Numerical approximation of one phase quadrature domains

作者：Bazarganzadeh Mahmoudreza; Bozorgnia Farid^*

来源：Numerical Methods for Partial Differential Equations, 2013, 29(5): 1709-1728.

DOI：10.1002/num.21773

• free boundary problem
• level set method
• quadrature domain
• shape optimization

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.

• 出版日期2013-9