On Openmp Parallelization of the Multilevel Fast Multipole Algorithm

Abstract

Abstract-Compared with MPI, OpenMP provides us an easy way to parallelize the multilevel fast multipole algorithm (MLFMA) on shared-memory systems. However, the implementation of OpenMP parallelization has many pitfalls because different parts of MLFMA have distinct numerical characteristics due to its complicated algorithm structure. These pitfalls often cause very low efficiency, especially when many threads are employed. Through an in-depth investigation on these pitfalls with analysis and numerical experiments, we propose an efficient OpenMP parallel MLFMA. Two strategies are proposed in the parallelization, including: 1) loop reorganization for far-field interaction in the MLFMA; 2) determination of a transition level. Numerical experiments on large scale targets show the proposed OpenMP parallel scheme can perform as efficiently as the MPI counterpart, and much more efficiently than the straightforward OpenMP parallel one.

A Comparison Between Pml, Infinite Elements and an Iterative Bem as Mesh Truncation Methods for Hp Self-Adaptive Procedures in Electromagnetics

“…However, the overhead of FE-IIEE corresponding to the brute-force accurate evaluation of the convolutional type operation of (5) (and its analogous for the normal derivative) is reflected as a shift of the FE-IIEE line towards larger computational times. Although the development of an efficient implementation of an acceleration technique (as FMM (Fast Multipole Method [44][45][46]) or ACA (Adaptive Cross Approximation [47]) using the hierarchy of the meshes (tree type data structures) is out of the scope of this paper, an estimation of the performance of FE-IIEE with an acceleration technique has been included. It corresponds to the line labeled as "FE-IIEE (fast)".…”

Parallel Shooting and Bouncing Ray Method on Gpu Clusters for Analysis of Electromagnetic Scattering

“…Previous parallel algorithms (e.g., parallel FDTD [10,11], parallel direct solver [12] and parallel MLFMM [13,14]) were mainly implemented on CPU clusters. Due to the high performance/cost ratio and the fast performance growth of GPUs, GPU clusters are becoming more and more popular.…”

Hierarchical Interpolative Decomposition Multilevel Fast Multipole Algorithm for Dynamic Electromagnetic Simulations

“…The finest ID level is the 6-th level. Z (6) NFI consumes 453 MB memory, while S (i) matrices at all ID levels require over 8.5 GB memory in total. The ID skeletonization approximation reduces the memory requirement by a factor of 6.0.…”

“…The computational complexity of MoM is O(N 3 ) for a conventional direct solver in terms of CPU time, such as LU, and O(mN 2 ) for an iterative algorithm, where N is the number of unknowns and m the iteration count. Consequently, rather than direct solvers, iterative ones in combination with some fast algorithms [1][2][3][4][5][6][7][8][9] are more popular in solving MoM systems. Most of these fast algorithms decompose interactions in MoM systems into near-field interactions (NFIs) and far-field interactions (FFIs), and then approximate FFIs in some efficient way.…”