Uniform convergence of multigrid v-cycle iterations for indefinite and nonsymmetric problems

Journal Article · Thu Dec 01 04:00:00 EST 1994 · SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States)

DOI:https://doi.org/10.1137/0731089· OSTI ID:6835604

Bramble, J H ^[1]; Kwak, D Y ^[2]; Pasciak, J E ^[3]

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1. Cornell Univ., Ithaca, NY (United States). Dept. of Mathematics
2. Korea Advanced Inst. of Science and Technology, Taejon (Korea, Republic of). Dept. of Mathematics
3. Brookhaven National Lab., Upton, NY (United States). Dept. of Applied Science

In this paper, an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems is presented. In this multigrid method various types of smothers may be used. One type of smoother considered is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. Smothers based entirely on the original operator are also considered. One smoother is based on the normal form, that is, the product of the operator and its transpose. Other smothers studied include point and line, Jacobi, and Gauss-Seidel. It is shown that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not dependent on the number of multigrid levels).

• DOE Contract Number: AC02-76CH00016
• OSTI ID: 6835604
• Journal Information: SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States), Journal Name: SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States) Vol. 31:6; ISSN 0036-1429; ISSN SJNAAM
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
BOUNDARY-VALUE PROBLEMS
CALCULATION METHODS
CONVERGENCE
DIFFERENTIAL EQUATIONS
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GALERKIN-PETROV METHOD
ITERATIVE METHODS
MESH GENERATION
PARTIAL DIFFERENTIAL EQUATIONS