Prof Matthew Hubbard

1. A.Cangiani, A,Dedner, M.E.Hubbard, H.Wells,
   Isoparametric virtual element methods,
   submitted, 2024.
2. P.Houston, M.E.Hubbard, T.J.Radley, O.J.Sutton, R.S.J.Widdowson,
   Efficient high-order space-angle-energy polytopic discontinuous Galerkin finite element methods for linear Boltzmann transport,
   submitted, 2023.
3. P.Houston, M.E.Hubbard, T.J.Radley,
   Analysis of iterative methods for the linear Boltzmann transport equation,
   accepted for publication, Comput Math Appl, 2024.
4. T.J.Radley, P.Houston, M.E.Hubbard,
   Quadrature-free polytopic discontinuous Galerkin methods for transport problems,
   Mathematics in Engineering, 6(1):192-220, 2024.
5. H.Wells, M.E.Hubbard, A.Cangiani,
   A velocity-based moving mesh virtual element method,
   Comput Math Appl, 155:110-125, 2024.
6. B.Morris, L.Curtin, A.Hawkins-Daarud, M.E.Hubbard, R.Rahman, S.J.Smith, D.Auer, N.L.Tran, L.S.Hu, J.M.Eschbacher, K.A.Smith, A.Stokes, K.R.Swanson, M.R.Owen,
   Identifying the spatial and temporal dynamics of molecularly-distinct glioblastoma sub-populations,
   Mathematical Biosciences and Engineering, 17(5):4905-4941, 2020.
7. M.E.Hubbard, M.Ricchiuto, D.Sármány,
   Space-time residual distribution on moving meshes,
   Comput Math Appl, 79:1561-1589, 2020.
8. C.Miles, K.G.van der Zee, M.E.Hubbard, R.MacKenzie,
   Thermomechanically consistent phase-field modelling of thin film flows,
   in Numerical Methods for Flows, Lecture Notes in Computational Science and Engineering, 132, 2020.
9. A.Alreheili, M.A.Walkley, P.K.Jimack, M.E.Hubbard,
   An efficient numerical algorithm for a multiphase tumour model,
   Comput Math Appl, 78(8):2734-2745, 2019.
10. M.Jove, J.A.Spencer, M.E.Hubbard, E.C.Holden, R.D.O'Dea, B.S.Brook, R.M.Phillips, S.W.Smye, P.M.Loadman, C.J.Twelves,
    Cellular uptake and efflux of palbociclib in vitro in single cell and spheroid models,
    J Pharmacol Exp Ther, 370(2):242-251, 2019.
11. M.E.Hubbard, M.Jove, P.M.Loadman, R.M.Phillips, C.J.Twelves, S.W.Smye,
    Drug delivery in a tumour cord model: a computational simulation,
    R Soc Open Sci, 4(5):170014, 2017. pdf
12. J.Collis, A.Connor, M.Paczkowski, P.Kannan, J.Pitt-Francis, H.M.Byrne, M.E.Hubbard,
    Bayesian calibration, validation and uncertainty quantification for predictive modelling of tumour growth: A tutorial,
    Bull Math Biol, 79(4):939-974, 2017. pdf
13. J.Collis, D.L.Brown, M.E.Hubbard, R.D.O'Dea,
    Effective equations governing an active poroelastic medium,
    Proc R Soc A, 473:20160755, 2017. pdf
14. J.Collis, M.E.Hubbard, R.O'Dea,
    A multiscale analysis of drug transport and response for a multiphase tumor model,
    Eur J Appl Math, 28(3):499-534, 2017. pdf
15. J.H.Chandler, D.A.Head, M.E.Hubbard, A.Neville, D.G.Jayne, P.R.Culmer,
    The impact of electrode resistance on the biogalvanic characterisation technique,
    Physiol Meas, 38:101-115, 2017. pdf
