Numerical approximation of one phase quadrature domains

Abstract

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. 14 5.2. Alternative viewpoint. 16 6. Numerical examples. 17 References 23 Key words and phrases. Quadrature domain, Free boundary problem, Level set method, Shape optimization. M. Bazarganzadeh thanks Stockholm University for supporting to visit IST, Lisbon. F. Bozorgnia was supported by the UT Austin-Portugal partnership through the FCT post-doctoral fellowship SFRH/BPD/33962/