Boundary element methods for potential problems with nonlinear boundary conditions |
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Authors: | M Ganesh O Steinbach |
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Institution: | School of Mathematics, University of New South Wales, Sydney 2052, Australia ; Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart,~Germany |
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Abstract: | Galerkin boundary element methods for the solution of novel first kind Steklov-Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in two- and three-dimensional Lipschitz domains with nonlinear boundary conditions. For the numerical solution of the resulting Newton iterate linear boundary integral equations, we propose practical variants of the Galerkin scheme and give corresponding error estimates. We also discuss the actual implementation process with suitable preconditioners and propose an optimal hybrid solution strategy. |
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Keywords: | Boundary element methods Nonlinear boundary conditions |
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