16. F.W.Yang, C.E.Goodyer, M.E.Hubbard, P.K.Jimack,
    An optimally efficient technique for the solution of systems of nonlinear parabolic partial differential equations,
    Adv Eng Softw, 103:65-84, 2017. pdf
17. J.Collis, M.E.Hubbard, R.O'Dea,
    Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth,
    Comput Method Appl M, 309:554-578, 2016. pdf
18. M.Sivapuratharasu, S.Hibberd, M.E.Hubbard, H.Power,
    Inertial effects on thin-film wave structures with imposed surface shear on an inclined plane,
    Physica D, 325:86-97, 2016. pdf
19. A.Warzynski, M.E.Hubbard, M.Ricchiuto,
    Runge-Kutta residual distribution schemes,
    J Sci Comput, doi:10.1007/s10915-014-9879-0, 62(3):772-802, 2015. pdf
20. K.J.Brabazon, M.E.Hubbard, P.K.Jimack,
    Nonlinear multigrid methods for second order differential operators with nonlinear diffusion coefficient,
    Comput Math Appl, 68(12A):1619-1634, 2014. pdf
21. C.M.Groh, M.E.Hubbard, P.F.Jones, P.M.Loadman, N.Periasamy, B.D.Sleeman, S.W.Smye, C.J.Twelves, R.M.Phillips,
    Mathematical and computational models of drug transport in tumours,
    J R Soc Interface, 11(94):20131173, 2014. pdf
22. M.Morales-Hernández, M.E.Hubbard, P.García-Navarro,
    A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries,
    J Comput Phys, 263:303-327, 2014. pdf
23. D.Sármány, M.E.Hubbard, M.Ricchiuto,
    Unconditionally stable space-time discontinuous residual distribution for shallow-water flows,
    J Comput Phys, 253:86-113, 2013. pdf
24. D.Sármány, M.E.Hubbard,
    Upwind residual distribution for shallow-water ocean modelling,
    Ocean Model, 64:1-11, 2013. pdf
25. M.E.Hubbard, H.M.Byrne,
    Multiphase modelling of vascular tumour growth in two spatial dimensions,
    J Theoret Biol, 316:70-89, 2013. pdf
26. M.J.Baines, M.E.Hubbard, P.K.Jimack,
    Velocity-based moving mesh methods for nonlinear partial differential equations,
    Commun Comput Phys, 10(3):509-576, 2011. pdf
27. R.Marlow, M.E.Hubbard, P.K.Jimack,
    Moving mesh methods for solving parabolic partial differential equations,
    Comput Fluids, 46(1):353-361, 2011. pdf
28. M.E.Hubbard, M.Ricchiuto,
    Discontinuous upwind residual distribution: A route to unconditional positivity and high order accuracy,
    Comput Fluids, 46(1):263-269, 2011. pdf
29. M.E.Hubbard, P.M.Jones, B.D.Sleeman,
    The foundations of a unified approach to mathematical modelling of angiogenesis,
    Int J Adv Eng Sci Appl Math, 1:43-52, 2009. pdf
30. M.E.Hubbard, M.J.Baines, P.K.Jimack,
    Consistent Dirichlet boundary conditions for moving boundary problems,
    Appl Numer Math, 59(6):1337-1353, 2009. pdf
31. M.J.Baines, M.E.Hubbard, P.K.Jimack, R.Mahmood,
    A moving-mesh finite element method and its application to the numerical solution of phase-change problems,
    Commun Comput Phys, 6(3):595-624, 2009. pdf
32. M.E.Hubbard,
    Discontinuous fluctuation distribution,
