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Geometric solution strategy of Laplace problems with free boundary

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Details

Original languageEnglish
Pages (from-to)723-746
Number of pages24
JournalInternational Journal for Numerical Methods in Engineering
Volume105
Issue number10
DOIs
Publication statusPublished - 9 Mar 2016
Publication typeA1 Journal article-refereed

Abstract

This paper introduces a geometric solution strategy for Laplace problems. Our main interest and emphasis is on efficient solution of the inverse problem with a boundary with Cauchy condition and with a free boundary. This type of problem is known to be sensitive to small errors. We start from the standard Laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another. This results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of Laplace's problem. Interpretation in terms of a geometric flow will provide us with stability considerations. The approach is demonstrated with several examples.

Keywords

  • Bernoulli problem, Cauchy condition, Differential equations, Elliptic partial differential equations, Equipotential layers, Field lines, Inverse problem, Laplace problem, Mean curvature, Shape design

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