Constraint interface preconditioning for topology optimization problems
For practitioners solving large-scale topology optimization problems, this method offers scalable and efficient solutions.
The paper addresses the computational challenges in topology optimization by combining interior-point methods with a novel substructuring domain decomposition method, achieving performance independent of problem size.
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity and size. In this work we propose a methodology which brings together existing fast algorithms, namely, interior-point for the optimization problem and a novel substructuring domain decomposition method for the ensuing large-scale linear systems. The main contribution is the choice of interface preconditioner which allows for the acceleration of the domain decomposition method, leading to performance independent of problem size.