FOURTH-ORDER COMPACT SCHEMES FOR HELMHOLTZ EQUATIONS WITH PIECEWISE WAVE NUMBERS IN THE POLAR COORDINATES  

作　　者：Xiaolu Su Xiufang Feng Zhilin Li 

机构地区：[1]School of Mathematics and Computer Science, NingXia University, YinChuan, 750021, China [2]Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA Nanjing Normal University, Nanjing, China

出　　处：《Journal of Computational Mathematics》2016年第5期499-510,共12页计算数学（英文）

摘　　要：In this paper, fourth-order compact finite difference schemes are proposed for solving Helmholtz equation with piecewise wave numbers in polar coordinates with axis-symmetric and in some cases that the solution depends both of independent variables. The idea of the immersed interface method is applied to deal with the discontinuities in the wave number and certain derivatives of the solution. Numerical experiments are included to confirm the accuracy and efficiency of the proposed method.In this paper, fourth-order compact finite difference schemes are proposed for solving Helmholtz equation with piecewise wave numbers in polar coordinates with axis-symmetric and in some cases that the solution depends both of independent variables. The idea of the immersed interface method is applied to deal with the discontinuities in the wave number and certain derivatives of the solution. Numerical experiments are included to confirm the accuracy and efficiency of the proposed method.

关 键 词：Helmholtz equation Compact finite difference schemes Polar coordinate Theimmersed interface method High order method. 

分 类 号：O[理学]