Dimensional reduction for Helmholtz's equation on an unbounded domain

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Abstract

The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain Ωd := ℝn x (-d, d) by replacing them with systems of equations in ℝn are investigated. Basic tool to analyze dimensional reduction technique for problems on an unbounded domain Ωd is the use of Fourier transformation. The error estimates between the exact solution and the dimensionally reduced solution in some Hilbert space are obtained when d and N are given. The rates of convergence depend on the smoothness of the data on the faces.

Original languageEnglish
Pages (from-to)81-111
Number of pages31
JournalMathematical Models and Methods in Applied Sciences
Volume7
Issue number1
DOIs
Publication statusPublished - 1997 Feb

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

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