## Novel surface-volume-surface electric field integral equations for electromagnetic analysis of 3-D metal-dielectric objects and H-matrix strategies for their fast direct solution

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##### Date

2019-12-11

##### Authors

Gholami, Reza

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##### Abstract

The hierarchical (H)-matrix acceleration method plays important role in electromagnetic analysis of large-scale problems. This thesis is about fast direct solution of 3-D
full-wave scattering and radiation problems with H-matrix acceleration of the method
of moments (MoM) for the novel surface-volume-surface electric field integral equation (SVS-EFIE) and the Locally Corrected Nystrom (LCN) method for traditional magnetic field integral equation (MFIE). Two new formulations of the SVS-EFIE are proposed. First, new SVS-EFIE formulation is developed for the scattering and radiation problems on metal-dielectric composite objects with arbitrary number of regions situated in free space. Second, new SVS-EFIE formulation is developed for scattering and radiation problems on dielectric-dielectric composite objects situated in multilayered medium. The proposed SVS-EFIE formulations introduce independent surface electric current density on the boundary of each region. Thus, in the new formulations, the scatterer regions can be meshed independently according to their local material properties. This improves the flexibility and efficiency of the proposed formulations in the analysis of both multiscale and large-scale composite structures. An H-matrix based fast direct solution strategies are proposed for acceleration of the MoM solution of the new SVS-EFIE formulations. The method is largely insensitive to the poor conditioning of the MoM matrix equation. The required theory for applying H-matrices to the new formulations as well as the construction of the block H-matrices pertinent to MoM discretization of the composite SVS-EFIE is described in detail. Numerical validation shows that the proposed methods have a wide-range of applications and generate accurate results using only the small fraction of memory and total CPU time needed by conventional MoM solution of the SVS-EFIE.
Fast error-controlled direct solution of the traditional integral equations for scattering problems on metal objects with H-matrices is also pioneered in this work. The proposed strategy for acceleration of the higher-order LCN method with H-matrices exhibits O(h^p) error behavior in the fast direct solution of the scattering problems on smooth metal objects with characteristic mesh elements size h and order of solution approximation p.

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##### Keywords

Electromagnetics, Integral Equations, Computational Electromagnetics, Numerical Analysis, Fast Algorithms, Method of Moments, Boundary Element Method, Electromagnetic Analysis, Multilayered Media, Single source integral equations, Composite objects, Higher-Order, high-order solution, Error controllable solution