A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations |
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Authors: | Qiya Hu Long Yuan |
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Institution: | 1.LSEC, Institute of Computational Mathematics and Scientic/Engineering Computing, Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing,China;2.College of Mathematics and Systems Science,Shan Dong University of Science and Technology,Qingdao,China;3.University of Chinese Academy of Sciences,Beijing,China |
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Abstract: | 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. |
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