Seamless integration of elliptic Dirichlet-to-Neumann boundary condition and high order spectral element method for scattering problem (Q2009493)
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scientific article; zbMATH DE number 7138579
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Seamless integration of elliptic Dirichlet-to-Neumann boundary condition and high order spectral element method for scattering problem |
scientific article; zbMATH DE number 7138579 |
Statements
Seamless integration of elliptic Dirichlet-to-Neumann boundary condition and high order spectral element method for scattering problem (English)
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28 November 2019
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A semi-analytic approach to the integration of elliptic Dirichlet-to-Neumann (DtN) boundary condition, and also high order spectral element method in solving scattering problem, are presented. With this, the DtN boundary condition can be truncated to high Mathieu expansion modes in the practical simulation. By using an appropriate elemental mapping in the spectral element discretization, an efficient semi-analytic approach is proposed for the computation of the global integrals along the elliptic outer boundary. The proposed semi-analytic formulas can also be used to calculate Mathieu expansion coefficients for functions with given values on spectral element grids. Numerical examples show the effectiveness of the proposed approach.
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scattering problem
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spectral element method
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elliptic Dirchlet-to-Neumann boundary condition
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semi-analytic formula
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Mathieu expansion mode
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