# View Profile

## Professor Jon Trevelyan, BSc PhD FIMechE CEng

**Professor in the Department of Engineering**

(email at jon.trevelyan@durham.ac.uk)

### Biography

After obtaining his PhD studying transfer function methods for the determination of the dynamic properties of arch dams and working as a graduate civil engineer for Gibb, Jon Trevelyan joined the Computational Mechanics (CM) Group to work on the commercial software BEASY. This was the world-leader in engineering software based on the boundary element method. He stayed with CM for twelve years, seven of which were spent as Vice-President of CM, Inc. in Massachusetts. In 1995, he returned to the UK and was appointed a Senior Lecturer at the University of Brighton. One year later he joined Durham University. From 2007-13 he was the Head of the Mechanics Research Group, and from 2013-17 he was Head of the School of Engineering and Computing Sciences.

Jon's research involves the use of the boundary element method (BEM) in various areas: enriched BEM algorithms for short wave propagation, enriched BEM algorithms for fracture mechanics, fast and interactive methods for stress analysis/re-analysis and topology optimisation. He also develops enriched finite element algorithms for transient radiation-conduction problems. A common feature of these works is to develop numerical methods, usually through enrichment of one kind or another, to address problems that would be inefficient, inaccurate or insoluble using conventional methods such as those built into commercial software.

For more details on research projects, see http://www.dur.ac.uk/jon.trevelyan/JTResearchPage.htm

### Research Groups

#### Department of Engineering

### Research Interests

- Boundary elements
- Enriched boundary elements for fracture mechanics
- Enriched boundary elements for short wave propagation
- Interactive stress analysis software development
- Boundary elements and level sets for topology optimisation
- Enriched finite elements for transient diffusion problems

