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In topology optimization, the design parameter with no contribution to theobjective function vanishes. This causes the stiffness matrix to becomesingular. We show that a local optimal solution is obtained by ConjugateResidual Method and Conjugate Gradient Method even if the stiffness matrixbecomes singular. We prove that CGMconverges to a local optimal solution inthat case. Computer simulation shows that CGM gives the same solutions obtainedby CRM in case of a cantilever beam problem.

A New Approach for Solving Singular Systems in Topology Optimization Using Krylov Subspace Methods