Supercomputer Aware Approach for the Solution of Challenging Electromagnetic Problems

Abstract

Abstract-It is a proven fact that The Fast Fourier Transform (FFT) extension of the conventional Fast Multipole Method (FMM) reduces the matrix vector product (MVP) complexity and preserves the propensity for parallel scaling of the single level FMM. In this paper, an efficient parallel strategy of a nested variation of the FMM-FFT algorithm that reduces the memory requirements is presented. The solution provided by this parallel implementation for a challenging problem with more than 0.5 billion unknowns has constituted the world record in computational electromagnetics (CEM) at the beginning of 2009.

Mlfma-FFT Parallel Algorithm for the Solution of Large-Scale Problems in Electromagnetics

“…The difficulties faced in successfully parallelizing it in computer clusters have been widely discussed by many research groups [8,10,14,15]. Considering the favorable MLFMA features in shared-memory computers, and taking into account the high scalability behavior of the FMM-FFT in distributed computers while maintaining a low numerical complexity, a proper combination of both techniques seems to be a good alternative to take a step further after the works of [19] and [22]. The MLFMA-FFT presented here combines both methods to get an optimal scheme from the point of view of modern mixed-memory supercomputers.…”

“…Later on, we have proposed the Nested FMM-FFT [22] to further reduce the memory consumption. From one or more refinement steps of the hierarchical oct-tree decomposition, the nested scheme is applied to the near field interactions in the MVP, which are obtained at the finest oct-tree level by using one or more local shared-memory FMM-FFT algorithms inside each computing node.…”

“…A problem with more than a half billion unknowns has been solved using the Nested FMM-FFT algorithm. The main aspects of the parallelization strategy considered for the algorithm in [22] are recalled here: (i) A mixed distribution for the far-field interactions is applied, by groups at the finest level and by k-space samples at the coarsest one. (ii) A wellbalanced load distribution by groups is considered for the near-field interactions at the finest level.…”

“…This method has demonstrated to be a good alternative to benefit from massively parallel distributed computers [19]. Recently, a hybrid Message Passing Interface (MPI)/OpenMP parallel implementation of a nested scheme of the FMM-FFT was proposed by the authors in [20][21][22]. In contrast with the conventional FMM-FFT, it shows a slightly worse parallel performance but in exchange for lower memory consumption.…”

Fast Antenna Characterization Using the Sources Reconstruction Method on Graphics Processors

“…Parallel computing applied to solving electromagnetic problems is broadly spread [6,27,32]. Among the growing number of parallel hardware, the Graphics Processing Units (GPUs) may be considered the most outstanding architecture, since they offer massive computing capabilities and they are widely deployed.…”