### Selected Publications

#### Journal Article

- El Kacimi, A., Laghrouche, O., Mohamed, M.S. &
**Trevelyan, J.**(2019). Bernstein - Bézier based finite elements for efficient solution of short wave problems.*Computer Methods in Applied Mechanics and Engineering***343**: 166-185. - Hattori, G.,
**Trevelyan, J.**&**Coombs, W.M.**(2018). A non-ordinary state-based peridynamics framework for anisotropic materials.*Computer Methods in Applied Mechanics and Engineering***339**: 416-442. - Li, S.,
**Trevelyan, J.**, Zhang, W. & Wang, D. (2018). Accelerating Isogeometric Boundary Element analysis for three-dimensional elastostatics problems through black-box Fast Multipole Method with Proper Generalised Decomposition.*International Journal for Numerical Methods in Engineering***114**(9): 975-998. - Ullah, B.,
**Trevelyan, J.**& Islam, S. (2017). A boundary element and level set based bi-directional evolutionary structural optimisation with a volume constraint.*Engineering Analysis with Boundary Elements***80**: 152-161. **Hattori, G.**,**Alatawi, I.A.**&**Trevelyan, J.**(2017). An extended boundary element method formulation for the direct calculation of the stress intensity factors in fully anisotropic materials.*International Journal for Numerical Methods in Engineering***109**(7): 965-981.- Drolia, M., Mohamed, M.S., Laghrouche, O.,
**Seaid, M.**&**Trevelyan, J.**(2017). Enriched finite elements for initial-value problem of transverse electromagnetic waves in time domain.*Computers and Structures***182**: 354-367. - Christodoulou, K., Laghrouche, O., Mohamed, M.S. &
**Trevelyan, J.**(2017). High-order finite elements for the solution of Helmholtz problems.*Computers and Structures***191**: 129-139. - Mahmood, M.S., Laghrouche, O.,
**Trevelyan, J.**& El Kacimi, A. (2017). Implementation and computational aspects of a 3D elastic wave modelling by PUFEM.*Applied Mathematical Modelling***49**: 568-586. - Hattori, G.,
**Trevelyan, J.**,**Augarde, C.E.**,**Coombs, W.M.**&**Aplin, A.C.**(2017). Numerical simulation of fracking in shale rocks: current state and future approaches.*Archives of Computational Methods in Engineering***24**(2): 281-317. - Sobhaniaragh, B.,
**Trevelyan, J.**, Mansur, W.J. & Peters, F.C. (2017). Numerical Simulation of MZF Design with Non-planar Hydraulic Fracturing from Multi-lateral Horizontal Wells.*Journal of Natural Gas Science and Engineering***46**: 93-107. - Ullah, B. &
**Trevelyan, J.**(2016). A boundary element and level set based topology optimisation using sensitivity analysis.*Engineering Analysis with Boundary Elements***70**: 80-98. - Cui, H., Lin, W., Zhang, H., Wang, X. &
**Trevelyan, J.**(2016). Backward waves with double zero-group-velocity points in a liquid-filled pipe.*Journal of the Acoustical Society of America***139**(3): 1179-1194. **Alatawi, I.A.**&**Trevelyan, J.**(2015). A direct evaluation of stress intensity factors using the Extended Dual Boundary Element Method.*Engineering Analysis with Boundary Elements***52**: 56-63.**Ullah, B.**,**Trevelyan, J.**&**Ivrissimtzis, I.**(2015). A three-dimensional implementation of the boundary element and level set based structural optimisation.*Engineering Analysis with Boundary Elements***58**: 176-194.- Peake, M.J.,
**Trevelyan, J.**&**Coates, G.**(2015). Extended isogeometric boundary element method (XIBEM) for three-dimensional medium-wave acoustic scattering problems.*Computer Methods in Applied Mechanics and Engineering***284**: 762-780. **Foster, T.M.**, Mohamed, M.S.,**Trevelyan, J.**,**Coates, G.**, Spence, S.H. & Walker, S.K. (2015). Interactive three-dimensional boundary element stress analysis of components in aircraft structures.*Engineering Analysis with Boundary Elements***56**: 190-200.- Diwan, G.C., Mohamed, M.S.,
**Seaid, M.**,**Trevelyan, J.**& Laghrouche, O. (2015). Mixed enrichment for the finite element method in heterogeneous media.*International Journal for Numerical Methods in Engineering***101**(1): 54-78. - Mohamed, M.S.,
**Seaid, M.**,**Trevelyan, J.**& Laghrouche, O. (2014). An enriched finite element model with q-refinement for radiative boundary layers in glass cooling.*Journal of Computational Physics***258**: 718-737. - Price, R.J. &
**Trevelyan, J.**(2014). Boundary element simulation of fatigue crack growth in multi-site damage.*Engineering Analysis with Boundary Elements***43**: 67-75. - Cui, H., Lin, W., Zhang, H., Wang, X. &
**Trevelyan, J.**(2014). Characteristics of group velocities of backward waves in a hollow cylinder.*The Journal of the Acoustical Society of America***135**(6): 3398-3408. - Ullah, B.,
**Trevelyan, J.**&**Matthews, P.C.**(2014). Structural optimisation based on the boundary element and level set methods.