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Numerical solution of the $ {\mathbb{R}}$-linear Beltrami equation


Authors: Marko Huhtanen and Allan Perämäki
Journal: Math. Comp. 81 (2012), 387-397
MSC (2010): Primary 65R20, 65F10, 45Q05
DOI: https://doi.org/10.1090/S0025-5718-2011-02541-X
Published electronically: August 9, 2011
MathSciNet review: 2833500
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Abstract: The $ \mathbb{R}$-linear Beltrami equation appears in applications, such as the inverse problem of recovering the electrical conductivity distribution in the plane. In this paper, a new way to discretize the $ \mathbb{R}$-linear Beltrami equation is considered. This gives rise to large and dense $ \mathbb{R}$-linear systems of equations with structure. For their iterative solution, norm minimizing Krylov subspace methods are devised. In the numerical experiments, these improvements combined are shown to lead to speed-ups of almost two orders of magnitude in the electrical conductivity problem.


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Additional Information

Marko Huhtanen
Affiliation: Institute of Mathematics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
Email: Marko.Huhtanen@tkk.fi

Allan Perämäki
Affiliation: Institute of Mathematics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
Email: Allan.Peramaki@tkk.fi

DOI: https://doi.org/10.1090/S0025-5718-2011-02541-X
Keywords: Beltrami equation, conductivity problem, dbar-equation, iterative methods
Received by editor(s): June 18, 2010
Received by editor(s) in revised form: December 15, 2010
Published electronically: August 9, 2011
Additional Notes: The research of both authors was supported by the Academy of Finland
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.