Construction of preconditioners for elliptic problems by substructuring, III

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

DOI:https://doi.org/10.1090/S0025-5718-1988-0935071-X· OSTI ID:6931777

Bramble, J H; Pasciak, J E; Schatz, A H

In earlier parts of this series of papers, we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems. The resulting algorithms are well suited for implementation on computers with parallel architecture. In this paper, we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners. The iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns. These preconditioners involve an incomplete Chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work. Theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods.

• Research Organization: 4 Physikalisches Institut, Universitaet Stuttgart, Pfaffenwaldring 57, D 7000 Stuttgart 80, West Germany
• OSTI ID: 6931777
• Journal Information: Math. Comput.; (United States), Vol. 51:184
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
PARTIAL DIFFERENTIAL EQUATIONS
NUMERICAL SOLUTION
ALGORITHMS
BOUNDARY CONDITIONS
CONVERGENCE
ELLIPTICAL CONFIGURATION
ITERATIVE METHODS
SYMMETRY
THEORETICAL DATA
CONFIGURATION
DATA
DIFFERENTIAL EQUATIONS
EQUATIONS
INFORMATION
MATHEMATICAL LOGIC
NUMERICAL DATA
990230* - Mathematics & Mathematical Models- (1987-1989)