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Jonathan Trevelyan's Outputs (108)

Fatigue growth modelling of three-dimensional cracks with the Extended Isogeometric Boundary Element Method (2025)
Journal Article
Rocha, M., Trevelyan, J., & Leonel, E. D. (in press). Fatigue growth modelling of three-dimensional cracks with the Extended Isogeometric Boundary Element Method. Engineering Analysis with Boundary Elements,

This paper proposes the fatigue crack growth modelling of three-dimensional geometries with the eXtended Isogeometric Boundary Element Method (XIGABEM). The formulation combines the advantages of the dual Boundary Element Method (BEM), the isogeometr... Read More about Fatigue growth modelling of three-dimensional cracks with the Extended Isogeometric Boundary Element Method.

An extended isogeometric boundary element formulation for three-dimensional linear elastic fracture mechanics (2024)
Journal Article
Rocha, M., Trevelyan, J., & Leonel, E. D. (2024). An extended isogeometric boundary element formulation for three-dimensional linear elastic fracture mechanics. Computer Methods in Applied Mechanics and Engineering, 423, Article 116872. https://doi.org/10.1016/j.cma.2024.116872

This paper presents a novel extended isogeometric boundary element formulation (XIGABEM) for three-dimensional linear elastic fracture mechanics. The formulation utilises the Dual BEM to accommodate coincident geometries for opposin... Read More about An extended isogeometric boundary element formulation for three-dimensional linear elastic fracture mechanics.

3D isogeometric indirect BEM solution based on virtual surface sources on the boundaries of Helmholtz acoustic problems (2024)
Journal Article
Shaaban, A. M., Trevelyan, J., & Rabczuk, T. (2024). 3D isogeometric indirect BEM solution based on virtual surface sources on the boundaries of Helmholtz acoustic problems. Engineering with Computers, 40(4), 2681-2702. https://doi.org/10.1007/s00366-023-01933-5

A solution for 3D Helmholtz acoustic problems is introduced based on an indirect boundary element method (indirect BEM) coupled with isogeometric analysis (IGA). The novelty of this work arises from using virtual surface sources placed directly on th... Read More about 3D isogeometric indirect BEM solution based on virtual surface sources on the boundaries of Helmholtz acoustic problems.

Direct evaluation of stress intensity factors and T-stress for bimaterial interface cracks using the extended isogeometric boundary element method (2023)
Journal Article
Andrade, H., Trevelyan, J., & Leonel, E. (2023). Direct evaluation of stress intensity factors and T-stress for bimaterial interface cracks using the extended isogeometric boundary element method. Theoretical and Applied Fracture Mechanics, 127, Article 104091. https://doi.org/10.1016/j.tafmec.2023.104091

This paper presents a new extended isogeometric boundary element method (XIGABEM) for the analysis of cracks in two-dimensional bimaterial interfaces. The classical NURBS approximations used in isogeometric formulations are augmented with functions b... Read More about Direct evaluation of stress intensity factors and T-stress for bimaterial interface cracks using the extended isogeometric boundary element method.

The solution of the wave-diffusion equation by a Caputo derivative-based Finite Element Method formulation (2023)
Journal Article
Correa, R., Carrer, J., Solheid, B., Trevelyan, J., Arndt, M., & Machado, R. (2023). The solution of the wave-diffusion equation by a Caputo derivative-based Finite Element Method formulation. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 45(5), Article 261. https://doi.org/10.1007/s40430-023-04175-0

A Finite Element Method approach is presented for the solution of the two-dimensional wave-diffusion equation. The fractional time derivative is considered as a Caputo derivative. Houbolt and Newmark methods are employed for the time-marching process... Read More about The solution of the wave-diffusion equation by a Caputo derivative-based Finite Element Method formulation.

An isogeometric boundary element formulation for stress concentration problems in couple stress elasticity (2023)
Journal Article
Hattori, G., Trevelyan, J., & Gourgiotis, P. (2023). An isogeometric boundary element formulation for stress concentration problems in couple stress elasticity. Computer Methods in Applied Mechanics and Engineering, 407, Article 115932. https://doi.org/10.1016/j.cma.2023.115932

An isogeometric boundary element method (IGABEM) is developed for the analysis of two-dimensional linear and isotropic elastic bodies governed by the couple stress theory. This theory is the simplest generalised continuum theory that can eectively mo... Read More about An isogeometric boundary element formulation for stress concentration problems in couple stress elasticity.

