Dynamic load balancing for the preconditioned GMRES solver in a parallel, adaptive finite element Euler code

The construction and performance of a parallel algorithm to solve the Euler equations on unstructured grids with dynamically distributed data is presented. The algorithm uses a linear, implicit version of the well known Taylor-Galerkin time marching scheme for time discretization. Finite Elements are employed for space discretization of one step problems and an overlapping domain decomposition algorithm combined with the preconditioned GMRES method is used to solve iteratively in parallel the resulting system of linear equations. A new mesh partition algorithm based on the idea of advancing front is introduced and tested in practice. The setting for the program is a general MIMD multicomputer and PVM is used for message passing. Performance figures refer to test cases for multiprocessor supercomputers as well as for workstation clusters.