Parallel Hierarchical Matrices with Adaptive Cross Approximation on Symmetric Multiprocessing Clusters

Abstract

We discuss a scheme for hierarchical matrices with adaptive cross approximation on symmetric multiprocessing clusters. We propose a set of parallel algorithms that are applicable to hierarchical matrices. The proposed algorithms are implemented using the flat-MPIand hybrid MPI+OpenMP programming models. The performance of these implementations is evaluated using an electric field analysis computed on two symmetric multiprocessing cluster systems. Although the flat-MPI version gives better parallel scalability when constructing hierarchical matrices, the speed-up reaches a limit in the hierarchical matrix-vector multiplication. We succeeded in developing a hybrid MPI+OpenMP version to improve the parallel scalability. In numerical experiments, the hybrid version exhibits a better parallel speed-up for the hierarchical matrix-vector multiplication up to 256 cores.