A fast algorithm for multiscale electromagnetic problems using interpolative decomposition and multilevel fast multipole algorithm

Abstract

.[1] The interpolative decomposition (ID) is combined with the multilevel fast multipole algorithm (MLFMA), denoted by ID-MLFMA, to handle multiscale problems. The ID-MLFMA first generates ID levels by recursively dividing the boxes at the finest MLFMA level into smaller boxes. It is specifically shown that near-field interactions with respect to the MLFMA, in the form of the matrix vector multiplication (MVM), are efficiently approximated at the ID levels. Meanwhile, computations on far-field interactions at the MLFMA levels remain unchanged. Only a small portion of matrix entries are required to approximate coupling among well-separated boxes at the ID levels, and these submatrices can be filled without computing the complete original coupling matrix. It follows that the matrix filling in the ID-MLFMA becomes much less expensive. The memory consumed is thus greatly reduced and the MVM is accelerated as well. Several factors that may influence the accuracy, efficiency and reliability of the proposed ID-MLFMA are investigated by numerical experiments. Complex targets are calculated to demonstrate the capability of the ID-MLFMA algorithm.Citation: Pan, X.-M., J.-G. Wei, Z. Peng, and X.-Q. Sheng (2012), A fast algorithm for multiscale electromagnetic problems using interpolative decomposition and multilevel fast multipole algorithm, Radio Sci., 47, RS1011,

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

“…It requires that the surface currents in each independent subdomain be radiated to all other subdomains. The computation is accomplished with two mathematical ingredients: (i) a hierarchical multi-level fast multipole method (H-MLFMM) [49,50], which leads to the seamless integration of multi-level skeletonization technique [51] into the FMM framework and results in an effective matrix compression for non-uniform DG discretizations; (ii) a primal-dual octree partitioning algorithm for separable subdomain coupling [52]. Namely, instead of partitioning the entire computational domain into a single octree as in the traditional FMM, we have created independent octrees for all subdomains.…”

Hierarchical Interpolative Decomposition Multilevel Fast Multipole Algorithm for Dynamic Electromagnetic Simulations

“…The methods involving multipole expansions of Green's functions [2] show bad convergence behavior at low frequencies. In ID-MLFMA [13], these problems can be eliminated by the skeletonization approximation [14,15]. In SVD/QR based methods [16], the original basis functions are linearly combined in the approximation.…”

“…Many efforts have been reported [10][11][12][13] (and references therein) to solve this problem. As pointed out in [10], the methods based on the evanescent wave expansion [11] or diagonalizations [12] require extra computational effort for evaluating the according translation operators with respect to the original MLFMA.…”

Localized Pseudo-Skeleton Approximation Method for Electromagnetic Analysis on Electrically Large Objects

“…The algorithm fills the rows and columns iteratively until the convergence of the approximate relative error. Recently, skeleton based techniques have been investigated deeply [4][5][6][7][8] which try to seek the dominant elements to represent the original obese couplings. Among them, Randomised pseudo-skeleton approximation (RPSA) [7] is based on the PSA [8] of the matrix.…”