The construction of preconditioners for elliptic problems by substructuring. I. (English) Zbl 0615.65112

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

Math. Comput. 47, 103-134 (1986).

Authors’ summary: 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 these discrete systems 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.

Reviewer: I.H.Mufti

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
35J25	Boundary value problems for second-order elliptic equations
65F35	Numerical computation of matrix norms, conditioning, scaling

Keywords:

finite element methods; preconditioners; substructuring; domain decomposition; parallel computing; convergence rate; numerical experiments