FMM/GPU-Accelerated Boundary Element Method for Computational Magnetics and Electrostatics

Highly parallel boundary element method for solving extremely large, wide-area power-line models

“…This linear system can be solved by conventional matrix decompositions, but this will be incredibly slow for even moderately sized problems because the required computation time scales cubically with N . Instead, we use the solvers previously developed in Adelman et al (2017), which use GMRES (Saad and Schultz, 1986) to solve the linear system, and the fast multipole method (FMM) (Greengard and Rokhlin, 1987) and GPU to accelerate the matrix-vector product that is computed during each iteration. These solvers scale linearly, and can solve problems with up to 10 million elements on a single workstation with 128 GB of memory.…”

“…The evaluation phase is when the solution is computed at the evaluation points. These three phases are present in the single-node version of the code in Adelman et al (2017) as well as the multi-node version described in this paper. In fact, many of the results in this paper have been broken down and shown for each phase separately.…”

“…All other components stayed entirely on the CPU (and used all 40 available cores). As a result, turning the GPU on had less effect on the multi-node solver than on the single-node solver, which generally sees a much bigger boost of around 200–300% (Adelman et al, 2017). However, even this modest improvement increases the efficiency from 88.2% with the GPU turned off to 108.2% with the GPU turned on, indicating that the GPU can counteract the performance penalty from decomposing the domain into more subdomains.…”

“…We previously developed fast multipole method (FMM)/GPU-accelerated BEM software for computational magnetics and electrostatics (Adelman et al, 2017). Our software uses the correction factor matrix method, which approximates the boundary integrals in the BEM using a quadrature.…”

Optimizations of a fast multipole symmetric Galerkin boundary element method code

“…Parallel computing techniques can significantly increase the performance of existing serial codes. Many researchers have used parallelization to accelerate the BEM (see for example [1,11,12,16]). In this work, a parallel implementation of the code presented by Trinh [25] is achieved.…”