高阶有限差分法求解Helmholtz方程  

Hight-order Finite Difference Method for Helmholtz Equation

作　　者：陈健军 揭蓉 朱小玲 隆广庆 CHEN Jian-jun;JIE Rong;ZHU Xiao-ling;LONG Guang-qing(School of Mathematics and Statistics,Nanning Normal University,Nanning 530299,China)

机构地区：[1]南宁师范大学数学与统计学院,广西南宁530299

出　　处：《南宁师范大学学报（自然科学版）》2020年第1期1-7,17,共8页Journal of Nanning Normal University：Natural Science Edition

基　　金：广西研究生教育创新计划项目(YCSW2019183);2017年广西研究生教育创新计划项目(JGY2017086);2019年度广西高等教育本科教学改革工程项目(2019JGA227)。

摘　　要：提出加权六阶有限差分方案对Helmholtz方程求解.采用中心六阶差分方案离散二阶导数项,匹配界面和边界(MIB)方法用于处理由此产生的边界问题.对于零阶项的离散化,通过利用所有13个点设计加权平均法,并通过最小化数值频散来确定权重参数.该新方案在抑制数值频散方面简单有效.最后,通过数值算例说明了新方案的数值收敛性和有效性.In this paper,we developed a sixth-order finite difference scheme based on weighting for the Helmholtz equation.The central sixth-order difference scheme is used to discretize the second-order derivative,and the matched interface and boundary(MIB) method is employed to deal with the resulting boundary problem.For the discretization of the zero-order term,a weighted average method is designed by utilizing all of the 13 points,and the weight parameters are determined by minimizing the numerical dispersion.The new method is simple and efficient in suppressing the numerical dispersion.Finally,numerical examples are presented to illustrate the numerical convergence and effectiveness of the new scheme.

关 键 词：HELMHOLTZ方程 有限差分法 数值频散 匹配界面和边界(MIB)方法 

分 类 号：O241.8[理学—计算数学]