声波导中非线性全局正交变换的研究  

Research into nonlinear global orthogonal transformation of the acoustic waveguide.

作　　者：朱建新[1] 陈芝花[1] 

机构地区：[1]浙江大学数学系,浙江杭州310027

出　　处：《浙江大学学报（理学版）》2008年第1期32-39,共8页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(No.10571162);浙江省自然科学基金资助项目(No.Y605181)

摘　　要：为能在带有极点的不平坦底部边界的声波导中实施快速步进计算Helmholtz方程,构造了几种能将弯曲底边界平坦化的非线性、非对称化全局坐标变换,这些变换一方面缓解了坐标曲线的局部"拥挤"状况,另一方面对步进计算中所涉及到的Helmholtz方程特征问题进行分析计算,提高了用Rayleigh迭代计算特征问题的效率,通过比较分析,指出了一个有效计算方法——分段步进法,为大步长计算波的传播提供了可靠的处理方法.For the acoustic waveguide in a region bounded by a flat top and a curved bottom with poles, some kinds of nonlinear and unsymmetrical global coordinate transformations to flatten the curved bottom of the waveguide are constructed to carry out fast marching computation or segment marching computation of Helmholtz equation. These transformations, improve the squeezed coordinate curves raise the effective of Rayleigh iteration for Helmholtz eigenvalue problem involved in the marching method. By comparison, it is pointed that there is and effective marching method called piece marching.

关 键 词：HELMHOLTZ方程 非线性全局正交变换 声波导 Rayleigh迭代 步进方法 

分 类 号：O241.8[理学—计算数学]