A VIE-based algebraic domain decomposition for analyzing electromagnetic scattering from inhomogeneous isotropy/anisotropy dielectric objects

A VIE-based domain decomposition method (DDM) is proposed for analyzing EM scattering from inhomogeneous electrically large dielectric objects. The volume integral equation (VIE) still uses tetrahedra to model the entire body and uses the SWG basis functions to expand the equivalent electric flux density. This new DDM is established by dividing the unknowns on the whole electrically large body into groups, serving as subdomains. Through necessary symmetry treatment of standard MoM impedance matrix, the DDM using subdomain-decoupling technology can be combined with the VIE model to reduce memory requirement. Actually, this is an algebraic DDM, not a geometric DDM. In other words, it has no requirement of physical location of basis functions belonging to the same subdomain. This decoupling procedure is completely eliminating the coupling impact of the primary subdomain with the rest of the dielectric body, until every subdomain is independent with each other. In this work, when solving ultimate decoupled impedance subdomain matrix, the LU decomposition process for solving interpolating coefficients of multiple right sides is accelerated by GPU parallel technology to significantly decrease CPU time. In brief, this paper first time combines the algebraic DDM with the conventional VIE model (including both isotropy and anisotropy VIE model) to significantly decrease the requirement of memory. At last, a few representative numerical examples are provided to demonstrate validity, efficiency and stability of the new method.