Acceleration of a multi-objective topology optimisation based on the BEM and the level set method by the H-matrix method

Abstract

In this paper, we discuss an acceleration with the H-matrix method of multi-objective topology optimisation using the boundary element method (BEM) and the level set method. In the sensitivity analysis for topology optimisations, we need to solve two boundary value problems; forward and adjoint problem. In the case that multiple objective functions are concerned, the number of boundary value problems to be solved increases in proportion to the number of the objective functions. We accelerate the sensitivity analysis for such problems with an accelerated LU decomposition or GMRES by the H-matrix method. We show the effectiveness of the proposed method by a numerical example of multi-objective topology optimisation in 2D electro-magnetic field.