Analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems

Journal Article · Sat Oct 01 00:00:00 EDT 1988 · Math. Comput.; (United States)

DOI:https://doi.org/10.1090/S0025-5718-1988-0930228-6· OSTI ID:6931781

Bramble, J H; Pasciak, J E; Xu, J

We prove some new estimates for the convergence of multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems. We provide results for the so-called 'symmetric' multigrid schemes. We show that for the variable V-script-cycle and the W-script-cycle schemes, multigrid algorithms with any amount of smoothing on the finest grid converge at a rate that is independent of the number of levels or unknowns, provided that the initial grid is sufficiently fine. We show that the V-script-cycle algorithm also converges (under appropriate assumptions on the coarsest grid) but at a rate which may deteriorate as the number of levels increases. This deterioration for the V-script-cycle may occur even in the case of full elliptic regularity. Finally, the results of numerical experiments are given which illustrate the convergence behavior suggested by the theory.

• Research Organization: 4 Physikalisches Institut, Universitaet Stuttgart, Pfaffenwaldring 57, D 7000 Stuttgart 80, West Germany
• OSTI ID: 6931781
• Journal Information: Math. Comput.; (United States), Journal Name: Math. Comput.; (United States) Vol. 51:184; ISSN MCMPA
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990230* -- Mathematics & Mathematical Models-- (1987-1989)
ALGORITHMS
BOUNDARY CONDITIONS
CONFIGURATION
CONVERGENCE
DIFFERENTIAL EQUATIONS
ELLIPTICAL CONFIGURATION
EQUATIONS
ITERATIVE METHODS
MATHEMATICAL LOGIC
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY