Browsing UAF Graduate School by Subject "Multigrid methods (Numerical analysis)"
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Toward an optimal solver for the obstacle problemAn 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.