REFACTORIZATION OF PRINCIPAL SUBMATRICES AND ITS APPLICATION TO TOPOLOGICAL OPTIMIZATION

In topological optimization, modified finite element models are frequently established as well solved step-by-step in terms of both changes in material and topology. Under the frame that step-by-step mesh is a part of the initial mesh through eliminating certain elements and nodes, sub linear systems corresponding to principal submatrices of the initial global stiffness matrix with modification in entries is encountered. This paper proposes a novel reanalysis algorithm based on finding updated triangular factorization of principal submatrices in sparse matrix solution. The key concept lies on the binary tree characteristics of the global stiffness matrix derived by a graph partitioner as fill-ins' reducer. Accommodating a local modification in material and topology, the update of the triangular factor happens only through a particular path of the binary tree. Numerical examples show that the proposed algorithm improves reanalysis efficiency significantly, especially for high-rank structural modification. In terms of implementation, little additional storage is needed to perform the proposed algorithm. This method can greatly improve efficiency of topological optimization.