Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 7 of 7 for “"Large-scale linear systems"”.
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Algebraic Multigrid for Discrete Differential Forms
… multigrid (AMG) which is designed to solve large-scale linear systems with optimal, or near-optimal efficiency. Since the k-form problems to be solved are arbitrarily large, the need for scalable numerical solvers is clear.
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Stochastic methods for large-scale linear problems, variational inequalities, and convex optimization
This thesis considers stochastic methods for large-scale linear systems, variational inequalities, and convex optimization problems. I focus on special structures that lend themselves to sampling, such as when the linear/nonlinear mapping or the objective function is an expected value or is the sum …
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GPU-accelerated Linear Solvers for High-order Finite Element Methods in Poisson Problems
Solving large-scale linear systems arising from high-order finite element discretizations for Poisson equations often represents the most expensive component of the high-order finite element solver. This dissertation develops and analyzes numerical methods and algorithms aimed at improving the …
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Stable Sparse Orthogonal Factorization of Ill-Conditioned Banded Matrices for Parallel Computing
… widely used in the problems of computation with large-scale ill-conditioned banded matrices. Great concerns on existing methods include ill-conditioning, sparsity of factor matrices, computational complexity, and scalability. In this dissertation, we study a sparse orthogonal factorization of a …
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Shape and Topology Optimization for electro-mechanical energy converters
… design (CAD) representation of indus- trial systems and the finite element method (FEM) to solve the partial differential equations (PDEs) that govern their behavior under certain physical conditions. This thesis addresses three main subjects. First, the sensitivity analysis of elec- …
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Faster algorithms for convex and combinatorial optimization
… on convex and combinatorial optimization: --Linear Programming: We obtain the first improvement to the running time for linear programming in 25 years. The convergence rate of this randomized algorithm nearly matches the universal barrier for interior point methods. As a corollary, we obtain …
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Novel Monte Carlo Methods for Large-Scale Linear Algebra Operations
<p>Linear algebra operations play an important role in scientific computing and data analysis. With increasing data volume and complexity in the "Big Data" era, linear algebra operations are important tools to process massive datasets. On one hand, the advent of modern high-performance computing …