http://hdl.handle.net/1721.1/33226 MIT's School of Engineering develops innovative technologies, thinking, and practice, as well as creative leaders equipped to address the world's complex problems. Search the Channel search http://dspace.mit.edu/simple-search http://hdl.handle.net/1721.1/39327 Title: A fast 3D full-wave solver for nanophotonics <br/> <br/>Authors: Zhang, Lei, S.M. Massachusetts Institute of Technology <br/> <br/>Abstract: Conventional fast integral equation solvers seem to be ideal approaches for simulating 3-D nanophotonic devices, as these devices are considered to be open structures, generating fields in both an interior channel and in the infinite exterior domain. However, many devices of interest, such as optical ring resonator filters or waveguides, have channels that can not be terminated without generating numerical reflections. Therefore, designing absorbers for these channels is a new problem for integral equation methods, as integral equation methods were initially developed for problems with finite surfaces. In this thesis we present a technique to eliminate reflections, making the channel volume conductive outside the domain of interest. The surface integral equation (SIE) method is employed to take advantage of the piecewise homogeneous medium. The Poggio-Miller-Chang-Harrington-Wu (PM-CHW) formulation is formed and the boundary element method is employed to construct and solve a linear system. Moreover, the block Toeplitz matrix property and using FFT helps reduce memory requirement, and accelerate the circulant matrix vector product. Numerical experiments are presented to demonstrate that this method can effectively reduce reflections to 1%, and is easily incorporated in an fast integral equation solver. <br/> <br/>Description: Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.; This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.; Includes bibliographical references (p. 57-61). Sun, 29 Oct 2006 22:58:59 GMT http://hdl.handle.net/1721.1/39326 Title: A linear multigrid preconditioner for the solution of the Navier-Stokes equations using a discontinuous Galerkin discretization <br/> <br/>Authors: Diosady, Laslo Tibor <br/> <br/>Abstract: A Newton-Krylov method is developed for the solution of the steady compressible Navier-Stokes equations using a Discontinuous Galerkin (DG) discretization on unstructured meshes. An element Line-Jacobi preconditioner is presented which solves a block tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (Block-ILU(O)) is also presented as a preconditioner, where the factorization is performed using a reordering of elements based upon the lines of maximum coupling used for the element Line-Jacobi preconditioner. This reordering is shown to be far superior to standard reordering techniques (Nested Dissection, One-way Dissection, Quotient Minimum Degree, Reverse Cuthill-Mckee) especially for viscous test cases. The Block-ILU(0) factorization is performed in-place and a novel algorithm is presented for the application of the linearization which reduces both the memory and CPU time over the traditional dual matrix storage format. A linear p-multigrid algorithm using element Line-Jacobi, and Block-ILU(O) smoothing is presented as a preconditioner to GMRES.; (cont.) The coarse level Jacobians are obtained using a simple Galerkin projection which is shown to closely approximate the linearization of the restricted problem except for perturbations due to artificial dissipation terms introduced for shock capturing. The linear multigrid preconditioner is shown to significantly improve convergence in terms of the number of linear iterations as well as to reduce the total CPU time required to obtain a converged solution. A parallel implementation of the linear multi-grid preconditioner is presented and a grid repartitioning strategy is developed to ensure scalable parallel performance. <br/> <br/>Description: Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.; This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.; Includes bibliographical references (p. 69-72). Sun, 29 Oct 2006 22:58:59 GMT http://hdl.handle.net/1721.1/39328 Title: Must linear algebra be block cyclic? : and other explorations into the expressivity of data parallel and task parallel languages <br/> <br/>Authors: Sundaresh, Harish Peruvamba <br/> <br/>Abstract: Prevailing Parallel Linear Algebra software block cyclically distributes data across its processors for good load balancing and communication between its nodes. The block cyclic distribution schema characterized by cyclic order allocation of row and column data blocks followed by consecutive elimination is widely used in scientific computing and is the default approach in ScaLA-PACK. The fact that we are not familiar with any software outside of linear algebra that has considered cyclic distributions for their execution presents incompatibility. This calls for possible change in approach as advanced computing platforms like Star-P are emerging allowing for interoperability of algorithms. This work demonstrates a data parallel column block cyclic elimination technique for LU and QR factorization. This technique yields good load balance and communication between nodes, and also eliminates superfluous overheads. The algorithms are implemented with consecutive allocation and cyclic elimination using the high level platform, Star-P. Block update tenders extensive performance enhancement making use of Basic Linear Algebra Subroutine-3 for delivering tremendous speedup. This project also provides an overview of threading in parallel systems through implementation of important task parallel algorithms: prefix, hexadecimal Pi digits and Monte-Carlo simulation. <br/> <br/>Description: Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.; Includes bibliographical references (leaves 68-69). Sun, 29 Oct 2006 22:58:59 GMT http://hdl.handle.net/1721.1/39325 Title: Computational modeling of crack initiation in cross-role piercing <br/> <br/>Authors: Chiluveru, Sudhir <br/> <br/>Abstract: Thle Mannesmann process is the preferred method in the oil industry for fabrication of hollow pipes. The critical phenomenon in this process is the formation of a small round hole at the center of the cylindrical billet ahead of the piercing plug. In this work the crack initiation that leads to the creation of tile small hole has been modeled. The Gurson-Tvergaard-Needlemnan model of porous plasticity is used to simulate the Mannesmann effect. The appearance of a crack at the center of the cylindrical bar is demonstrated and the stress profiles, plastic equivalent strain profiles and porosity distribution during the deformation process are analyzed. The influence of various parameters in the model on the evolution of porosity in tile specimen is studied. Other simple ductile fracture criteria that are proposed in literature are also implemented. An interface model for fracture using the discontinuous Galerkin framework combined with a cohesive fracture law is implemented. This approach and its advantages are illustrated in the application of tensile loading of a simple beam specimen. <br/> <br/>Description: Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.; Includes bibliographical references (p. 81-89). Sun, 29 Oct 2006 22:58:59 GMT