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Volume 21, Issue 3
Fast Numerical Solvers for Subdiffusion Problems with Spatial Interfaces

Boyang Yu, Yonghai Li & Jiangguo Liu

DOI: 10.4208/ijnam2024-1017

Int. J. Numer. Anal. Mod., 21 (2024), pp. 431-458.

Published online: 2024-05

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  • Abstract

This paper develops novel fast numerical solvers for subdiffusion problems with spatial interfaces. These problems are modeled by partial differential equations that contain both fractional order and conventional first order time derivatives. The former is non-local and approximated by L1 and L2 discretizations along with fast evaluation algorithms based on approximation by sums of exponentials. This results in an effective treatment of the “long-tail” kernel of subdiffusion. The latter is local and hence conventional implicit Euler or Crank-Nicolson discretizations can be used. Finite volumes are utilized for spatial discretization based on consideration of local mass conservation. Interface conditions for mass and fractional fluxes are incorporated into these fast solvers. Computational complexity and implementation procedures are briefly discussed. Numerical experiments demonstrate accuracy and efficiency of these new fast solvers.

  • Keywords

Caputo and Riemann-Liouville derivatives, fast numerical solvers, fractional order fluxes, interface problems, subdiffusion, sum of exponentials (SOE).

  • AMS Subject Headings

35R11, 65M08, 65Y04, 65Y20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-21-431, author = {Yu , BoyangLi , Yonghai and Liu , Jiangguo}, title = {Fast Numerical Solvers for Subdiffusion Problems with Spatial Interfaces}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {3}, pages = {431--458}, abstract = {

This paper develops novel fast numerical solvers for subdiffusion problems with spatial interfaces. These problems are modeled by partial differential equations that contain both fractional order and conventional first order time derivatives. The former is non-local and approximated by L1 and L2 discretizations along with fast evaluation algorithms based on approximation by sums of exponentials. This results in an effective treatment of the “long-tail” kernel of subdiffusion. The latter is local and hence conventional implicit Euler or Crank-Nicolson discretizations can be used. Finite volumes are utilized for spatial discretization based on consideration of local mass conservation. Interface conditions for mass and fractional fluxes are incorporated into these fast solvers. Computational complexity and implementation procedures are briefly discussed. Numerical experiments demonstrate accuracy and efficiency of these new fast solvers.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1017}, url = {http://global-sci.org/intro/article_detail/ijnam/23130.html} }
TY - JOUR T1 - Fast Numerical Solvers for Subdiffusion Problems with Spatial Interfaces AU - Yu , Boyang AU - Li , Yonghai AU - Liu , Jiangguo JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 431 EP - 458 PY - 2024 DA - 2024/05 SN - 21 DO - http://doi.org/10.4208/ijnam2024-1017 UR - https://global-sci.org/intro/article_detail/ijnam/23130.html KW - Caputo and Riemann-Liouville derivatives, fast numerical solvers, fractional order fluxes, interface problems, subdiffusion, sum of exponentials (SOE). AB -

This paper develops novel fast numerical solvers for subdiffusion problems with spatial interfaces. These problems are modeled by partial differential equations that contain both fractional order and conventional first order time derivatives. The former is non-local and approximated by L1 and L2 discretizations along with fast evaluation algorithms based on approximation by sums of exponentials. This results in an effective treatment of the “long-tail” kernel of subdiffusion. The latter is local and hence conventional implicit Euler or Crank-Nicolson discretizations can be used. Finite volumes are utilized for spatial discretization based on consideration of local mass conservation. Interface conditions for mass and fractional fluxes are incorporated into these fast solvers. Computational complexity and implementation procedures are briefly discussed. Numerical experiments demonstrate accuracy and efficiency of these new fast solvers.

Boyang Yu, Yonghai Li & Jiangguo Liu. (2024). Fast Numerical Solvers for Subdiffusion Problems with Spatial Interfaces. International Journal of Numerical Analysis and Modeling. 21 (3). 431-458. doi:10.4208/ijnam2024-1017
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