Performance analysis of parallel stabilized mixed Galerkin method for three-dimensional transient Darcy flow using mesh reordering techniques

Abstract

This study is related to parallel stabilized mixed Galerkin method for 3-D transient flow through porous media using OpenMP specifications for shared type memory architectures. The stabilized mixed Galerkin formulation employs standard finite elements and first-order backward difference for transient analysis. The computational complexity of the finite element method increases by increasing the number of elements requisite for large and complicated systems specifically for petroleum crude reservoirs, which leads to a large number of data elements for high performance. The shared memory architecture provides a platform for solving such difficult and big problems of new areas. In parallel finite element methods, the mesh reorganizing/partitioning is considered to be a significant preprocessing process to improve efficiency. The focus of the present case-study is to analyze the performances of octree-based and multilevel-based mesh reordering techniques. The analysis is carried out by running the parallel Darcy flow algorithms on AMD Opteron processors using tetrahedral and hexahedral meshes. The performance of the algorithm is estimated by computing the respective execution time, running time and algorithm efficiency. Major findings of this study are: (1) the octree-based mesh reordering outclasses multilevel graph-based method by at least 200% in terms of execution time, (2) the hexahedral meshes which are structured meshes show better scalability as compared to the tetrahedral meshes by a factor of 5, and (3) finally, octree mesh reordering demonstrates poor scalability in multithreaded environment as compared to multilevel graph partitioning method due to O(P2) overhead.