Integral-Equation Based Fast Solvers developed for microwave and RF applications

Integral-Equation Based Fast Solvers have been developed with a lot of efforts and emphases. There are a few kinds of algorithms originally developed and widely applied to many engineering problems, and they includes the fast multipole method (FMM) and its multi-level fast multipole algorithm (MLFMA); conjugate-gradient fast Foriour transform (CG-FFT) method; adaptive integral method (AIM), and the precorrcted fast Foriour transform (pFFT) method. In this talk, the emphasis will be focused on the development and extension of the adaptive integral method (AIM), and the precorrcted fast Foriour transform (pFFT) method and also their applications to the antenna designs and also the microwave circuit designs. The combined field integral equations (CFIEs) consisting of the electric field integral equations (EFIEs) and magnetic field integral equations (MFIEs) were formulated and applied to some specific examples. The surface intgral equation (SIE), volume integral equation (VIE), and also the hybrid volume-surface integral equations (VSIE) were formulated as well. It will also case-show some results obtained using the method of moments for solving the above equations and accelerated using the AIM and pFFT method. Demonstrations of these approaches will be made on characterizing various electromagnetic and microwave problems consisting of metallic objects, homogenueous and inhomogenueous materials, and homogenueous composite materials (such as chiral, anisotropic, and bi-ansotropic media). Efficiency, accuracy, and also computational complexity and expenses (such as the memory and CPU time requirements) will be also shown.