    J Comput Phys, 227(24):10125-10147, 2008. pdf
33. M.E.Hubbard,
    A framework for discontinuous fluctuation distribution,
    Int J Numer Methods Fluids, 56(8):1305-1311, 2008. pdf
34. M.E.Hubbard,
    Non-oscillatory third order fluctuation splitting schemes for steady scalar conservation laws,
    J Comput Phys, 222(2):740-768, 2007. pdf
35. M.J.Baines, M.E.Hubbard, P.K.Jimack, A.C.Jones,
    Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions,
    Appl Numer Math, 56:230-252, 2006. pdf
36. M.E.Hubbard, J.A.Leach, J.C.Wei,
    Pattern formation in a two-dimensional simple chemical system with general orders of autocatalysis and decay,
    IMA J Appl Math, 70(6):723-747, 2005. pdf
37. M.J.Baines, M.E.Hubbard, P.K.Jimack,
    A moving mesh finite element algorithm for fluid flow problems with moving boundaries,
    Int J Numer Methods Fluids, 47(10/11):1077-1083, 2005. pdf
38. M.J.Baines, M.E.Hubbard, P.K.Jimack,
    A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries,
    Appl Numer Math, 54:450-469, 2005. pdf
39. M.E.Hubbard, A.L.Laird,
    Achieving high-order fluctuation splitting schemes by extending the stencil,
    Comput Fluids, 34(4/5):443-459, 2005. pdf
40. M.E.Hubbard, N.Nikiforakis,
    A three-dimensional, adaptive, Godunov-type model for global atmospheric flows,
    Mon Weather Rev, 131:1848-1864, 2003. pdf
41. M.E.Hubbard, N.Dodd,
    A 2d numerical model of wave run-up, overtopping and regeneration,
    Coast Eng, 47(1):1-26, 2002. pdf
42. M.E.Hubbard,
    Adaptive mesh refinement for three-dimensional off-line tracer advection over the sphere,
    Int J Numer Methods Fluids, 40:369-377, 2002. pdf
43. M.J.Baines, S.J.Leary, M.E.Hubbard,
    Multidimensional least squares fluctuation distribution schemes with adaptive mesh movement for steady hyperbolic equations,
    SIAM J Sci Comput, 23(5):1485-1502, 2002. pdf (pictures missing)
44. M.E.Hubbard,
    On the accuracy of one dimensional models of steady converging/diverging open channel flows,
    Int J Numer Methods Fluids, 35(7):785-808, 2001. pdf
45. M.E.Hubbard, P.Garcia-Navarro,
    Flux difference splitting and the balancing of source terms and flux gradients,
    J Comput Phys, 165(1):89-125, 2000. pdf (some odd-sized pictures)
46. M.E.Hubbard, P.L.Roe,
    Compact high resolution algorithms for time dependent advection on unstructured grids,
    Int J Numer Methods Fluids, 33(5):711-736, 2000. pdf (abstract missing)
47. M.E.Hubbard,
    Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids,
    J Comput Phys, 155:54-74, 1999. pdf
48. M.E.Hubbard, M.J.Baines,
    Conservative multidimensional upwinding for the steady two dimensional shallow water equations,
    J Comput Phys, 138:419-448, 1997. pdf
49. P.Garcia-Navarro, M.E.Hubbard, A.Priestley,
    Genuinely multidimensional upwinding for the 2d shallow water equations,
    J Comput Phys, 121(1):79-93, 1995. pdf (pictures missing)

