J.A.M. Carrer
The Boundary Element Method applied to the solution of the Diffusion-Wave problem
Carrer, J.A.M.; Solheid, B.S.; Trevelyan, J.; Seaid, M.
Authors
B.S. Solheid
Jonathan Trevelyan jon.trevelyan@durham.ac.uk
Emeritus Professor
Dr Mohammed Seaid m.seaid@durham.ac.uk
Associate Professor
Abstract
A Boundary Element Method formulation is developed for the solution of the two-dimensional diffusion-wave problem, which is governed by a partial differential equation presenting a time fractional derivative of order α, with 1.0 < α < 2.0. In the proposed formulation, the fractional derivative is transferred to the Laplacian through the Riemann–Liouville integro-differential operator; then, the basic integral equation of the method is obtained through the Weighted Residual Method, with the fundamental solution of the Laplace equation as the weighting function. In the final expression, the presence of additional terms containing the history contribution of the boundary variables constitutes the main difference between the proposed formulation and the standard one. The proposed formulation, however, works well for 1.5 ≤ α < 2.0, producing results with good agreement with the analytical solutions and with the Finite Difference ones.
Citation
Carrer, J., Solheid, B., Trevelyan, J., & Seaid, M. (2020). The Boundary Element Method applied to the solution of the Diffusion-Wave problem. Engineering Analysis with Boundary Elements, 117, 13-25. https://doi.org/10.1016/j.enganabound.2020.03.027
Journal Article Type | Article |
---|---|
Acceptance Date | Apr 1, 2020 |
Online Publication Date | May 12, 2020 |
Publication Date | Aug 31, 2020 |
Deposit Date | Apr 1, 2020 |
Publicly Available Date | May 12, 2021 |
Journal | Engineering Analysis with Boundary Elements |
Print ISSN | 0955-7997 |
Electronic ISSN | 1873-197X |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 117 |
Pages | 13-25 |
DOI | https://doi.org/10.1016/j.enganabound.2020.03.027 |
Public URL | https://durham-repository.worktribe.com/output/1266954 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/
Copyright Statement
© 2020 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
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