PIE-MLFMA Implementation for Solving Complex Subwavelength Electromagnetic Problems

Gur, Ugur Meric
Cetin, Isa Can
Karaosmanoglu, Bariscan
Ergül, Özgür Salih
We present stable solutions of low-frequency electromagnetic problems involving small objects and their dense discretizations with respect to wavelength. Recently developed potential integral equations (PIEs), which are based on the boundary conditions for the magnetic vector potential and the electric scalar potential, are used to formulate complex problems. A multilevel fast multipole algorithm (MLFMA) based on scaled plane waves for stable computations of short-distance interactions is further employed to achieve fast iterative solutions. The accuracy and stability of the developed PIE-MLFMA implementation are demonstrated on complex subwavelength structures.


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We present fast and accurate solutions of large-scale electromagnetics problems involving three-dimensional homogeneous dielectric objects. Problems are formulated rigorously with the electric and magnetic current combined-field integral equation (JMCFIE) and solved iteratively with the multilevel fast multipole algorithm (MLFMA). In order to solve large-scale problems, MLFMA is parallelized efficiently on distributed-memory architectures using the hierarchical partitioning strategy. Efficiency and accuracy...
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We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving closed conductors. We consider the solutions of relatively large scattering problems by employing the multilevel fast multipole algorithm. Accuracy problems of MFIE and CFIE arising from their implementations with the conventional Rao-Wilton-Glisson (RWG) basis functions can...
Citation Formats
U. M. Gur, I. C. Cetin, B. Karaosmanoglu, and Ö. S. Ergül, “PIE-MLFMA Implementation for Solving Complex Subwavelength Electromagnetic Problems,” 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36191.