An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

B. Tomas Johansson, Vladimir A. Kozlov

Research output: Contribution to journalArticle

Abstract

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.
Original languageEnglish
Pages (from-to)62-73
Number of pages12
JournalIMA Journal of Applied Mathematics
Volume74
Issue number1
Early online date3 Jul 2008
DOIs
Publication statusPublished - 2009

Fingerprint

Hermann Von Helmholtz
Cauchy Problem
Adjoint System
Operator
Iterative methods
Elliptic Operator
Algebra
Iteration
Requirements

Keywords

  • Cauchy problem
  • Helmholtz equation

Cite this

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abstract = "Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.",
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An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium. / Johansson, B. Tomas; Kozlov, Vladimir A.

In: IMA Journal of Applied Mathematics, Vol. 74, No. 1, 2009, p. 62-73.

Research output: Contribution to journalArticle

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AU - Johansson, B. Tomas

AU - Kozlov, Vladimir A.

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AB - Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

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KW - Helmholtz equation

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