Extension of reanalysis method, analysis of heat conduction by using CA and IC methods

Abstract

Two fast heat transfer solvers by using Node-based Smooth FEM method (NS-FEM) and reanalysis methods are suggested. The reanalysis is an auxiliary solver which can predict the response of a given problems instead of full analysis. In this study, combined approximations (CA) and independent coefficients (IC) methods are investigated. The CA might be the most popular reanalysis method and has been widely applied to structural analysis. In the CA method, binomial series is used as high quality basis vectors for reduced basis expression. The IC method is suggested to reanalyze structures with local modifications which lead to a low-rank change in the stiffness matrix. Steady temperature fields can be calculated without solving a complete set of linear system equations by both of them. Compared with the CA method, the IC method requires only the initial solution as input and can determine the independent coefficients for each degree of freedoms (DOFs) influenced by structural modifications without matrix decomposition operation. In order to verify the performances of the CA method and the IC methods, several numerical examples are tested. The results demonstrate that the CA and the IC methods have high accuracy as well as efficiency when the modification is local.