Computational electromagnetics: The physics of smooth versus oscillatory fields

W. C. Chew

Research output: Contribution to journalArticle

Abstract

This paper starts by discussing the difference in the physics between solutions to Laplace's equation (static) and Maxwell's equations for dynamic problems (Helmholtz equation). Their differing physical characters are illustrated by how the two fields convey information away from their source point. The paper elucidates the fact that their differing physical characters affect the use of Laplacian field and Helmholtz field in imaging. They also affect the design of fast computational algorithms for electromagnetic scattering problems. Specifically, a comparison is made between fast algorithms developed using wavelets, the simple fast multipole method, and the multi-level fast multipole algorithm for electrodynamics. The impact of the physical characters of the dynamic field on the parallelization of the multi-level fast multipole algorithm is also discussed. The relationship of diagonalization of translators to group theory is presented. Finally, future areas of research for computational electromagnetics are described.

Original languageEnglish (US)
Pages (from-to)579-602
Number of pages24
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume362
Issue number1816
DOIs
StatePublished - Mar 15 2004

Keywords

  • Electromagnetics
  • Fast multipole method
  • Helmholtz problem
  • Integral equation
  • Laplace problem
  • Parallelization

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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