A Mixed-Form Thin-Stratified Medium Fast-Multipole Algorithm for Both Low and Mid-Frequency Problems

• Published in: IEEE transactions on antennas and propagation Vol. 59; no. 6; pp. 2341 - 2349
• Main Authors: Chen, Y P, Xiong, J L, Weng Cho Chew
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Addition theorem; Algorithms; Antenna radiation patterns; Antennas; Applied classical electromagnetism; Computer simulation; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Exact sciences and technology; Fast multipole algorithm; Fundamental areas of phenomenology (including applications); Green's function methods; Heuristic algorithms; layered medium; Microstrip; Microstrip antenna arrays; mixed form; Multilevel; multipole expansion; Multipoles; Physics; plane wave expansion; Plane waves; Switches; Wave physics; Microstrip lines; Quasi static theory; Two dimensional model; multipole expansion; Fast multipole algorithm; Low frequency; Green function; Implementation; Stratified medium; layered medium; Matrix multiplication; Simulation; Plane waves; Computational electromagnetics; mixed form; plane wave expansion; Fast algorithm; Multilevel system
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2011.2143675

A mixed-form thin-stratified medium fast-multipole algorithm is proposed for fast simulation of general microstrip structures at both low and mid-frequencies. The newly developed matrix-friendly formula of layered medium Green's function is applied in this algorithm. For well-separated interactions, the path deformation technique is implemented to achieve a smoother and exponentially convergent integral. The two-dimensional addition theorem is then incorporated into the integrand to expedite the matrix-vector product. In our approach, multipole expansion (low-frequency fast-multiple algorithm) as well as the plane wave expansion (mid-frequency fast-multipole algorithm) of the translational addition theorem are combined into a single multilevel tree to capture quasi-static physics and wave physics simultaneously. The outgoing wave is represented first in terms of multipole expansion at leafy levels, and then switched to plane wave expansion automatically at higher levels. This seamless connection makes the algorithm applicable in simulations, where subwavelength interaction and wave physics both exist.