Соловьев С.А.  

Parallel implementation of the multifrontal hierarchically semi-separable solver for 3D Helmholtz problem

This paper presents a parallel implementation of the multifrontal sparse solver to solve 3D Helmholtz problem. It is based on Gauss-elimination direct solver coupled with Nested Dissection reordering approach and compressing factors by using low-rank approximation technique and HSS format.   Proposed algorithm is dedicated for on distributed memory systems using hybrid OpenMP and MPI features. OpenMP parallelization is performed due to optimized BLAS and LAPACK functions. MPI parallelization is based on distributing nodes of elimination tree between cluster nodes. While performing factorization process there are two types of cluster nodes: the first ones save factorized data and send them by request to other nodes for computing Schur complement; the other group of cluster nodes perform factorization. Proposed scheme is memory effective and can solve problems provided that compressed LDL^t-factors fit total clusters RAM (CRAM).  The MPI-scalability of proposed scheme depends on the size of factors relative to the size of CRAM and increases with increasing number of cluster nodes.
The project has been partially supported by grants 14-01-31340, 14-05-31222, 14-05-00049, 14-05-93090.

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