Dimensional reduction for Helmholtz's equation on an unbounded domain

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 Jan 1

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Helmholtz equation
Dimensional Reduction
Helmholtz Equation
Unbounded Domain
Fourier Transformation
Hilbert spaces
Reduction Method
Boundary value problems
System of equations
Error Estimates
Smoothness
Rate of Convergence
Exact Solution
Hilbert space
Boundary Value Problem
Face

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

Cite this

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Dimensional reduction for Helmholtz's equation on an unbounded domain. / Liu, Kang-Man.

In: Mathematical Models and Methods in Applied Sciences, Vol. 7, No. 1, 01.01.1997, p. 81-111.

Research output: Contribution to journalArticle

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