Thin-stratified medium fast-multipole algorithm for solving microstrip structures

Jun Sheng Zhao, Weng Cho Chew, Cai Cheng Lu, Eric Michielssen, Jiming Song

Research output: Contribution to journalArticlepeer-review

88 Scopus citations


An accurate and efficient technique called the thinstratified medium fast-multipole algorithm (TSM-FMA) is presented for solving integral equations pertinent to electromagnetic analysis of microstrip structures, which consists of the fullwave analysis method and the application of the multilevel fast multipole algorithm (MLFMA) to thin stratified structures. In this approach, a new form of the electric-field spatial-domain Green's function is developed in a symmetrical form which simplifies the discretization of the integral equation using the method of moments (MoM). The patch may be of arbitrary shape since their equivalent electric currents are modeled with subdomain triangular patch basis functions. TSM-FMA is introduced to speed up the matrix-vector multiplication which constitutes the major computational cost in the application of the conjugate gradient (CG) method. TSM-FMA reduces the central processing unit (CPU) time per iteration to O(Nlog N) for sparse structures and to O(N) for dense structures, from O(N3) for the Gaussian elimination method and O(N2) per iteration for the CG method. The memory requirement for TSM-FMA also scales as O(NlogN) for sparse structures and as O(N) for dense structures. Therefore, this approach is suitable for solving large-scale problems on a small computer.

Original languageEnglish
Pages (from-to)395-403
Number of pages9
JournalIEEE Transactions on Microwave Theory and Techniques
Issue number4
StatePublished - 1998

Bibliographical note

Funding Information:
Manuscript received June 17, 1997; revised October 13, 1997. This work was supported by Air Force Office of Scientific Research under MURI Grant F49620-96-1-0025, by the Office of Naval Research under Grant N00014-95-1-0872, and by the National Science Foundation (NSF) under Grant NSF ECS93-02145.


  • Fast multipole
  • Integral equation
  • Method of moments
  • Microstrip
  • Multilevel algorithm

ASJC Scopus subject areas

  • Radiation
  • Condensed Matter Physics
  • Electrical and Electronic Engineering


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