The solution of the anomalous diffusion equation by a Finite Element Method based on the Caputo derivative (2022)
Journal Article
Correa, R., Carrer, J., Solheid, B., & Trevelyan, J. (2022). The solution of the anomalous diffusion equation by a Finite Element Method based on the Caputo derivative. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 44(6), Article 250. https://doi.org/10.1007/s40430-022-03544-5

A Finite Element Method formulation is developed for the solution of the anomalous diffusion equation. This equation belongs to the branch of mathematics called fractional calculus; it is governed by a partial differential equation in which a fractio... Read More about The solution of the anomalous diffusion equation by a Finite Element Method based on the Caputo derivative.

An isogeometric boundary element method for heat transfer problems of multiscale structures in electronic packaging with arbitrary heat sources (2022)
Journal Article
Gong, Y., Chin, F., Dong, C., & Trevelyan, J. (2022). An isogeometric boundary element method for heat transfer problems of multiscale structures in electronic packaging with arbitrary heat sources. Applied Mathematical Modelling, 109, 161-185. https://doi.org/10.1016/j.apm.2022.03.047

We present an isogeometric boundary element method (IGABEM) capable of studying heat transfer problems for multiscale structures in electronic packaging problems. This method offers a number of key improvements compared with current analysis methods... Read More about An isogeometric boundary element method for heat transfer problems of multiscale structures in electronic packaging with arbitrary heat sources.

Analysis of 2D contact problems under cyclic loads using IGABEM with Bezier decomposition (2022)
Journal Article
Loyola, F., Doca, T., Campos, L., Trevelyan, J., & Albuquerque, E. (2022). Analysis of 2D contact problems under cyclic loads using IGABEM with Bezier decomposition. Engineering Analysis with Boundary Elements, 139, 246-263. https://doi.org/10.1016/j.enganabound.2022.03.017

Non-uniform rational B-splines (NURBS) are a convenient way to integrate CAD software and analysis codes, saving time from the operator and allowing efficient solution schemes that can be employed in the analysis of complex mechanical problems. In th... Read More about Analysis of 2D contact problems under cyclic loads using IGABEM with Bezier decomposition.

A NURBS-discontinuous and enriched isogeometric boundary element formulation for two-dimensional fatigue crack growth (2021)
Journal Article
Andrade, H., Trevelyan, J., & Leonel, E. (2022). A NURBS-discontinuous and enriched isogeometric boundary element formulation for two-dimensional fatigue crack growth. Engineering Analysis with Boundary Elements, 134, 259-281. https://doi.org/10.1016/j.enganabound.2021.09.019

A new extended isogeometric boundary element method (XIGABEM) formulation is proposed for simulating multiple fatigue crack propagation in two-dimensional domains. The classical use of NURBS in isogeometric formulations is further extended by repeate... Read More about A NURBS-discontinuous and enriched isogeometric boundary element formulation for two-dimensional fatigue crack growth.

Frequency domain Bernstein-Bezier finite element solver for modelling short waves in elastodynamics (2021)
Journal Article
Benatia, N., El Kacimi, A., Laghrouche, O., El Alaoui, M., & Trevelyan, J. (2022). Frequency domain Bernstein-Bezier finite element solver for modelling short waves in elastodynamics. Applied Mathematical Modelling, 102, 115-136. https://doi.org/10.1016/j.apm.2021.09.034

This work presents a high-order Bernstein-Bézier finite element (FE) discretisation to accurately solve time harmonic elastic wave problems on unstructured triangular mesh grids. Although high-order FEs possess many advantages over standard FEs, the... Read More about Frequency domain Bernstein-Bezier finite element solver for modelling short waves in elastodynamics.

A boundary element method formulation based on the Caputo derivative for the solution of the diffusion-wave equation (2021)
Journal Article
Carrer, J., Solheid, B., Trevelyan, J., & Seaid, M. (2022). A boundary element method formulation based on the Caputo derivative for the solution of the diffusion-wave equation. Engineering with Computers, 38(Suppl 4), 3563–3580. https://doi.org/10.1007/s00366-021-01480-x

A boundary element method formulation is developed and validated through the solution of problems governed by the diffusion-wave equation, for which the order of the time derivative, say α, ranges in the interval (1, 2). This fractional time derivati... Read More about A boundary element method formulation based on the Caputo derivative for the solution of the diffusion-wave equation.