1. N.R.Kirk, A.P.Benson, C.E.Goodyer, M.E.Hubbard,
   A computational study of the effects of remodelled electrophysiology and mechanics on initiation of ventricular fibrillation in human heart failure,
   http://arxiv.org/abs/1406.1701, 2014.

1. F.W.Yang, C.E.Goodyer, M.E.Hubbard, P.K.Jimack,
   Parallel implementation of an adaptive, multigrid solver for the implicit solution of nonlinear parabolic systems, with application to a multi-phase-field model for tumour growth,
   in Proceedings of the 4th International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, P.Ivanyi, B.H.V.Topping (Eds.), 2015.
2. A.Warzynski, M.E.Hubbard, M.Ricchiuto,
   Discontinuous residual distribution schemes for time-dependent problems,
   in Proceedings of the 8th International Conference on Scientific Computing and Applications, J.Li, H.Yang (Eds.), 2012. pdf
3. N.R.Kirk, A.P.Benson, M.E.Hubbard, C.E.Goodyer,
   An efficient coupled electromechanical solver for studying human re-entrant arrhythmias,
   in Proceedings of Computing in Cardiology, 2011. pdf
4. M.E.Hubbard,
   Discontinuous fluctuation distribution for time-dependent problems,
   in Computational Fluid Dynamics 2008, H.Choi, H.G.Choi, J.Y.Yoo (Eds.), Springer-Verlag, pp. 711-716, 2009. pdf
5. M.E.Hubbard, N.Z.Mebrate,
   Very high order, non-oscillatory fluctuation distribution schemes,
   in Computational Fluid Dynamics 2006, H.Deconinck, E.Dick (Eds.), Springer-Verlag, pp. 65-70, 2009. pdf
6. M.E.Hubbard,
   A framework for discontinuous fluctuation distribution,
   in Proceedings of the 9th Conference on Numerical Methods for Fluid Dynamics, P.K.Sweby (Ed.), ICFD Reading, 2007. pdf
7. M.E.Hubbard,
   Non-oscillatory, third order fluctuation splitting schemes,
   in Finite Volumes for Complex Applications IV, F.Benkhaldoun, D.Ouazar, S.Raghay (Eds.), pp. 377-387, Hermes Science Publishing, 2005. pdf (pictures missing)
8. M.J.Baines, M.E.Hubbard, P.K.Jimack,
   A moving mesh finite element algorithm for fluid flow problems with moving boundaries,
   in Proceedings of the 8th Conference on Numerical Methods for Fluid Dynamics, M.J.Baines (Ed.), ICFD Oxford, 2004. pdf
9. M.J.Baines, M.E.Hubbard, P.K.Jimack,
   A Lagrangian moving finite element method incorporating monitor functions,
   in Advances in Scientific Computing and Applications, Y.Y.Lu, W.W.Sun, T.Tang (Eds.), Scientific Press, Beijing, pp. 32-44, 2004. pdf
10. M.J.Baines, M.E.Hubbard, P.K.Jimack,
    Adaptive finite element solutions of time-dependent partial differential equations using moving mesh algorithms,
    in "Modelling and Simulation in Chemical Engineering, Centro Internacional de Matematica 22", A.E.Rodrigues, P.de Oliveira, J.A.Castro, J.A.Ferreira (Eds.), Coimbra, Portugal, paper 3, 2003. pdf
11. M.E.Hubbard, M.Berzins,
    A positivity preserving finite element method for hyperbolic partial differential equations,
    in Computational Fluid Dynamics 2002, S.Armfield, P.Morgan, K.Srinivas (Eds.), Springer-Verlag, pp. 205-210, 2003. pdf
12. M.E.Hubbard,
    Adaptive mesh refinement for three-dimensional off-line tracer advection over the sphere,
    in Numerical Methods for Fluid Dynamics VII, M.J.Baines (Ed.), ICFD Oxford, pp. 355-361, 2001. pdf
13. M.E.Hubbard, P.Garcia-Navarro,
    Balancing source terms and flux gradients in finite volume schemes,
    in Godunov Methods: Theory and Applications, E.F.Toro (Ed.), Kluwer Academic/Plenum Publishers, pp. 477-483, 2001. pdf
14. P.Garcia-Navarro, P.Brufau, M.E.Hubbard,
    Upwinding in two dimensions,
    Invited Lecture in Godunov Methods: Theory and Applications, E.F.Toro (Ed.), Kluwer Academic/Plenum Publishers, pp. 343-365, 2001. pdf (some pictures missing)
15. M.E.Hubbard,
    Multidimensional upwind schemes for the shallow water equations,
    Invited Lecture in Numerical Simulation of Hydrodynamic Systems, pp. 131-154, 1999. pdf
16. M.J.Baines, S.J.Leary, M.E.Hubbard,
    A finite volume method for steady hyperbolic equations incorporating mesh movement,
    in Finite Volumes for Complex Applications - Problems and Perspectives, R.Vilsmeier, F.Benkhaldoun, D.Hanel (Eds.), Hermes, pp. 787-794, 1999.
17. P.Sims, M.E.Hubbard, M.J.Baines,
    Multidimensional upwinding for the Euler equations,
    in International Workshop on New Models and Numerical Codes for Shock Wave Processes in Condensed Media, pp. 781-786, 1999.
18. M.J.Baines, M.E.Hubbard,
    Multidimensional upwinding with grid adaptation,
    in Numerical Methods for Wave Propagation, E.F.Toro, J.F.Clarke (Eds.), Kluwer Academic Publishers, pp. 33-54, 1998. pdf (pictures missing)
19. M.E.Hubbard, P.L.Roe,
    Multidimensional upwind fluctuation distribution schemes for time dependent problems,
    in Numerical Methods for Fluid Dynamics VI, M.J.Baines (Ed.), ICFD Oxford, pp. 363-369, 1998. pdf
20. M.E.Hubbard, M.J.Baines,
    Multidimensional upwinding and grid adaptation,
    in Numerical Methods for Fluid Dynamics V, K.W.Morton, M.J.Baines (Eds.), Oxford University Press, pp. 431-437, 1995. pdf (pictures missing)
21. P.Garcia-Navarro, M.E.Hubbard, A.Priestley, M.J.Baines,
    Two dimensional shallow water flows on unstructured grids,
    in Proceedings of 1st Asian CFD Conference, pp. 335-340, 1995. pdf (pictures missing)

