In this paper we compare different parallel implementations of the same algorithm for solving nonlinear simulation problems on unstructured meshes. In the first implementation, making use of the message-passing programming model and the PVM system, the domain decomposition of unstructured mesh is implemented, while the second implementation takes advantage of the inherent parallelism of the algorithm by adopting the shared-memory programming model. Both implementations are applied to the preconditioned GMRES method that solves iteratively the system of linear equations. A combined approach, the hybrid programming model suitable for multicomputers with SMP nodes, is introduced. For performance measurements we use compressible fluid flow simulation in which sequences of finite element solutions form time approximations to the Euler equations. The tests are performed on HP SPP1600, HP S2000 and SGI Origin2000 multiprocessors and report wall-clock execution time and speedup for different number of processing nodes and for different meshes. Experimentally, the explicit programming model proves to be more efficient than the implicit model by 20—70%, depends on the mesh and the machine.
Solving an Ill-Posed Cauchy Problem for a Two-Dimensional Parabolic PDE with Variable Coefficients Using a Preconditioned GMRES Method
