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

Iterative solution of large-scale scattering problems in computational electromagnetics with the multilevel fast multipole algorithm (MLFMA) requires strong preconditioners, especially for the electric-field integral equation (EFIE) formulation. Incomplete LU (ILU) preconditioners are widely used and available in several solver packages. However, they lack robustness due to potential instability problems. In this study, we consider various ILU-class preconditioners and investigate the parameters that render them safely applicable to common surface integral formulations without increasing the O(n log n) complexity of MLFMA. We conclude that the no-fill ILU(0) preconditioner is an optimal choice for the combined-field integral equation (CFIE). For EFIE, we establish the need to resort to methods depending on drop tolerance and apply pivoting for problems with high condition estimate. We propose a strategy for the selection of the parameters so that the preconditioner can be used as a black-box method. Robustness and efficiency of the employed preconditioners are demonstrated over several test problems. Introduction.A popular approach in studying wave scattering phenomena in computational electromagnetics (CEM) is to solve discretized surface integral equations, which give rise to large, dense, complex systems in the form of A · x = b. Two kinds of surface integral equations are commonly used. The electric-field integral equation (EFIE) can be used for both open and closed geometries, but it results in poorly conditioned systems, especially when the geometry is large in terms of the wavelength. On the other hand, the combined-field integral equation (CFIE) produces well-conditioned systems, but it is applicable to closed geometries only [21].For the solution of such dense systems, direct methods based on Gaussian elimination are still widely used due to their robustness [34]. However, the large problem sizes confronted in computational electromagnetics prohibit the use of these methods which have O(n 2 ) memory and O(n 3 ) computational complexity for n unknowns. On the other hand, by making use of the multilevel fast multipole algorithm (MLFMA) [12], the dense matrix-vector products required at least once in each step of the iterative solvers can be performed in O(n log n) time and by storing only the sparse near-field matrix elements, rendering these solvers very attractive for large problems.However, the iterative solver may not converge, or convergence may require too many iterations. We need to have a suitable preconditioner to reach convergence in

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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.