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Volume 19, Issue 4
A Multiscale Parallel Algorithm for Parabolic Integro-Differential Equation in Composite Media

Fangman Zhai & Liqun Cao

Int. J. Numer. Anal. Mod., 19 (2022), pp. 542-562.

Published online: 2022-06

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  • Abstract

This paper studies the multiscale algorithm for parabolic integro-differential equations in composite media combining with Laplace transformation. The new contributions reported in this study are threefold: the convergence estimates with an explicit rate for the multiscale solutions of the equations in general domains are proved, the boundary layer solution is defined and the multiscale finite element algorithm which is suitable for parallel computation is presented. Numerical simulations are then carried out to validate the theoretical results.

  • Keywords

Parabolic integro-differential equation, the multiscale asymptotic method, Laplace transformation, composite media.

  • AMS Subject Headings

65F10, 65W05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-542, author = {Zhai , Fangman and Cao , Liqun}, title = {A Multiscale Parallel Algorithm for Parabolic Integro-Differential Equation in Composite Media}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {4}, pages = {542--562}, abstract = {

This paper studies the multiscale algorithm for parabolic integro-differential equations in composite media combining with Laplace transformation. The new contributions reported in this study are threefold: the convergence estimates with an explicit rate for the multiscale solutions of the equations in general domains are proved, the boundary layer solution is defined and the multiscale finite element algorithm which is suitable for parallel computation is presented. Numerical simulations are then carried out to validate the theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20658.html} }
TY - JOUR T1 - A Multiscale Parallel Algorithm for Parabolic Integro-Differential Equation in Composite Media AU - Zhai , Fangman AU - Cao , Liqun JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 542 EP - 562 PY - 2022 DA - 2022/06 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20658.html KW - Parabolic integro-differential equation, the multiscale asymptotic method, Laplace transformation, composite media. AB -

This paper studies the multiscale algorithm for parabolic integro-differential equations in composite media combining with Laplace transformation. The new contributions reported in this study are threefold: the convergence estimates with an explicit rate for the multiscale solutions of the equations in general domains are proved, the boundary layer solution is defined and the multiscale finite element algorithm which is suitable for parallel computation is presented. Numerical simulations are then carried out to validate the theoretical results.

Zhai , Fangman and Cao , Liqun. (2022). A Multiscale Parallel Algorithm for Parabolic Integro-Differential Equation in Composite Media. International Journal of Numerical Analysis and Modeling. 19 (4). 542-562. doi:
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