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Numerical approximation of one phase quadrature domains



In this work, we present two numerical schemes for a free boundary problem that is called one phase quadrature domain. In the first method, using the properties of a given free boundary problem, we derive a method that leads us to a fast iterative solver. The iteration procedure is adapted 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. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013