The Boundary Element Method applied to the solution of the diffusion-wave problem. (August 2020)

• Record Type: Journal Article
• Authors: Carrer, J.A.M.; Solheid, B.S.; Trevelyan, J.; Seaid, M.
• Is Part Of: Engineering analysis with boundary elements. Volume 117(2020)
• Page Start: 13
• Page End: 25
• Publication Date: 2020-08
• Subjects: Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2020.03.027
• Languages: English
• ISSNs: 0955-7997

Abstract

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.