A Quasi-3D Thin-Stratified Medium Fast-Multipole Algorithm for Microstrip Structures

Abstract

An accurate and efficient full-wave simulation method is proposed for general microstrip structures. It is called the quasi-3D thin-stratified medium fast-multipole algorithm (TSM-FMA). Different from the 2D TSM-FMA method, it is constructed on a vector wave function based dyadic Green's function for layered medium (DGLM) instead of the symmetric form DGLM. This new form of DGLM is represented in terms of only two Sommerfeld integrals and is suitable for developing fast algorithm in quasi-3D cases. Similar to the 2D TSM-FMA, the path deformation technique and the multipole-based acceleration is used to transform the Sommerfeld integral and expedite the matrix-vector multiplication. The computational time per iteration and the memory requirement is <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> log <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ) in the quasi-3D TSM-FMA. It is suitable to perform a full-wave analysis of a large microstrip array with less computational resource.