Constraint interface preconditioning for topology optimization problems

2015/10/15 by Kocvara, Michal, Loghin, Daniel, Turner, James
#49N90 #65F10 #65K10 #65N55 #90C51 #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1510.04568

Abstract

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.

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