Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations

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This e-book presents several research areas of elliptical problems solved by differential equations. The mathematical models explained in this e-book have been contributed by experts in the field and ...
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Block Preconditioners for Saddle Point Problems Resulting from Discretizations of Partial Differential Equations

Pp. 44-65 (22)

Piotr Krzyzanowski

Abstract

We discuss a family of block preconditioners for iterative solution of symmetric saddle point type problems arising from PDE discretizations. The building blocks consist of preconditioners for smaller sized, symmetric positive definite operators, which induce a norm in which the whole system is continuous and stable uniformly with respect to the mesh size h. We provide eigenvalue estimates and derive conditions under which the conjugate residual method using block preconditioners has convergence rate bounded independently of h.

Keywords:

saddle point systems, partial differential equations, discretizations, stability, iterative solution, conjugate residual method, block preconditioners, robust

Affiliation:

Institute of Applied Mathematics, University of Warsaw, Poland.