A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations
A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations
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DOI：
10.1007/s10444-017-9542-z
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发表时间：
2018-02
影响因子：
1.7
通讯作者：
Q. Hu;Long Yuan
中科院分区：
文献类型：
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作者：
Q. Hu;Long Yuan
在本文中，我们关注非齐次亥姆霍兹方程和时谐麦克斯韦方程的平面波离散化。为此，我们设计了一种结合局部谱元素的平面波方法来离散化此类非齐次方程。该方法包含两个步骤：首先用谱元法求解辅助光滑子域上的一系列非齐次局部问题，然后应用平面波方法在全局解域上对所得的（局部齐次）残差问题进行离散化。我们得出此方法生成的近似解的误差估计。数值结果表明，所得到的近似解具有较高的精度。
In this paper we are concerned with plane wave discretizations of nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations. To this end, we design a plane wave method combined with local spectral elements for the discretization of such nonhomogeneous equations. This method contains two steps: we first solve a series of nonhomogeneous local problems on auxiliary smooth subdomains by the spectral element method, and then apply the plane wave method to the discretization of the resulting (locally homogeneous) residue problem on the global solution domain. We derive error estimates of the approximate solutions generated by this method. The numerical results show that the resulting approximate solutions possess high accuracy.