A well simulator for homogeneous reservoirs based on formulations of the isogeometric boundary element method (2021)
Journal Article
Nascimento, L., Gontijo, G., Albuquerque, E., Campos, L., Trevelyan, J., & Fortaleza, E. (2021). A well simulator for homogeneous reservoirs based on formulations of the isogeometric boundary element method. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43, Article 206. https://doi.org/10.1007/s40430-021-02924-7

The development of a simulator for homogeneous reservoirs with application in producer wells (represented by a sink) and the aquifer analysis is obtained by combining the Boundary Element Method (BEM), the Isogeometric Formulation using NURBS (Non Un... Read More about A well simulator for homogeneous reservoirs based on formulations of the isogeometric boundary element method.

Quadrature methods for highly oscillatory singular integrals (2020)
Journal Article
Gao, J., Condon, M., Iserles, A., Gilvey, B., & Trevelyan, J. (2021). Quadrature methods for highly oscillatory singular integrals. Journal of computational mathematics, 39(2), 227-260. https://doi.org/10.4208/jcm.1911-m2019-0044

We address the evaluation of highly oscillatory integrals, with power-law and logarithmic singularities. Such problems arise in numerical methods in engineering. Notably, the evaluation of oscillatory integrals dominates the run-time for wave-enriche... Read More about Quadrature methods for highly oscillatory singular integrals.

A comparison of high-order and plane wave enriched boundary element basis functions for Helmholtz problems (2020)
Journal Article
Gilvey, B., & Trevelyan, J. (2021). A comparison of high-order and plane wave enriched boundary element basis functions for Helmholtz problems. Engineering Analysis with Boundary Elements, 122, 190-201. https://doi.org/10.1016/j.enganabound.2020.10.008

When undertaking a numerical solution of Helmholtz problems using the Boundary Element Method (BEM) it is common to employ low-order Lagrange polynomials, or more recently Non-Uniform Rational B-Splines (NURBS), as basis functions. A popular alternat... Read More about A comparison of high-order and plane wave enriched boundary element basis functions for Helmholtz problems.

A boundary element method formulation based on the Caputo derivative for the solution of the anomalous diffusion problem (2020)
Journal Article
Carrer, J., Solheid, B., Trevelyan, J., & Seaid, M. (2021). A boundary element method formulation based on the Caputo derivative for the solution of the anomalous diffusion problem. Engineering Analysis with Boundary Elements, 122, 132-144. https://doi.org/10.1016/j.enganabound.2020.10.017

This work presents a boundary element method formulation for the solution of the anomalous diffusion problem. By keeping the fractional time derivative as it appears in the governing differential equation of the problem, and by employing a Weighted R... Read More about A boundary element method formulation based on the Caputo derivative for the solution of the anomalous diffusion problem.

Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures (2020)
Journal Article
Gong, Y., Dong, C., Qin, F., Hattori, G., & Trevelyan, J. (2020). Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures. Computer Methods in Applied Mechanics and Engineering, 367, Article 113099. https://doi.org/10.1016/j.cma.2020.113099

The isogeometric boundary element method (IGABEM) has great potential for the simulation of elasticity problems because of its exact geometric representation and good approximation properties. These advantages can be extended to thin structures, incl... Read More about Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures.

The Boundary Element Method applied to the solution of the Diffusion-Wave problem (2020)
Journal Article
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

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 pro... Read More about The Boundary Element Method applied to the solution of the Diffusion-Wave problem.

Singular enrichment functions for Helmholtz scattering at corner locations using the Boundary Element Method (2019)
Journal Article
Gilvey, B., Trevelyan, J., & Hattori, G. (2020). Singular enrichment functions for Helmholtz scattering at corner locations using the Boundary Element Method. International Journal for Numerical Methods in Engineering, 121(3), 519-533. https://doi.org/10.1002/nme.6232

In this paper we use an enriched approximation space for the efficient and accurate solution of the Helmholtz equation in order to solve problems of wave scattering by polygonal obstacles. This is implemented in both Boundary Element Method (BEM) and... Read More about Singular enrichment functions for Helmholtz scattering at corner locations using the Boundary Element Method.