Parallel Stabilized Mixed Galerkin Method for Three-Dimensional Darcy Flow using OpenMP

This paper presents a parallel stabilized mixed Galerkin method for three-dimensional steady-state Darcy flow using OpenMP for shared memory architecture. In finite element problems, the computational complexity increases with increasing number of elements needed for large and complex geometry. Shared memory architecture offers a platform for solving such large and complex problems for practical applications. In parallel solvers, the mesh reordering has proved to be an important preprocessing operation to enhance performance. The objective of this study is to compare the performance of octree-based mesh reordering with multilevel-based reordering in the parallel solution. The reported results include execution time, speedup and efficiency of the solution using hexahedral and tetrahedral meshes of various sizes. The numerical results suggest that the octree-based mesh reordering outperforms multilevel-based method with tetrahedral meshes.