Parallel iterative solution of sparse linear systems in computational fluid dynamics

Abstract

This thesis deals with the solution of large sparse systems of linear equations on manycore architectures with distributed memory using iterative krylov methods. It focusses on preconditioning techniques, especially those that are based on a Schur-complement- Ansatz.

These preconditioners can be considered as an iterative correction of block-Jacobi preconditioning that uses an incomplete LU-decomposition to approximately invert the diagonal blocks of the matrix.

Sample linear systems stem from CFD (computational fluid dynamics) simulation systems, which were developed by DLR (German Aerospace Center).

The runtime and numerical characteristics of the parallel preconditioned solvers developed are discussed by means of empirical tests with these systems.

The results of these tests demonstrate that Schur-complement preconditioners can considerably improve the parallel scalability of an iterative solver in comparison to block-Jacobi preconditioning.