Utilization of wavelet concepts in finite elements for an efficient solution of Maxwell's equations

Tapan K. Sarkar, Raviraj S. Adve, Luis Emilio García‐Castillo, Magdalena Salazar‐Palma

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

The principles of dilation and shift are two important properties that are attributed to wavelets. It is shown that inclusion of such properties in the choice of a basis in Galerkin's method can lead to a slow growth of the condition number of the system matrix obtained from the discretization of the differential form of Maxwell's equations. It is shown that for one‐dimensional problems the system matrix can be diagonalized. For two‐dimensional problems, however, the system matrix can be made mostly diagonal. This paper illustrates the application of the new type of “dilated” basis for a Galerkin's method (or equivalent, for example, finite element method) for the efficient solution of waveguide problems. Typical numerical results are presented to illustrate the concepts.

Original languageEnglish (US)
Pages (from-to)965-977
Number of pages13
JournalRadio Science
Volume29
Issue number4
DOIs
StatePublished - Jan 1 1994

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Earth and Planetary Sciences(all)
  • Electrical and Electronic Engineering

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