VIE-ODDM-FFT Method Using Nested Uniform Cartesian Grid for the Analysis of Electrically Large Inhomogeneous Dielectric Objects

A hybrid method of the volume integral equation-based overlapping domain decomposition method and the fast Fourier transform (FFT)-based method (VIE-ODDM-FFT) using nested uniform Cartesian grid is proposed for the analysis of electrically large inhomogeneous dielectric objects whose usual fast algorithm models are too large for the user's computer to accommodate. The integral equation is first built in the entire volumetric domain, and then the entire volumetric domain is partitioned into some nonoverlapping geometric subdomains. The SWG basis functions are used to expand the equivalent electric flux density in the entire domain. Then, several concepts such as basic subdomain, extended region, and complementary region are introduced. The subproblem in an extended region is quickly solved by using the FFT-based method with DILU preconditioner, and the action of the complementary region of an extended region on this extended region itself is quickly calculated by means of FFT. In this scheme, FFT acceleration is achieved by fitting Green's function (FG) onto the nodes of one or more nested uniform Cartesian grid. The convergence of the outer iterative scheme of the proposed VIE-ODDM is investigated theoretically and numerically, and demonstrated to be very good and, hence, a very large problem can be effectively solved in an ordinary computer. Some numerical examples are provided to demonstrate the correctness, robustness, and efficiency of the proposed method.