修正Helmholtz方程的小波配点区域分解法  

Domain Decomposition Method of Wavelet-collocation for Modified Helmholtz Equations

作　　者：房保言[1] 王志刚[2] 梁波[2] 田双亮[1] 

机构地区：[1]西北民族大学计算机科学与信息工程学院 [2]西安理工大学理学院

出　　处：《武汉理工大学学报》2010年第3期120-123,共4页Journal of Wuhan University of Technology

基　　金：国家自然科学基金(10771091);国家民委科研基金(08XB07)

摘　　要：将小波配点法和区域分解结合用于求解修正Helmholtz方程。该方法克服了在求解大规模问题时用一般的全域小波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。给出小波配点求解修正Helmholtz方程解的存在唯一性。通过数值结果表明该算法在降低了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。A method for modified Helmholtz equations is developed,which is based on the wavelet-collocation and the domain decomposition method.This method slows down the ill-conditioned problem caused by asymmetry and full-rank of the coefficient matrix when the wavelet-collocation is applied for a large-scale region.In this paper the existence and uniqueness of solution to the wavelet-collocation method for modified Helmholtz equations is established.Numerical results show that the method of this paper slows down the condition number of the coefficient matrix and calculation errors,and can achieve satisfactory results.

关 键 词：修正Helmholtz方程 小波配点法 区域分解法 解的存在唯一性 

分 类 号：O175[理学—数学]