Helmholtz方程的楔形基区域分解法

计算机工程与应用 ›› 2013, Vol. 49 ›› Issue (13): 40-42.

Helmholtz方程的楔形基区域分解法

童小红，秦新强

西安理工大学理学院，西安 710054

出版日期:2013-07-01 发布日期:2013-06-28

Domain decomposition method for Helmholtz equations based on ridge basis function

TONG Xiaohong, QIN Xinqiang

School of Sciences, Xi’an University of Technology, Xi’an 710054, China

Online:2013-07-01 Published:2013-06-28

摘要/Abstract

摘要： 基于楔形基函数和无网格配点法，提出了一种求解Helmholtz型方程区域分解法。该方法克服了在求解大规模问题时用一般的全域配点法所带来的配置矩阵为非对称满阵，且高度病态的问题。通过数值结果表明，该算法在求解Helmholtz型方程降低系数矩阵条件数的同时，也能够降低误差，并达到满意的收敛效果。

关键词: Helmholtz型方程, 配点法, 楔形基函数, 区域分解法

Abstract: A meshless collocation method for Helmholtz-type equations is developed, which is based on domain decomposition method and ridge basis function. This method overcomes the ill-conditioned problems caused by much larger condition number of the coefficient matrix when collocation method is used for solving Helmholtz-type equations defined large-scale regions. According to numerical example and analysis, it is seen that the method Helmholtz-type equations slows down the condition number of the coefficient matrix and calculation errors, and can achieve satisfactory results.

Key words: Helmholtz-type equations, collocation method, ridge basis function, domain decomposition method

童小红，秦新强. Helmholtz方程的楔形基区域分解法[J]. 计算机工程与应用, 2013, 49(13): 40-42.

TONG Xiaohong, QIN Xinqiang. Domain decomposition method for Helmholtz equations based on ridge basis function[J]. Computer Engineering and Applications, 2013, 49(13): 40-42.

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