Simulation of a free boundary problem using boundary element method and restarted re-analysis technique

In this work, we deal with the numerical approximation of a free boundary problem reformulated as an optimal shape design one. The boundary element method is used for the approximation of this problem. The iterative method used to solve the discrete problem requires the resolution of intermediate linear systems associated with the successive modification in the design process. In many cases one of the main obstacles is the high computational cost involved in the solution of large-scale problems. To reduce the computational cost, a restarted re-analysis technique is introduced to solve these systems. Numerical examples including comparison results are presented to show the efficiency of the proposed approach.