COUPLING BOUNDARY ELEMENT METHOD WITH LEVEL SET METHOD TO SOLVE INVERSE PROBLEM - Rymarczyk, Tomasz; Tchórzewski, Paweł; Sikora, Jan (Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska, 2017)
The boundary element method and the level set method can be used in order to solve the inverse problem for electric field. In this approach the adjoint equation arises in each iteration step. Results of the numerical calculations show that the boundary element method can be applied successfully to obtain approximate solution of the adjoint equation. The proposed solution algorithm is initialized by using topological sensitivity analysis. Shape derivatives and material derivatives have been incorporated with the level set method to investigate shape optimization problems. The shape derivative measures the sensitivity of boundary perturbations. The coupled algorithm is a relatively new procedure to overcome this problem. Experimental results have demonstrated the efficiency of the proposed approach to achieve the solution of the inverse problem.