We consider fast and accurate solutions of scattering problems involving increasingly large dielectric objects formulated by surface integral equations. We compare various formulations when the objects are discretized with Rao-Wilton-Glisson functions, and the resulting matrix equations are solved iteratively by employing the multilevel fast multipole algorithm (MLFMA). For large problems, we show that a combined-field formulation, namely, the electric and magnetic current combined-field integral equation (JMCFIE), requires fewer iterations than other formulations within the context of MLFMA. In addition to its efficiency, JMCFIE is also more accurate than the normal formulations and becomes preferable, especially when the problems cannot be solved easily with the tangential formulations.Index Terms-Dielectrics, iterative solutions, multilevel fast multipole algorithm (MLFMA), surface integral equations.
Cataloged from PDF version of article.We present a novel hierarchical partitioning strategy\ud
for the efficient parallelization of the multilevel fast multipole algorithm\ud
(MLFMA) on distributed-memory architectures to solve\ud
large-scale problems in electromagnetics. Unlike previous parallelization\ud
techniques, the tree structure of MLFMA is distributed\ud
among processors by partitioning both clusters and samples\ud
of fields at each level. Due to the improved load-balancing, the\ud
hierarchical strategy offers a higher parallelization efficiency than\ud
previous approaches, especially when the number of processors\ud
is large. We demonstrate the improved efficiency on scattering\ud
problems discretized with millions of unknowns. In addition, we\ud
present the effectiveness of our algorithm by solving very large\ud
scattering problems involving a conducting sphere of radius 210\ud
wavelengths and a complicated real-life target with a maximum\ud
dimension of 880 wavelengths. Both of the objects are discretized\ud
with more than 200 million unknowns
We present fast and accurate solutions of large-scale scattering problems involving three-dimensional closed conductors with arbitrary shapes using the multilevel fast multipole algorithm (MLFMA). With an efficient parallelization of MLFMA, scattering problems that are discretized with tens of millions of unknowns are easily solved on a cluster of computers. We extensively investigate the parallelization of MLFMA, identify the bottlenecks, and provide remedial procedures to improve the efficiency of the implementations. The accuracy of the solutions is demonstrated on a scattering problem involving a sphere of radius 110 discretized with 41 883 638 unknowns, the largest integral-equation problem solved to date. In addition to canonical problems, we also present the solution of real-life problems involving complicated targets with large dimensions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.