Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776197 | Journal of Computational and Applied Mathematics | 2017 | 22 Pages |
Abstract
A Schwarz-type preconditioner is formulated for a class of parallel adaptive finite elements where the local meshes cover the whole domain. With this preconditioner, the convergence rate of the conjugate gradient method is shown to depend only on the ratio of the second largest and smallest eigenvalues of the preconditioned system. These eigenvalues can be bounded independently of the mesh sizes and the number of subdomains, which proves the proposed preconditioner is optimal. Numerical results are provided to support the theoretical findings.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Sébastien Loisel, Hieu Nguyen,