*Computers & Structures***137**: 14-30. **Peake, M.J.**,**Trevelyan, J.**&**Coates, G.**(2014). The equal spacing of N points on a sphere with application to partition-of-unity wave diffraction problems.*Engineering Analysis with Boundary Elements***40**: 114-122.**Diwan, G.C.**,**Trevelyan, J.**&**Coates, G.**(2013). A comparison of techniques for overcoming non-uniqueness of boundary integral equations for the collocation partition of unity method in two dimensional acoustic scattering.*International journal for numerical methods in engineering***96**(10): 645-664.**Allen, J.G.**,**Coates, G.**&**Trevelyan, J.**(2013). A hyper-heuristic approach to aircraft structural design optimization.*Structural and Multidisciplinary Optimization***48**(4): 807-819.**Mohamed, M.S.**,**Seaid, M.**,**Trevelyan, J.**& Laghrouche, O. (2013). A partition of unity FEM for time-dependent diffusion problems using multiple enrichment functions.*International Journal for Numerical Methods in Engineering***93**(3): 245-265.- Simpson, R.N., Bordas, S.P.A., Lian, H. &
**Trevelyan, J.**(2013). An Isogeometric Boundary Element Method for elastostatic analysis: 2D implementation aspects.*Computers & Structures***118**: 2-12. - Whittle, M.,
**Trevelyan, J.**&**Tavner, P.J.**(2013). Bearing currents in wind turbine generators.*Journal of Renewable and Sustainable Energy***5**: 053128. **Ullah, B.**&**Trevelyan, J.**(2013). Correlation between hole insertion criteria in a boundary element and level set based topology optimisation method.*Engineering Analysis with Boundary Elements***37**(11): 1457-1470.**Peake, M.J.**,**Trevelyan, J.**&**Coates, G.**(2013). Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems.*Computer Methods in Applied Mechanics and Engineering***259**: 93-102.- Whittle, M.W.G.,
**Trevelyan, J**, Shin, W. &**Tavner, P.J.**(2013). Improving wind turbine drivetrain bearing reliability through pre-misalignment.*Wind Energy***17**(8): 1217-1230. - Mohamed, M.S.,
**Seaid, M.**,**Trevelyan, J.**& Laghrouche, O. (2013). Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media.*Journal of Computational Physics***251**: 81-101. - Simpson, R.N., Bordas, S.P.A.,
**Trevelyan, J.**& Rabczuk, T. (2012). A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis.*Computer Methods in Applied Mechanics and Engineering***209-212**: 87-100. - Cui, H., Zhang, B., Johnstone, S. &
**Trevelyan, J.**(2012). Excitation mechanisms and dispersion characteristics of guided waves in multilayered cylindrical solid media.*Journal of the Acoustical Society of America***131**(3): 2048-2062. - Laghrouche, O., El-Kacimi, A. &
**Trevelyan, J.**(2012). Extension of the PUFEM to elastic wave propagation in layered media.*Journal of Computational Acoustics***20**(02): 1240006, 1240006-1. **Peake, M.J.**,**Trevelyan, J.**&**Coates, G.**(2012). Novel basis functions for the partition of unity boundary element method for Helmholtz problems.*International Journal for Numerical Methods in Engineering***93**(9): 905-918**Foster, T.M.**,**Mohamed, M.S.**,**Trevelyan, J.**&**Coates, G.**(2012). Rapid re-meshing and re-solution of three-dimensional boundary element problems for interactive stress analysis.*Engineering Analysis with Boundary Elements***36**(9): 1331-1343.- Simpson, Robert &
**Trevelyan, Jon**(2011). A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics.*Computer Methods in Applied Mechanics and Engineering***200**(1-4): 1-10. **Cui, H.**,**Trevelyan, J.**&**Johnstone, S.**(2011). Anomalous dispersion of flexural guided waves in clad rods.*IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control***58**(7): 1525-1528.**Simpson, R.**&**Trevelyan, J.**(2011). Evaluation of J1 and J2 integrals for curved cracks using an enriched Boundary Element Method.*Engineering Fracture Mechanics***78**(4): 623-637.**Cui, H.**,**Trevelyan, J.**&**Johnstone, S.**(2011). Stoneley waves in three-layered cylindrical solid media.*Journal of the Acoustical Society of America***130**(1): EL44-49.**Bird, G.E.**,**Trevelyan, J.**&**Augarde, C.E.**(2010). A coupled BEM/Scaled Boundary FEM formulation for accurate computations in linear elastic fracture mechanics.*Engineering Analysis with Boundary Elements***34**(6): 599-610.**Mohamed, M.S.**, Laghrouche, O. &**Trevelyan, J.**(2010). A q-adaptive partition of unity finite element method for the solution of the 2D Helmholtz equation.*Materials Science and Engineering***10**: 1-8.**Honnor, M. E.**,**Trevelyan, J.**& Huybrechs, D. (2010). Numerical evaluation of two-dimensional partition of unity boundary integrals for Helmholtz problems.*Journal of Computational and Applied Mathematics***234**(6): 1656-1662.**Trevelyan, J.**&**Coates, G.