Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10356412 | Journal of Computational Physics | 2005 | 13 Pages |
Abstract
Two related approaches for solving linear systems that arise from a higher-order finite element discretization of elliptic partial differential equations are described. The first approach explores direct application of an algebraic-based multigrid method (AMG) to iteratively solve the linear systems that result from higher-order discretizations. While the choice of basis used on the discretization has a significant impact on the performance of the solver, results indicate that AMG is capable of solving operators from both Poisson's equation and a first-order system least-squares (FOSLS) formulation of Stoke's equation in a scalable manner, nearly independent of basis order, p, for 3 < p ⩽ 8. The second approach incorporates preconditioning based on a bilinear finite element mesh overlaying the entire set of degrees of freedom in the higher-order scheme. AMG is applied to the operator based on bilinear finite elements and is used as a preconditioner in a conjugate gradient (CG) iteration to solve the algebraic system derived from the high-order discretization. This approach is also nearly independent of p. Although the total iteration count is slightly higher than using AMG accelerated by CG directly on the high-order operator, the preconditioned approach has the advantage of a straightforward matrix-free implementation of the high-order operator, thereby avoiding typically large computational and storage costs.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
J.J. Heys, T.A. Manteuffel, S.F. McCormick, L.N. Olson,