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The boundary element method applied to the solution of the diffusion-wave problem.

Carrer, J.A.M. and Solheid, B.S. and Trevelyan, J. and Seaid, M. (2020) 'The boundary element method applied to the solution of the diffusion-wave problem.', Engineering analysis with boundary elements., 117 . pp. 13-25.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.enganabound.2020.03.027
Publisher 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/
Date accepted:01 April 2020
Date deposited:02 April 2020
Date of first online publication:12 May 2020
Date first made open access:12 May 2021

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