Details

Autor(en) / Beteiligte

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

Titel

The Construction of Preconditioners for Elliptic Problems by Substructuring. I

Ist Teil von

• Mathematics of computation, 1986-07, Vol.47 (175), p.103-134

Ort / Verlag

Providence, RI: American Mathematical Society

Erscheinungsjahr

1986

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.