关键词: Epsilon算法, 矩阵分解, 区间参数, 声压响应, 修正Neumann级数, 有限元法

Abstract: To further improve the computational accuracy and efficiency of the modified interval perturbation finite element method (MIPFEM), a decomposed interval matrix perturbation finite element method (DIMPFEM) is proposed. In the proposed method, the dynamic stiffness matrix of an acoustic system is decomposed into the sum of several sub-matrices whose perturbation matrix can be expressed as the products of perturbation factors and determine matrices, thus the errors arising from the first-order Taylor expansion can be avoided. To achieve a higher computational efficiency, the inverse perturbation matrix, approximated by the modified Neumann series expansion is calculated by the epsilon-algorithm. Numerical examples on a 2D acoustic tube and a 2D acoustic cavity of a multi-purpose vehicle (MPV) with interval parameters verify that the computational accuracy and efficiency of DIMPFEM are higher than those of MIPFEM.

Key words: Epsilon-algorithm, finite element method, interval parameters, matrix decomposition, modified Neumann series, sound pressure response