Premium
A hybrid geometric + algebraic multigrid method with semi‐iterative smoothers
Author(s) -
Lu Cao,
Jiao Xiangmin,
Missirlis Nikolaos
Publication year - 2014
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1925
Subject(s) - mathematics , multigrid method , algebraic number , iterative method , mathematical optimization , real algebraic geometry , algebra over a field , algorithm , mathematical analysis , partial differential equation , pure mathematics
SUMMARY We propose a multigrid method for solving large‐scale sparse linear systems arising from discretizations of partial differential equations, such as those from finite element and generalized finite difference methods. Our proposed method has the following two characteristics. First, we introduce a hybrid geometric+algebraic multigrid method, or HyGA , to leverage the rigor, accuracy, and efficiency of geometric multigrid (GMG) for hierarchical unstructured meshes, with the flexibility of algebraic multigrid (AMG). Second, we introduce efficient smoothers based on the Chebyshev–Jacobi method for both symmetric and asymmetric matrices. We also introduce a unified derivation of restriction and prolongation operators for weighted‐residual formulations over unstructured hierarchical meshes and apply it to both finite element and generalized finite difference methods. We present numerical results of our method for Poisson equations in both 2‐D and 3‐D and compare our method against the classical GMG and AMG as well as Krylov subspace methods. Copyright © 2014 John Wiley & Sons, Ltd.