An unstructured mesh control volume method for two-dimensional space fractional diffusion equations with variable coefficients on convex domains
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Description
In this paper, we propose a novel unstructured mesh control volume method to deal with the space fractional derivative on arbitrarily shaped convex domains, which to the best of our knowledge is a new contribution to the literature. Firstly, we present the finite volume scheme for the two-dimensional space fractional diffusion equation with variable coefficients and provide the full implementation details for the case where the background interpolation mesh is based on triangular elements. Secondly, we explore the property of the stiffness matrix generated by the integral of the space fractional derivative. We find that the stiffness matrix is sparse and not regular. Therefore, we choose a suitable sparse storage format for the stiffness matrix and develop a fast iterative method to solve the linear system, which is more efficient than using the Gaussian elimination method. Finally, we present several examples to verify our method, in which we make a comparison of our method with the finite element method for solving a Riesz space fractional diffusion equation on a circular domain. The numerical results demonstrate that our method can reduce CPU time significantly while retaining the same accuracy and approximation property as the finite element method. The numerical results also illustrate that our method is effective and reliable and can be applied to problems on arbitrarily shaped convex domains.
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ID Code: | 131404 | ||||||
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Item Type: | Contribution to Journal (Journal Article) | ||||||
Refereed: | Yes | ||||||
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Measurements or Duration: | 18 pages | ||||||
DOI: | 10.1016/j.cam.2019.06.035 | ||||||
ISSN: | 0377-0427 | ||||||
Pure ID: | 41232463 | ||||||
Divisions: | Current > Research Centres > Centre for Biomedical Technologies Past > Institutes > Institute for Future Environments Past > QUT Faculties & Divisions > Science & Engineering Faculty ?? 3232 ?? Current > QUT Faculties and Divisions > Faculty of Engineering |
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Copyright Owner: | Consult author(s) regarding copyright matters | ||||||
Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au | ||||||
Deposited On: | 15 Jul 2019 00:28 | ||||||
Last Modified: | 01 Mar 2024 05:17 |
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