Toward an optimal solver for the obstacle problem

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Show simple item record Heldman, Max 2019-01-10T00:01:07Z 2019-01-10T00:01:07Z 2018-04
dc.description Master's Project (M.S.) University of Alaska Fairbanks, 2018 en_US
dc.description.abstract An optimal algorithm for solving a problem with m degrees of freedom is one that computes a solution in O (m) time. In this paper, we discuss a class of optimal algorithms for the numerical solution of PDEs called multigrid methods. We go on to examine numerical solvers for the obstacle problem, a constrained PDE, with the goal of demonstrating optimality. We discuss two known algorithms, the so-called reduced space method (RSP) [BM03] and the multigrid-based projected full-approximation scheme (PFAS) [BC83]. We compare the performance of PFAS and RSP on a few example problems, finding numerical evidence of optimality or near-optimality for PFAS. en_US
dc.language.iso en_US en_US
dc.subject Differential equations, Partial en_US
dc.subject Numerical solutions en_US
dc.subject Multigrid methods (Numerical analysis) en_US
dc.title Toward an optimal solver for the obstacle problem en_US
dc.type Other en_US ms
dc.identifier.department Department of Mathematics and Statistics
dc.contributor.chair Bueler, Ed
dc.contributor.committee Maxwell, David
dc.contributor.committee Rhodes, John

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