A filter in constructing the preconditioner for solving linear equation systems of radiation diffusion problems

Abstract

The coefficient matrices of the linear equation systems arising from the radiation diffusion problems usually have orders of magnitude difference between their off-diagonal entries. While solving these linear equations with a preconditioned iterative method, the entries with small magnitudes may be insignificant to the preconditioner efficiency. In this paper, we use a filter to remove such small entries in the coefficient matrix while constructing the preconditioner. The proposed filter eliminates the small entries first according to a so-called weak dependence matrix, which relies on the conception of the strength of connections in algebraic multigrid. The preconditioner is then built based on the filtered matrix instead of the original one. Four strategies of filtering out entries are designed and investigated. Numerical results for various model-type problems and two real application problems, i.e., the multi-group radiation diffusion equations and the three temperature energy equations, are provided to show the effectiveness of the proposed method. In particular, this paper provides a practical approach to choose a proper parameter in the proposed method, which should help solve linear equation systems of radiation diffusion problems.