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 20 of 24 for “"Linear solvers"”.
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Application of nearly linear solvers to electric power system computation
… rely on the solution of a very large linear system. As the demands on power systems continue to grow, there is a greater computational complexity involved in solving these large linear systems within reasonable time.</p><p>This project expands on the current work in fast linear …
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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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Designing Hardware Accelerators for Solving Sparse Linear Systems
Solving sparse linear systems is a key primitive that sits at the heart of many important numeric algorithms. Because of this primitive’s importance, algorithm designers have spent many decades optimizing linear solvers for high performance hardware. However, despite their efforts, existing …
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A hybrid parallel framework for computational solid mechanics
… types of elements and a number of different linear and non-linear solvers. In addition, native, seamless support is included for hardware acceleration by Graphics Processing Units (GPUs) via NVIDIA's CUDA architecture for both single GPU workstations and heterogenous clusters of GPUs. The …
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Analysis and algorithms for parametrization, optimization and customization of sled hockey equipment and other dynamical systems
… implement numerical algorithms to study the nonlinear dynamics described by 4th-order nonlinear PDEs. The non-linear solvers apply multidimensional Newton's method with a Jacobian-free approach and a generalized conjugate residual (GCR) approach.
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Implicit Finite Element Contact With a Multigrid Solver on Parallel Computers
… non-smooth as well as algebraically non-linear makes them difficult to solve. Since the bulk of the work in a contact algorithm is associated with solving systems of linear equations, efficient linear solvers are attractive. The geometric multigrid method is an iterative linear equation …
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IMPLEMENTATION OF A VERTICALLY INTEGRATED ICE SHEET MOMENTUM BALANCE MODEL
… costly sorting routines in the underlying linear solvers. The code was not only developed for standards-compliant FORTRAN 90 compilers but also for automatic differentiation tools. The model is verified against published model intercomparison projects.
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IMPLEMENTATION OF A VERTICALLY INTEGRATED ICE SHEET MOMENTUM BALANCE MODEL
… costly sorting routines in the underlying linear solvers. The code was not only developed for standards-compliant FORTRAN 90 compilers but also for automatic differentiation tools. The model is verified against published model intercomparison projects.
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Machine Learning Regularized Solution of the Lippmann-Schwinger Equation
… Solving the equation requires the inversion of a linear operator specified by the scattering potential, which is ill-conditioned. To resolve numerical difficulty originating from such ill-conditionedness, we propose a machine learning approach to find an appropriate regularization. Inspired by the …
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A parallel numerical solver using hierarchically tiled arrays
Solving linear systems is an important problem for scientific computing. Exploiting parallelism is essential for solving complex systems, and this traditionally involves writing parallel algorithms on top of a library such as MPI. The SPIKE family of algorithms is one well-known example of a …
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A vertex based discretisation scheme applied to material non-linearity within a multi-physics finite volume framework
… Solid Mechanics(CSM) problems involving non-linear material behavior, specifically materials described by an elasto-visco-plastic constitutive relationship and a von-Mises yield criterion. The motivation is to contribute the non-linear CSM capability to an integrated FV framework for the …
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Parallel Black Oil Solvers on GPU
… users. In this thesis, a GPU-based parallel linear solver package, named Parallel Accelerated Simulation Solvers (PASS), is developed to speed up the reservoir simulation using the GPU. For this new solver package, several different linear solvers and preconditioners have been implemented …
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Advanced response matrix methods for full core analysis
… transport. In particular, advanced transport solvers were studied for application to the relatively small and frequently repeated problems characteristic of response function generation. This includes development of preconditioners based on diffusion for use in multigroup Krylov linear …
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A Computational Framework for Simulating Entanglement-Based Drone Countermeasures with Flexible Filaments Immersed in Viscous Flow
… through the use of fast GPU-based dense linear solvers. The BI formulation is coupled to the filament solid mechanics by enforcing momentum balance at the dynamically evolving filament-fluid interface. Additionally, the solid contact interactions between filaments are modeled with a …
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Hodge Laplacians on simplicial meshes and graphs
… computational evidence that algebraic multigrid linear solvers for the resulting linear systems on Erdős-Rényi random graphs and on Barabási-Albert graphs do not perform very well in comparison with iterative Krylov solvers.
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Adaptive Finite Elements for Systems of PDEs: Software Concepts, Multi-level Techniques and Parallelization
… methods, high order discretization, fast linear and non-linear solvers and multi-level methods. The application of these methods in a large class of problems demands for suitable and robust tools for a flexible and efficient implementation. In order to play a crucial role in scientific and …
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Electric neutron polarizability and eigenspectrum subtraction techniques for disconnected quark loops.
I present an analysis for the mass shift of the neutron in order to obtain the neutron electric polarizability. Neutron electric polarizability can be studied by implementing a static electric field on the lattice. The implementation of this field, though, is non-trivial and the "proper" form for …
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Reducing communication in sparse solvers
Sparse matrix operations dominate the cost of many scientific applications. In parallel, the performance and scalability of these operations is limited by irregular point-to-point communication. Multiple methods are investigated throughout this dissertation for reducing the cost associated with …
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On Efficient Solution Methods for Mixed-Integer Nonlinear and Mixed-Integer Quadratic Optimization Problems
… on solution methods for convex mixed-integer nonlinear optimization problems (MINLP). As one main result, we propose a new algorithm guaranteeing global optimality for convex MINLPs under standard assumptions. The new algorithm called MIQP-supported outer approximation (MIQPSOA) incorporates the …
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A Parallel Boundary Conforming Method on Adaptive Moving Meshes for Multiphase Flows
… the Finite Element Method (Li, 2013); parallel linear solvers provided by PETSc are used to solve the discretised incompressible Navier-Stokes equations. There are several important advantages of the boundary conforming method on unstructured meshes. The method is accurate in computing curvature …
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