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Volume 29, Issue 1
High-Order Local Absorbing Boundary Conditions for Heat Equation in Unbounded Domains

Xiaonan Wu & Jiwei Zhang

DOI: 10.4208/jcm.1004-m3195

J. Comp. Math., 29 (2011), pp. 74-90.

Published online: 2011-02

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  • Abstract

With the development of numerical methods the numerical computations require higher and higher accuracy. This paper is devoted to the high-order local absorbing boundary conditions (ABCs) for heat equation. We proved that the coupled system yields a stable problem between the obtained high-order local ABCs and the partial differential equation in the computational domain. This method has been used widely in wave propagation models only recently. We extend the spirit of the methodology to parabolic ones, which will become a basis to design the local ABCs for a class of nonlinear PDEs. Some numerical tests show that the new treatment is very efficient and tractable.

  • Keywords

Heat equation, High-order method, Absorbing boundary conditions, Parabolic problems in unbounded domains.

  • AMS Subject Headings

65M06, 65M12, 65M15.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-29-74, author = {Xiaonan Wu and Jiwei Zhang}, title = {High-Order Local Absorbing Boundary Conditions for Heat Equation in Unbounded Domains}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {1}, pages = {74--90}, abstract = {

With the development of numerical methods the numerical computations require higher and higher accuracy. This paper is devoted to the high-order local absorbing boundary conditions (ABCs) for heat equation. We proved that the coupled system yields a stable problem between the obtained high-order local ABCs and the partial differential equation in the computational domain. This method has been used widely in wave propagation models only recently. We extend the spirit of the methodology to parabolic ones, which will become a basis to design the local ABCs for a class of nonlinear PDEs. Some numerical tests show that the new treatment is very efficient and tractable.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1004-m3195}, url = {http://global-sci.org/intro/article_detail/jcm/8465.html} }
TY - JOUR T1 - High-Order Local Absorbing Boundary Conditions for Heat Equation in Unbounded Domains AU - Xiaonan Wu & Jiwei Zhang JO - Journal of Computational Mathematics VL - 1 SP - 74 EP - 90 PY - 2011 DA - 2011/02 SN - 29 DO - http://doi.org/10.4208/jcm.1004-m3195 UR - https://global-sci.org/intro/article_detail/jcm/8465.html KW - Heat equation, High-order method, Absorbing boundary conditions, Parabolic problems in unbounded domains. AB -

With the development of numerical methods the numerical computations require higher and higher accuracy. This paper is devoted to the high-order local absorbing boundary conditions (ABCs) for heat equation. We proved that the coupled system yields a stable problem between the obtained high-order local ABCs and the partial differential equation in the computational domain. This method has been used widely in wave propagation models only recently. We extend the spirit of the methodology to parabolic ones, which will become a basis to design the local ABCs for a class of nonlinear PDEs. Some numerical tests show that the new treatment is very efficient and tractable.

Xiaonan Wu and Jiwei Zhang. (2011). High-Order Local Absorbing Boundary Conditions for Heat Equation in Unbounded Domains. Journal of Computational Mathematics. 29 (1). 74-90. doi:10.4208/jcm.1004-m3195
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