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The Boundary Element Method applied to the solution of the Diffusion-Wave problem

Carrer, J.A.M.; Solheid, B.S.; Trevelyan, J.; Seaid, M.

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Authors

J.A.M. Carrer

B.S. Solheid



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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