Jacob B. Schroder

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We consider optimal-scaling multigrid solvers for the linear systems that arise from the discretization of problems with evolutionary behavior. Typically, solution algorithms for evolution equations are based on a time-marching approach, solving sequentially for one time step after the other. Parallelism in these traditional time-integration techniques is(More)
We develop a smoothed aggregation-based algebraic multigrid solver for high-order discontinuous Galerkin discretizations of the Poisson problem. Algebraic multigrid is a popular and effective method for solving the sparse linear systems that arise from discretizing partial differential equations. However, high-order discontinuous Galerkin discretizations(More)
Algebraic multigrid methods solve sparse linear systems Ax = b by automatic construction of a multilevel hierarchy. This hierarchy is defined by grid transfer operators that must accurately capture algebraically smooth error relative to the relaxation method. We propose a methodology to improve grid transfers through energy minimization. The proposed(More)
Algebraic-based multilevel solution methods (e.g. classical Ruge–Stüben and smoothed aggregation style algebraic multigrid) attempt to solve or precondition sparse linear systems without knowledge of an underlying geometric grid. The automatic construction of a multigrid hierarchy relies on strength-of connection information to coarsen the matrix graph and(More)
We outline a smoothed aggregation algebraic multigrid method for 1D and 2D scalar Helmholtz problems with exterior radiation boundary conditions. We consider standard 1D finite difference discretizations and 2D discontinuous Galerkin discretizations. The scalar Helmholtz problem is particularly difficult for algebraic multigrid solvers. Not only can the(More)
Algebraic multigrid (AMG) is an O(n) solution process for many large sparse linear systems. A hierarchy of progressively coarser grids is constructed that utilize complementary relaxation and interpolation operators. High-energy error is reduced by relaxation, while low-energy error is mapped to coarse-grids and reduced there. However, large parallel(More)
Computational simulation in the physical and information sciences continues to place demands on the underlying linear solvers used in the process. Algebraicbased multigrid methods offer a flexible medium for adapting to a wide range of problems, yet traditional approaches have designed the multigrid components for basic, isotropic, and well-behaved(More)