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On the Numerical Solution of the Laplace Equation with Complete and Incomplete Cauchy Data Using Integral Equations
Ukrainian Engn Pedag Acad, Ukraine.
Ivan Franko National University of Lviv, Ukraine.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
2014 (English)In: CMES - Computer Modeling in Engineering & Sciences, ISSN 1526-1492, E-ISSN 1526-1506, Vol. 101, no 5, 299-317 p.Article in journal (Refereed) Published
Abstract [en]

We consider the numerical solution of the Laplace equations in planar bounded domains with corners for two types of boundary conditions. The first one is the mixed boundary value problem (Dirichlet-Neumann), which is reduced, via a single-layer potential ansatz, to a system of well-posed boundary integral equations. The second one is the Cauchy problem having Dirichlet and Neumann data given on a part of the boundary of the solution domain. This problem is similarly transformed into a system of ill-posed boundary integral equations. For both systems, to numerically solve them, a mesh grading transformation is employed together with trigonometric quadrature methods. In the case of the Cauchy problem the Tikhonov regularization is used for the discretized system. Numerical examples are included both for the well-posed and ill-posed cases showing that accurate numerical solutions can be obtained with small computational effort.

Place, publisher, year, edition, pages
TECH SCIENCE PRESS , 2014. Vol. 101, no 5, 299-317 p.
Keyword [en]
Laplace equation; Cauchy problem; Corner domain; Mixed problem; Mesh grading transform; Single-layer potential; Tikhonov regularization
National Category
Civil Engineering
URN: urn:nbn:se:liu:diva-114261DOI: 10.3970/cmes.2014.101.299ISI: 000348259000001OAI: diva2:788594
Available from: 2015-02-16 Created: 2015-02-16 Last updated: 2015-02-16

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