Uppsala University Department of Information Technology

Licentiate thesis 2005-006

Robust Preconditioned Iterative Solution Methods for Large-Scale Nonsymmetric Problems

Erik Bängtsson

3 November 2005


We study robust, preconditioned, iterative solution methods for large-scale linear systems of equations, arising from different applications in geophysics and geotechnics.

The first type of linear systems studied here, which are dense, arise from a boundary element type of discretization of crack propagation in brittle material. Numerical experiment show that simple algebraic preconditioning strategies results in iterative schemes that are highly competitive with a direct solution method.

The second type of algebraic systems are nonsymmetric and indefinite and arise from finite element discretization of the partial differential equations describing the elastic part of glacial rebound processes. An equal order finite element discretization is analyzed and an optimal stabilization parameter is derived.

The indefinite algebraic systems are of 2-by-2-block form, and therefore block preconditioners of block-factorized or block-triangular form are used when solving the indefinite algebraic system. There, the required Schur complement is approximated in various ways and the quality of these approximations is compared numerically.

When the block preconditioners are constructed from incomplete factorizations of the diagonal blocks, the iterative scheme show a growth in iteration count with increasing problem size. This growth is stabilized by replacing the incomplete factors with an inner iterative scheme with a (nearly) optimal order multilevel preconditioner.

Note: Typos corrected 2005-11-21

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