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Volume 15, Issue 1
Hierarchical Absorbing Interface Conditions for Wave Propagation on Non-Uniform Meshes

Shuyang Dai, Zhiyuan Sun, Fengru Wang, Jerry Zhijian Yang & Cheng Yuan

DOI: 10.4208/nmtma.OA-2021-0135

Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 251-278.

Published online: 2022-02

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  • Abstract

In this paper, we propose hierarchical absorbing interface conditions to solve the problem of wave propagation in domains with a non-uniform space discretization or grid size inhomogeneity using Padé Via Lanczos (PVL) method. The proposed interface conditions add an auxiliary variable in the wave system to eliminate the spurious reflection at the interface between regions with different mesh sizes. The auxiliary variable with proper boundary condition can suppress the spurious reflection by cancelling the boundary source term produced by the space inhomogeneity in variational perspective. The new hierarchical interface conditions with the help of PVL implementation can effectively reduce the degree of freedom in solving the wave propagation problem.

  • Keywords

Wave equation, absorbing interface condition, spurious reflection, Padé via Lanczos.

  • AMS Subject Headings

65K10, 65N22, 35L05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-15-251, author = {Dai , ShuyangSun , ZhiyuanWang , FengruYang , Jerry Zhijian and Yuan , Cheng}, title = {Hierarchical Absorbing Interface Conditions for Wave Propagation on Non-Uniform Meshes}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2022}, volume = {15}, number = {1}, pages = {251--278}, abstract = {

In this paper, we propose hierarchical absorbing interface conditions to solve the problem of wave propagation in domains with a non-uniform space discretization or grid size inhomogeneity using Padé Via Lanczos (PVL) method. The proposed interface conditions add an auxiliary variable in the wave system to eliminate the spurious reflection at the interface between regions with different mesh sizes. The auxiliary variable with proper boundary condition can suppress the spurious reflection by cancelling the boundary source term produced by the space inhomogeneity in variational perspective. The new hierarchical interface conditions with the help of PVL implementation can effectively reduce the degree of freedom in solving the wave propagation problem.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2021-0135}, url = {http://global-sci.org/intro/article_detail/nmtma/20230.html} }
TY - JOUR T1 - Hierarchical Absorbing Interface Conditions for Wave Propagation on Non-Uniform Meshes AU - Dai , Shuyang AU - Sun , Zhiyuan AU - Wang , Fengru AU - Yang , Jerry Zhijian AU - Yuan , Cheng JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 251 EP - 278 PY - 2022 DA - 2022/02 SN - 15 DO - http://doi.org/10.4208/nmtma.OA-2021-0135 UR - https://global-sci.org/intro/article_detail/nmtma/20230.html KW - Wave equation, absorbing interface condition, spurious reflection, Padé via Lanczos. AB -

In this paper, we propose hierarchical absorbing interface conditions to solve the problem of wave propagation in domains with a non-uniform space discretization or grid size inhomogeneity using Padé Via Lanczos (PVL) method. The proposed interface conditions add an auxiliary variable in the wave system to eliminate the spurious reflection at the interface between regions with different mesh sizes. The auxiliary variable with proper boundary condition can suppress the spurious reflection by cancelling the boundary source term produced by the space inhomogeneity in variational perspective. The new hierarchical interface conditions with the help of PVL implementation can effectively reduce the degree of freedom in solving the wave propagation problem.

Dai , ShuyangSun , ZhiyuanWang , FengruYang , Jerry Zhijian and Yuan , Cheng. (2022). Hierarchical Absorbing Interface Conditions for Wave Propagation on Non-Uniform Meshes. Numerical Mathematics: Theory, Methods and Applications. 15 (1). 251-278. doi:10.4208/nmtma.OA-2021-0135
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