An efficient localized collocation solver for anomalous diffusion on surfaces
- verfasst von
- Zhuochao Tang, Zhuojia Fu, Hongguang Sun, Xiaoting Liu
- Abstract
This paper introduces an efficient collocation solver, the generalized finite difference method (GFDM) combined with the recent-developed scale-dependent time stepping method (SD-TSM), to predict the anomalous diffusion behavior on surfaces governed by surface time-fractional diffusion equations. In the proposed solver, the GFDM is used in spatial discretization and SD-TSM is used in temporal discretization. Based on the moving least square theorem and Taylor series, the GFDM introduces the stencil selection algorithms to choose the stencil support of a certain node from the whole discretization nodes on the surface. It inherits the similar properties from the standard FDM and avoids the mesh generation, which is available particularly for high-dimensional irregular discretization nodes. The SD-TSM is a non-uniform temporal discretization method involving the idea of metric, which links the fractional derivative order with the non-uniform discretization strategy. Compared with the traditional time stepping methods, GFDM combined with SD-TSM deals well with the low accuracy in the early period. Numerical investigations are presented to demonstrate the efficiency and accuracy of the proposed GFDM in conjunction with SD-TSM for solving either single or coupled fractional diffusion equations on surfaces.
- Organisationseinheit(en)
-
Institut für Kontinuumsmechanik
- Externe Organisation(en)
-
Hohai University
Nanjing University of Aeronautics and Astronautics
- Typ
- Artikel
- Journal
- Fractional Calculus and Applied Analysis
- Band
- 24
- Seiten
- 865-894
- Anzahl der Seiten
- 30
- ISSN
- 1311-0454
- Publikationsdatum
- 06.2021
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Analysis, Angewandte Mathematik
- Elektronische Version(en)
-
https://doi.org/10.1515/fca-2021-0037 (Zugang:
Geschlossen)