1. M.E.Hubbard,
   Multidimensional upwinding and grid adaptation for conservation laws,
   Ph.D. thesis, The University of Reading, Department of Mathematics, 1996.

* indicates it has subsequently been published in a refereed journal.

INRIA, Bordeaux

1. * RR-7958: D.Sármány, M.E.Hubbard, M.Ricchiuto, pdf
   Unconditionally stable space-time discontinuous residual distribution for shallow-water flows, 2012.

The University of Leeds, School of Computing

1. * 2003.04: M.J.Baines, M.E.Hubbard and P.K.Jimack, pdf
   A moving finite element method using monitor functions, 2003.

The University of Reading, Department of Mathematics

1. NA-4/99: M.E.Hubbard, pdf (some pictures missing)
   Aspects of multidimensional upwinding: time-dependent nonlinear systems, source terms, spherical geometries and three-dimensional grid adaptation, 1999.
2. * NA-3/99: M.E.Hubbard, P.Garcia-Navarro, pdf
   Flux difference splitting and the balancing of source terms and flux gradients, 2000.
3. * NA-1/99: M.E.Hubbard, pdf
   On the accuracy of one dimensional models of steady converging/diverging open channel flows, 1999.
4. * NA-8/98: M.E.Hubbard, pdf
   Multidimensional slope limiters for MUSCL-type finite volume schemes II - on improving existing unstructured grid techniques, 1998.
5. NA-2/98: M.E.Hubbard, pdf
   Multidimensional slope limiters for MUSCL-type finite volume schemes, 1998.
6. * NA-1/98: M.E.Hubbard, P.L.Roe, pdf
   Multidimensional upwind fluctuation distribution schemes for scalar time-dependent problems, 1998.
7. NA-6/97: M.E.Hubbard, pdf
   Least squares minimisation and steepest descent methods for the scalar advection equation and a Cauchy-Riemann system on an adaptive grid, 1997.
8. * NA-1/97: M.E.Hubbard, M.J.Baines, pdf
   Conservative multidimensional upwinding for the steady two dimensional shallow water equations, 1997.
9. NA-4/95: M.E.Hubbard, P.Garcia-Navarro, M.J.Baines, pdf (pictures and references missing)
   Conservative multidimensional upwinding for the shallow water equations, 1995.
10. NA-8/94: M.E.Hubbard, pdf
    Grid adaptation and multidimensional upwinding, 1994.
11. * NA-3/94: P.Garcia-Navarro, M.E.Hubbard, A.Priestley, pdf (pictures missing)
    Genuinely multidimensional upwinding for the 2d shallow water equations, 1994.
12. NA-7/93: M.E.Hubbard, pdf
    A survey of genuinely multi-dimensional upwinding techniques, 1993.
13. NA-2/93: M.E.Hubbard, pdf
    A hybrid central/upwind approach to the solution of the one dimensional Euler equations, 1993.

Unpublished

1. M.E.Hubbard, pdf (full draft, started in 2000)
   Data structures for visualising structured AMR data.
2. M.E.Hubbard, pdf (unfinished and dates from 1995)
   A geometric view of the PSI scheme.

1. M.E.Hubbard, N.Dodd,
   ANEMONE: OTT-2D, A user manual (version 1),
   Report TR-65, HR Wallingford Ltd., 2000.
2. M.E.Hubbard, N.Dodd,
   ANEMONE: LFW-2D, A user manual (version 1),
   Report TR-86, HR Wallingford Ltd., 2000.
3. M.E.Hubbard,
   AMR3D: a user's guide,
   DAMTP, 2001.