**(2010). On adaptive definition of the plane wave basis for wave boundary elements in acoustic scattering: the 2D case.*Computer Modeling in Engineering and Sciences***55**(2): 147-170.**Trevelyan, J.**& Honnor, M. E. (2009). A numerical coordinate transformation for efficient evaluation of oscillatory integrals over wave boundary elements.*Journal of Integral Equations and Applications***21**(3): 447-468.**Honnor, M.E.**,**Trevelyan, J.**, Bettess, P., El hachemi, M., Hassan, O., Morgan, K. & Shirron, J. (2009). An integration scheme for electromagnetic scattering using plane wave edge elements.*Advances in Engineering Software***40**(1): 58-65.- Chidgzey, S.R.,
**Trevelyan, J.**& Deeks, A.J. (2008). Coupling of the boundary element method and the scaled boundary finite element method for computations in fracture mechanics.*Computers and Structures***86**(11-12): 1198-1203. - Lewis, A.P., Stewart, C., Postans, N. &
**Trevelyan, J.**(2007). Development of an instrumented pole test for use as a gait laboratory quality check.*Gait and Posture***26**(2): 317-322. **Trevelyan, J.**& Scales, D.J. (2007). Techniques to accelerate BEM computation to provide virtual reality update of stress solutions.*Engineering Analysis with Boundary Elements***31**(11): 875-889.- Cervera, E. &
**Trevelyan, J.**(2005). Evolutionary structural optimisation based on boundary representation of NURBS: Part I: 2D algorithms.*Computers & Structures***83**(23-24): 1902-1916. - Cervera, E. &
**Trevelyan, J.**(2005). Evolutionary structural optimisation based on boundary representation of NURBS: Part II: 3D algorithms.*Computers & Structures***83**(23-24): 1917-1929. - Perrey-Debain, E.,
**Trevelyan, J.**& Bettess, P. (2005). On wave boundary elements for radiation and scattering problems with piecewise constant impedance.*IEEE transactions on antennas and propagation***53**(2): 876-879. - Laghrouche, O., Bettess, P., Perrey-Debain, E. &
**Trevelyan, J.**(2005). Wave interpolation finite elements for Helmholtz problems with jumps in the wave speed.*Computer Methods In Applied Mechanics And Engineering***194**(2-5): 367-381. - Perrey-Debain, E., Laghrouche, O., Bettess, P. &
**Trevelyan, J.**(2004). Plane-wave basis finite elements and boundary elements for three-dimensional wave scattering.*Philosophical transactions mathematical, physical and engineering sciences***362**(1816): 561-577. - Perrey-Debain, E.,
**Trevelyan, J.**& Bettess, P. (2004). Wave boundary elements a theoretical overview presenting applications in scattering of short waves.*Engineering analysis with boundary elements***28**(2): 131-141. - Bettess, P., Shirron, J., Laghrouche, O., Peseux, B., Sugimoto, R. &
**Trevelyan, J.**(2003). A numerical integration scheme for special finite elements for the Helmholtz equation.*International Journal For Numerical Methods In Engineering***56**(4): 531-552. - Sugimoto, R., Bettess, P. &
**Trevelyan, J.**(2003). A numerical integration scheme for special quadrilateral finite elements for the Helmholtz equation.*Communications In Numerical Methods In Engineering***19**(3): 233-245. - Perrey-Debain, E.,
**Trevelyan, J.**& Bettess, P. (2003). P-wave and S-wave decomposition in boundary integral equation for plane elastodynamic problems.*Communications In Numerical Methods In Engineering***19**(12): 945-958. - Laghrouche, O., Bettess, P., Perrey-Debain, E. &
**Trevelyan, J.**(2003). Plane wave basis finite-elements for wave scattering in three dimensions.*Communications In Numerical Methods In Engineering***19**(9): 715-723. - Perrey-Debain, E.,
**Trevelyan, J.**& Bettess, P. (2003). Plane wave interpolation in direct collocation boundary element method for radiation and wave scattering numerical aspects and applications.*Journal of sound and vibration***261**(5): 839-858. - Perrey-Debain, E.,
**Trevelyan, J.**& Bettess, P. (2003). Use of wave boundary elements for acoustic computations.*Journal Of Computational Acoustics***11**(2): 305-321. **Trevelyan, J.**, Wang, P. & Walker, S.K. (2002). A scheme for engineer-driven mechanical design improvement.*Engineering Analysis With Boundary Elements***26**(5): 425-433.- Perrey-Debain, E.,
**Trevelyan, J.**& Bettess, P. (2002). New special wave boundary elements for short wave problems.*Communications In Numerical Methods In Engineering***18**(4): 259-268. **Trevelyan, J.**& Wang, P. (2001). Interactive re-analysis in mechanical design evolution: Part I: Background and implementation.*Computers & Structures***79**(9): 929-938.**Trevelyan, J.**& Wang, P. (2001). Interactive re-analysis in mechanical design evolution: Part II: Rapid evaluation of boundary element integrals.*Computers & Structures***79**(9): 939-951.