Dimensional reduction for Helmholtz's equation on a bounded domain

Kang-Man Liu, Ivo Babuška

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5 Citations (Scopus)

Abstract

The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain Ωd := Ω x (-d , d) ⊂ ℝn+1 by replacing them with systems of equations in n-dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution u and the dimensionally reduced solution uN of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference between u and uN in H1d) is estimated as d and N are fixed. Finally, some numerical experiments in a domain Ω = (0, 1) x (0, 1) are given in order to compare theretical results.

Original languageEnglish
Pages (from-to)501-533
Number of pages33
JournalNumerische Mathematik
Volume77
Issue number4
DOIs
Publication statusPublished - 1997 Jan 1

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All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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