Construction of preconditioners for elliptic problems by substructuring. I

Journal Article · Tue Jul 01 00:00:00 EDT 1986 · Math. Comput.; (United States)

DOI:https://doi.org/10.1090/S0025-5718-1986-0842125-3· OSTI ID:6485968

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

We consider the problem of solving the algebraic system of equations which arise from the discretization of symmetric elliptic boundary value problems via finite element methods. A new class of preconditioners for the discrete system is developed based on substructuring (also known as domain decomposition). The resulting preconditioned algorithms are well suited to emerging parallel computing architectures. The proposed methods are applicable to problems on general domains involving differential operators with rather general coefficients. A basic theory for the analysis of the condition number of the preconditioned system (which determines the iterative convergence rate of the algorithm) is given. Techniques for applying the theory and algorithms to problems with irregular geometry are discussed and the results of extensive numerical experiments are reported.

• Research Organization: Institute of Modern Physics, Academia Sinica, Lanzhou
• OSTI ID: 6485968
• Journal Information: Math. Comput.; (United States), Journal Name: Math. Comput.; (United States) Vol. 47:175; ISSN MCMPA
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990230* -- Mathematics & Mathematical Models-- (1987-1989)
ALGORITHMS
BOUNDARY-VALUE PROBLEMS
DIFFERENTIAL EQUATIONS
DIRICHLET PROBLEM
EQUATIONS
FINITE ELEMENT METHOD
MATHEMATICAL LOGIC
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS