Topology Optimization Using Multiscale Finite Element Method for High-Contrast Media

The focus of this paper is on the applicability of multiscale finite element coarse spaces for reducing the computational burden in topology optimization. The coarse spaces are obtained by solving a set of local eigenvalue problems on overlapping patches covering the computational domain. The approach is relatively easy for parallelization, due to the complete independence of the subproblems, and ensures contrast independent convergence of the iterative state problem solvers. Several modifications for reducing the computational cost in connection to topology optimization are discussed in details. The method is exemplified in minimum compliance designs for linear elasticity.