Distributed fast boundary element methods for Helmholtz problems

A parallel space–time boundary element method for the heat equation

“…The solver is parallelized using MPI in the distributed memory. The distribution of the system matrices is based on [5,8,9]. The space-time boundary mesh is decomposed into time slices which define blocks in the system matrices.…”

“…, G P−1 . In [5,8] we employ a cyclic decomposition algorithm -first, a generator graph G 0 on a minimal number of vertices (corresponding to blocks to be assembled by the process 0) is constructed; the remaining graphs G 1 , . .…”

“…We present a parallelization technique which is based on a decomposition of the input mesh into submeshes and a distribution of the corresponding blocks of the system matrices among processors. To ensure load balancing, the distribution is based on a cyclic decomposition of complete graphs [8,9]. In addition, the solution of the global linear system requires an efficient preconditioner.…”

Parallel Adaptive Cross Approximation for the Multi-trace Formulation of Scattering Problems

“…The parallelization of the method based on the cyclic graph decomposition was presented in [13] where only certain special numbers of processors were discussed. In [12] we further extended the approach to support general number of processors. In the following section we recollect its basic principle and extend it to support the solution of MTF systems.…”

“…In Sect. 3 we propose a strategy to parallelize the assembly of the MTF matrix blocks and their application in an iterative solver based on the approach presented in [11][12][13] for single domain problems. Except for the distributed parallelism, the method takes full advantage of the BEM4I library [14,20,21] and its assemblers parallelized in shared memory and vectorized by OpenMP.…”