A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations

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...

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Bibliographic Details
Published in:Advances in computational mathematics 2018-02, Vol.44 (1), p.245-275
Main Authors: Hu, Qiya, Yuan, Long
Format: Article
Language:English
Subjects:
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Discretization
Helmholtz equations
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Maxwell's equations
Spectra
Spectral element method
Visualization
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Summary: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.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-017-9542-z