A New Approach for Solving Singular Systems in Topology Optimization Using Krylov Subspace Methods
Computational Engineering, Finance, and Science
2013-01-16 v1 Numerical Analysis
Abstract
In topology optimization, the design parameter with no contribution to the objective function vanishes. This causes the stiffness matrix to become singular. We show that a local optimal solution is obtained by Conjugate Residual Method and Conjugate Gradient Method even if the stiffness matrix becomes singular. We prove that CGMconverges to a local optimal solution in that case. Computer simulation shows that CGM gives the same solutions obtained by CRM in case of a cantilever beam problem.
Cite
@article{arxiv.1301.2354,
title = {A New Approach for Solving Singular Systems in Topology Optimization Using Krylov Subspace Methods},
author = {Teruyoshi Washizawa and Akira Asai and Nobuhiro Yoshikawa},
journal= {arXiv preprint arXiv:1301.2354},
year = {2013}
}
Comments
21 pages, 4 figures