Topology optimization for the elasticity problem (2019)
In this work, we propose several preconditioners for the elasticity equation. The preconditioners are built based on domain decomposition and multiscale methods for the heat and elasticity equations. The main goal of the application of preconditioners is to decrease the condition number of the matrix associated with the elasticity problem and the number of iterations needed to arrive at the solution of the elasticity equation. We also present an elasticity topology optimization problem, where we apply the preconditioners to the minimum compliance design problems. We present numerical experiments in order to show the advantages of our approach to the solution of these type of problems.