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Mapped Regularization Methods for the Cauchy Problem of the Helmholtz and Laplace Equations

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Abstract

In this paper, Spectral Galerkin Method is applied for Cauchy problem of Helmholtz and Laplace equations in the regular domains. It is well known that these problems have severely ill-posed solutions. Accordingly, regularization methods are required to overcome the ill-posedness issue. In this paper, we utilize the regularization method based upon mapped methods. These methods include Tikhonov and truncated singular value decomposition methods and additionally several new filters of regularization which are introduced. Finally, some test examples are given to demonstrate the capability and efficiency of the proposed method.

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Authors and Affiliations

  1. Amirkabir University of Technology, Tehran, Iran

    Hojjatollah Shokri Kaveh & Hojjatollah Adibi

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  1. Hojjatollah Shokri Kaveh
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  2. Hojjatollah Adibi
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Correspondence to Hojjatollah Adibi.

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Shokri Kaveh, H., Adibi, H. Mapped Regularization Methods for the Cauchy Problem of the Helmholtz and Laplace Equations. Iran J Sci Technol Trans Sci 45, 669–682 (2021). https://doi.org/10.1007/s40995-020-01050-8

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  • DOI: https://doi.org/10.1007/s40995-020-01050-8

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