Numerical Approximation of One Phase Quadrature Domains

Details Numerical Approximation of One Phase Quadrature Domains Numerical Approximation of One Phase Quadrature Domains

2012-03-05

arxiv.org/abs/1203.0915v1

Mathematics

Numerical Analysis

25 pages, 12 figures

Scientific paper

In this work, we present two numerical schemes for a free boundary problem called one phase quadrature domain. In the first method by applying the proprieties of given free boundary problem, we derive a method that leads to a fast iterative solver. The iteration procedure is adapted in order to work in the case when topology changes. The second method is based on shape reconstruction to establish an efficient Shape-Quasi-Newton-Method. Various numerical experiments confirm the efficiency of the derived numerical methods.

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