Acceleration of a multi-objective topology optimisation in 2D electro-magnetic field based on the level-set method and the boundary element method by the H-matrix method

In this study, we develop an efficient topology optimisation method with the H-matrix method and the boundary element method (BEM). In sensitivity analyses of topology optimisation, we need to solve a set of two algebraic equations whose coefficient matrices are common, particularly in many cases. For such cases, by using a direct solver such as LU decomposition to factorise the coefficient matrix, we can reduce the computational time for the sensitivity analysis. A coefficient matrix derived by the BEM is, however, fully populated, which causes high numerical costs for the LU decomposition. In this research, the LU decomposition is accelerated by using the H-matrix method for the sensitivity analyses of topology optimisation problems. We demonstrate the efficiency of the proposed method by a numerical example of a multi-objective optimisation problem for 2D electromagnetic field.