二维系数不连续Helmholtz方程的高阶紧致差分格式  

High order compact scheme for solving two-dimensional Helmholtz equation with discontinuous coefficient

作　　者：辛世友 殷俊锋[1] 

机构地区：[1]同济大学数学系,上海200092

出　　处：《应用数学与计算数学学报》2017年第1期43-54,共12页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11271289);中央高校基本科研业务费专项资金资助项目

摘　　要：针对二维系数不连续Helmholtz方程,提出和研究了高阶紧致差分格式,在波数跳跃位置引入局部网格加密技巧进行网格加密.数值实验验证,该高阶紧致差分格式用于求解二维系数不连续Helmholtz方程可以达到四阶精度,局部网格加密技巧能够有效地提高数值解的精度.We present and study the high order compact scheme for the solution to the two-dimensional Helmholtz equation with discontinuous coefficients. The local mesh grid refinement technology is applied to refine the jump position on non-uniform grid. Numerical experiments verify the fourth-order accuracy of the proposed high order compact scheme combined with the local mesh grid refinement technology, which can greatly improve the the Helmholtz equation with discontinuous accuracy of the numerical solution of coefficient.

关 键 词：二维Helmholtz方程 高阶紧致格式 局部网格加密技巧 系数不连续 

分 类 号：O241.82[理学—计算数学]