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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Construction of Preconditioners by Mapping Properties for Systems of Partial Differential Equations

Pp. 66-83 (18)

Kent-Andre Mardal and Ragnar Winther

Abstract

The purpose of this chapter is to discuss a general approach to the construction of preconditioners for the linear systems of algebraic equations arising from discretizations of systems of partial differential equations. The discussion here is closely tied to our earlier paper [1], where we gave a comprehensive review of a mathematical theory for constructing preconditioners based on the mapping properties of the coefficient operator of the underlying differential systems. In the presentation given below we focus more on specific examples, while just an outline of the general theory is given.

Keywords:

partial differential equations, discretizations, linear systems, algebraic, preconditioners, mathematical theory, Hilbert space, operator

Affiliation:

Center for Biomedical Computing, Simula Research Laboratory, Lysaker, Norway.