复波数Helmholtz方程和时谐Maxwell方程组的平面波间断Petrov-Galerkin方法  

A PLANE WAVE DISCONTINUOUS PETROV-GALERKIN METHOD FOR HELMHOLTZ EQUATION AND TIME-HARMONIC MAXWELL EQUATIONS WITH COMPLEX WAVE NUMBERS

作　　者：袁龙[1] 胡齐芽[2] 

机构地区：[1]STETML,中国电子科技集团公司第四十一研究所,青岛266555 [2]LSEC,中国科学院,数学与系统科学研究院,计算数学研究所,北京100190

出　　处：《数值计算与计算机应用》2015年第3期185-196,共12页Journal on Numerical Methods and Computer Applications

基　　金：中国国家重点基础研究发展计划(G91130015;G11031006;G2011309702);国家自然科学基金青年基金(11501529)资助项目

摘　　要：平面波方法己证明是实波数Helmholtz方程和时谐Maxwell方程组的高效离散化方法,但是还鲜有工作研究复波数情形的平面波离散化方法.本文基于平面波间断Galerkin方法的思想,导出了离散复波数Helmholtz方程和时谐Maxwell方程组的平面波间断Petrov-Galerkin方法.数值结果表明由该方法得到的数值解具有高的精度.The plane wave method becomes popular for discretization of Helmholtz and time-harmonic Maxwell＇s equations with real wave numbers in the recent years.However,there is few work to study the plane wave method for discretization of Helmholtz and Maxwell＇s equations with complex wave numbers.Based on the plane wave Discontinuous-Galerkin method,we derive a plane wave discontinuous Petrov-Galerkin method for discretization of Helmholtz equation and Maxwell＇s equations with complex wave numbers.The numerical results show that the resulting approximate solutions possess high accuracy.

关 键 词：HELMHOLTZ方程 MAXWELL方程组 平面波方法 间断Petrov-Galerkin 变分公式 

分 类 号：O241.82[理学—计算数学]