivalent of a theoretical plate (HETP) and skewness of the eluted peak, are investigated using computational fluid dynamics (CFD). Gradually expanding and contracting sections are introduced at the inlet and outlet, respectively, in columns with and without frits and their performance was compared with that of the conventional columns without expanding and contracting regions.
2003-01-01T00:00:00ZData Smoothing: Research 2002
https://hdl.handle.net/1721.1/3699
Data Smoothing: Research 2002
Strang, Gilbert
My research is concentrated on applications of linear algebra in engineering, including wavelet analysis and structured matrices. This paper will appear in the book Mathematical Systems Theory (J. Rosenthal and D. Gilliam, editors) IMA Volumes in Mathematics, Springer 2002.
2003-01-01T00:00:00ZComputing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation
https://hdl.handle.net/1721.1/3698
Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation
Sauer-Budge, A.M.; Huerta, A.; Bonet, J.; Peraire, Jaime
We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of linear functional outputs of the exact weak solution of the infinite dimensional continuum problem using traditional finite element approximations. The guarantee holds uniformly for any level of refinement, not just in the asymptotic limit of refinement. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity which is linear in the number of elements in the finite element discretization.
2003-01-01T00:00:00ZA Comparative Study on Optimization of Constrained Layer Damping for Vibration Control of Beams
https://hdl.handle.net/1721.1/3697
A Comparative Study on Optimization of Constrained Layer Damping for Vibration Control of Beams
Pau, G.S.H.; Zheng, H.; Liu, Guirong
This paper presents a comparison of optimization algorithms for constrained damping (CLD) patches’ layout to minimize the maximum vibration response of the odd modes, which constitutes the dominant acoustic radiation, of a simply-supported beam excited by a harmonic transverse force. An analytical model based on Euler-Bernoulli beam assumptions is derived first to relate the displacement response of the beam with bonded CLD patches and their layout. Four different nonlinear optimization methods/algorithms are then respectively used to optimize the CLD patches’ locations and lengths with aim of minimum displacement amplitude at middle of the beam. The considered methods include subproblem approximation method, the first-order method, sequential quadratic programming (SQP) and genetic algorithm (GA). The efficiency of each considered optimization method is evaluated and also compared in terms of obtained optimal beam displacement. The results show that GA is most efficient in obtaining the best optimum for this optimization problem in spite of highest computation efforts required to improve its stability.
2003-01-01T00:00:00ZCharacterizing Scattering by 3-D Arbitrarily Shaped Homogeneous Dielectric Objects Using Fast Multipole Method
https://hdl.handle.net/1721.1/3696
Characterizing Scattering by 3-D Arbitrarily Shaped Homogeneous Dielectric Objects Using Fast Multipole Method
Li, Jian-Ying; Li, Le-Wei
Electromagnetic scattering by 3-D arbitrarily shaped homogeneous dielectric objects is characterized. In the analysis, the method of moments is first employed to solve the combined field integral equation for scattering properties of these three-dimensional homogeneous dielectric objects of arbitrary shape. The fast multipole method, and the multi-level fast multipole algorithm are implemented into our codes for matrix-vector manipulations. Specifically, four proposals are made and discussed to increase convergence and accuracy of iterative procedures (conjugate gradient method). Numerical results are obtained using various methods and compared to each other.
2003-01-01T00:00:00ZBubble Simulation Using Level Set-Boundary Element Method
https://hdl.handle.net/1721.1/3695
Bubble Simulation Using Level Set-Boundary Element Method
Tan, Kiok Lim; Khoo, Boo Cheong; White, Jacob K.
In bubble dynamics, an underwater bubble may evolve from being singly-connected to being toroidal. Furthermore, two or more individual bubbles may merge to form a single large bubble. These dynamics involve significant topological changes such as merging and breaking, which may not be handled well by front-tracking boundary element methods. In the level set method, topological changes are handled naturally through a higher-dimensional level set function. This makes it an attractive method for bubble simulation. In this paper, we present a method that combines the level set method and the boundary element method for the simulation of bubble dynamics. We propose a formulation for the update of a potential function in the level set context. This potential function is non-physical off the bubble surface but consistent with the physics on the bubble surface. We consider only axisymmetric cavitation bubbles in this paper. Included in the paper are some preliminary results and findings.
2003-01-01T00:00:00ZApplications of Proper Orthogonal Decomposition for Inviscid Transonic Aerodynamics
https://hdl.handle.net/1721.1/3694
Applications of Proper Orthogonal Decomposition for Inviscid Transonic Aerodynamics
Tan, Bui-Thanh; Willcox, Karen E.; Damodaran, Murali
Two extensions to the proper orthogonal decomposition (POD) technique are considered for steady transonic aerodynamic applications. The first is to couple the POD approach with a cubic spline interpolation procedure in order to develop fast, low-order models that accurately capture the variation in parameters, such as the angle of attack or inflow Mach number. The second extension is a POD technique for the reconstruction of incomplete or inaccurate aerodynamic data. First, missing flow field data is constructed with an existing POD basis constructed from complete aerodynamic data. Second, a technique is used to develop a complete snapshots from an incomplete set of aerodynamic snapshots.
2003-01-01T00:00:00Z