http://hdl.handle.net/1721.1/3652 http://dspace.mit.edu:80/retrieve/3314 http://hdl.handle.net/1721.1/3652 http://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. Thu, 29 Dec 2005 22:58:59 GMT http://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. Thu, 29 Dec 2005 22:58:59 GMT http://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. Thu, 29 Dec 2005 22:58:59 GMT http://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. Thu, 29 Dec 2005 22:58:59 GMT