Seamless integration of elliptic Dirichlet-to-Neumann boundary condition and high order spectral element method for scattering problem. (English) Zbl 1530.65176
A semi-analytic approach to the integration of an elliptic Dirichlet-to-Neumann (DtN) boundary condition, and also a high order spectral element method in solving a scattering problem, are presented. With this, the DtN boundary condition can be truncated to high Mathieu expansion modes in a practical simulation. By using an appropriate elemental mapping in a spectral element discretization, an efficient semi-analytic approach is proposed for the computation of some global integrals along an 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.
Reviewer: V. L. Leontiev (Sankt-Peterburg)
MSC:
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 65D20 | Computation of special functions and constants, construction of tables |
| 74J20 | Wave scattering in solid mechanics |
Keywords:
scattering problem; spectral element method; elliptic Dirchlet-to-Neumann boundary condition; semi-analytic formula; Mathieu expansion modeSoftware:
DLMFReferences:
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