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Volume 24, Issue 4
Nonlocal Wave Propagation in Unbounded Multi-Scale Media

Qiang Du, Jiwei Zhang & Chunxiong Zheng

DOI: 10.4208/cicp.2018.hh80.10

Commun. Comput. Phys., 24 (2018), pp. 1049-1072.

Published online: 2018-06

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  • Abstract

This paper focuses on the simulation of nonlocal wave propagations in unbounded multi-scale mediums. To this end, we consider two issues: (a) the design of artificial/absorbing boundary conditions; and (b) the construction of an asymptotically compatible (AC) scheme for the nonlocal operator with general kernels. The design of ABCs facilitates us to reformulate unbounded domain problems into bounded domain problems. The construction of AC scheme facilitates us to simulate nonlocal wave propagations in multi-scale mediums. By applying the proposed ABCs and the proposed AC scheme, we investigate different wave propagation behaviors in the "local" and nonlocal mediums through numerical examples.

  • Keywords

Asymptotically compatible, absorbing boundary method, nonlocal wave equation, nonlocal wave propagation, multi-scale mediums.

  • AMS Subject Headings

49M25, 65N22, 65N06, 65R20, 82C21, 46N40, 45A05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-1049, author = {Qiang Du, Jiwei Zhang and Chunxiong Zheng}, title = {Nonlocal Wave Propagation in Unbounded Multi-Scale Media}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {4}, pages = {1049--1072}, abstract = {

This paper focuses on the simulation of nonlocal wave propagations in unbounded multi-scale mediums. To this end, we consider two issues: (a) the design of artificial/absorbing boundary conditions; and (b) the construction of an asymptotically compatible (AC) scheme for the nonlocal operator with general kernels. The design of ABCs facilitates us to reformulate unbounded domain problems into bounded domain problems. The construction of AC scheme facilitates us to simulate nonlocal wave propagations in multi-scale mediums. By applying the proposed ABCs and the proposed AC scheme, we investigate different wave propagation behaviors in the "local" and nonlocal mediums through numerical examples.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2018.hh80.10}, url = {http://global-sci.org/intro/article_detail/cicp/12317.html} }
TY - JOUR T1 - Nonlocal Wave Propagation in Unbounded Multi-Scale Media AU - Qiang Du, Jiwei Zhang & Chunxiong Zheng JO - Communications in Computational Physics VL - 4 SP - 1049 EP - 1072 PY - 2018 DA - 2018/06 SN - 24 DO - http://doi.org/10.4208/cicp.2018.hh80.10 UR - https://global-sci.org/intro/article_detail/cicp/12317.html KW - Asymptotically compatible, absorbing boundary method, nonlocal wave equation, nonlocal wave propagation, multi-scale mediums. AB -

This paper focuses on the simulation of nonlocal wave propagations in unbounded multi-scale mediums. To this end, we consider two issues: (a) the design of artificial/absorbing boundary conditions; and (b) the construction of an asymptotically compatible (AC) scheme for the nonlocal operator with general kernels. The design of ABCs facilitates us to reformulate unbounded domain problems into bounded domain problems. The construction of AC scheme facilitates us to simulate nonlocal wave propagations in multi-scale mediums. By applying the proposed ABCs and the proposed AC scheme, we investigate different wave propagation behaviors in the "local" and nonlocal mediums through numerical examples.

Qiang Du, Jiwei Zhang and Chunxiong Zheng. (2018). Nonlocal Wave Propagation in Unbounded Multi-Scale Media. Communications in Computational Physics. 24 (4). 1049-1072. doi:10.4208/cicp.2018.hh80.10
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