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Volume Integral Equations (VIEs) are indispensable for electromagnetic (EM) analysis by integral equation approach when inhomogeneous penetrable objects are involved. In the conventional method of moment (MoM) for solving the VIEs, unknown functions are expanded by a well-designed basis function like Schaubert-Wilton-Glisson (SWG) basis function, and a tedious testing procedure is required to transform...
The fast multipole algorithm (FMA) has been thought of as one of top ten algorithms in science and engineering in the 20th century and its multilevel variant (MLFMA) was first proposed in electromagnetics. The memory usage and CPU time for solving a dense matrix equation iteratively are of O(N2) complexity, where N is the number of unknowns, and this cost usually prevents one from solving large-scale...
In the meshless scheme for solving volume integral equations (VIEs), one needs to evaluate hypersingular integrals over a small cylindrical domain excluded from the whole domain for the sake of regularizing integrands. Those integrals can be evaluated semi-numerically but the implementation may not be convenient. In this work, we present some new formulas which are purely analytical for those integrals...
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