Improved trial methods for a class of generalized Bernoulli problems

Harbrecht, Helmut and Mitrou, Giannoula. (2013) Improved trial methods for a class of generalized Bernoulli problems. Preprints Fachbereich Mathematik, 2013 (22).

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Official URL: https://edoc.unibas.ch/70032/

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The aim of this article is to develop improved trial methods for the solution of a generalized exterior Bernoulli free boundary problem. At the free boundary, we prescribe the Neumann boundary condition and update the free boundary with the help of the remaining Dirichlet boundary condition. Appropriate update rules are obtained by expanding the Dirichlet data at the actual boundary via a Taylor expansion of first and second order. The resulting trial methods converge linearly for both cases, although the trial method based on the second order Taylor expansion is much more robust. Nevertheless, via results of shape sensitivity analysis, we are able to modify the update rules such that their convergence is improved. The feasibility of the proposed trial methods and their performance is demonstrated by numerical results.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Harbrecht, Helmut and Mitrou, Giannoula
Item Type:Preprint
Publisher:Universität Basel
edoc DOI:
Last Modified:13 May 2019 05:28
Deposited On:28 Mar 2019 09:52

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