Professor Matthew Hubbard's Outputs (21)

Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport (2024)
Journal Article
Houston, P., Hubbard, M. E., Radley, T. J., Sutton, O. J., & Widdowson, R. S. J. (2024). Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport. Journal of Scientific Computing, 100(2), Article 52. https://doi.org/10.1007/s10915-024-02569-3

We introduce an hp–version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented in an almost... Read More about Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport.

Iterative solution methods for high-order/hp–DGFEM approximation of the linear Boltzmann transport equation (2024)
Journal Article
Houston, P., Hubbard, M. E., & Radley, T. J. (2024). Iterative solution methods for high-order/hp–DGFEM approximation of the linear Boltzmann transport equation. Computers and Mathematics with Applications, 166, 37-49. https://doi.org/10.1016/j.camwa.2024.04.011

In this article we consider the iterative solution of the linear system of equations arising from the discretisation of the poly-energetic linear Boltzmann transport equation using a high-order/hp–version discontinuous Galerkin finite element approxi... Read More about Iterative solution methods for high-order/hp–DGFEM approximation of the linear Boltzmann transport equation.

Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems (2024)
Journal Article
Radley, T. J., Houston, P., & Hubbard, M. E. (2024). Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems. Mathematics in Engineering, 6(1), 192-220. https://doi.org/10.3934/mine.2024009

In this article we consider the application of Euler’s homogeneous function theorem to- gether with Stokes’ theorem to exactly integrate families of polynomial spaces over general polygonal and polyhedral (polytopic) domains in two and three dimensio... Read More about Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems.

A velocity-based moving mesh virtual element method (2023)
Journal Article
Wells, H., Hubbard, M., & Cangiani, A. (2024). A velocity-based moving mesh virtual element method. Computers and Mathematics with Applications, 155, 110-125. https://doi.org/10.1016/j.camwa.2023.12.005

We present a velocity-based moving mesh virtual element method for the numerical solution of PDEs involving boundaries which are free to move. The virtual element method is used for computing both the mesh velocity and a conservative Arbitrary Lagran... Read More about A velocity-based moving mesh virtual element method.

Identifying the spatial and temporal dynamics of molecularly-distinct glioblastoma sub-populations (2020)
Journal Article
Morris, B., Curtin, L., Hawkins-Daarud, A., Hubbard, M. E., Rahman, R., Smith, S. J., Auer, D., Tran, N. L., Hu, L. S., Eschbacher, J. M., Smith, K. A., Stokes, A., Swanson, K. R., & Owen, M. R. (2020). Identifying the spatial and temporal dynamics of molecularly-distinct glioblastoma sub-populations. Mathematical Biosciences and Engineering, 17(5), 4905-4941. https://doi.org/10.3934/mbe.2020267

Glioblastomas (GBMs) are the most aggressive primary brain tumours and have no known cure. Each individual tumour comprises multiple sub-populations of genetically-distinct cells that may respond differently to targeted therapies and may contribute t... Read More about Identifying the spatial and temporal dynamics of molecularly-distinct glioblastoma sub-populations.

Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows (2020)
Book Chapter
Zee, K. G. D., Zee, K. G. V. D., Miles, C., van der Zee, K. G., Hubbard, M. E., & MacKenzie, R. (2020). Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows. In H. van Brummelen, A. Corsini, S. Perotto, & G. Rozza (Eds.), Numerical methods for flows: FEF 2017 selected contributions (121-129). Springer Verlag. https://doi.org/10.1007/978-3-030-30705-9_11

© Springer Nature Switzerland AG 2020. We use phase-field techniques coupled with a Coleman–Noll type procedure to derive a family of thermomechanically consistent models for predicting the evolution of a non-volatile thin liquid film on a flat subst... Read More about Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows.

Space–time residual distribution on moving meshes (2019)
Journal Article
Hubbard, M. E., Ricchiuto, M., & Sármány, D. (2020). Space–time residual distribution on moving meshes. Computers and Mathematics with Applications, 79(5), 1561-1589. https://doi.org/10.1016/j.camwa.2019.09.019

This article investigates the potential for an r-adaptation algorithm to improve the efficiency of space–time residual distribution schemes in the approximation of time-dependent hyperbolic conservation laws, e.g. scalar advection, shallow water flow... Read More about Space–time residual distribution on moving meshes.

Cellular uptake and efflux of palbociclib in vitro in single cell and spheroid models (2019)
Journal Article
Jove, M., Spencer, J. A., Hubbard, M. E., Holden, E. C., O'Dea, R. D., Brook, B. S., Phillips, R. M., Smye, S. W., Loadman, P., & Twelves, C. J. (2019). Cellular uptake and efflux of palbociclib in vitro in single cell and spheroid models. Journal of Pharmacology and Experimental Therapeutics, 370(2), 242-251. https://doi.org/10.1124/jpet.119.256693

Adequate drug distribution through tumors is essential for treatment to be effective. Palbociclib is a cyclin-dependent kinase 4/6 inhibitor approved for use in patients with hormone receptor positive, human epidermal growth factor receptor 2 negativ... Read More about Cellular uptake and efflux of palbociclib in vitro in single cell and spheroid models.

An efficient numerical algorithm for a multiphase tumour model (2019)
Journal Article
Alrehaili, A. H., Walkley, M. A., Jimack, P., & Hubbard, M. E. (2019). An efficient numerical algorithm for a multiphase tumour model. Computers and Mathematics with Applications, 78(8), 2734-2745. https://doi.org/10.1016/j.camwa.2019.04.017

© 2019 This paper is concerned with the development and application of optimally efficient numerical methods for the simulation of vascular tumour growth. This model used involves the flow and interaction of four different, but coupled, phases which... Read More about An efficient numerical algorithm for a multiphase tumour model.

Drug delivery in a tumour cord model: a computational simulation (2017)
Journal Article
Hubbard, M. E., Jove, M., Loadman, P., Phillips, R., Twelves, C., & Smye, S. (2017). Drug delivery in a tumour cord model: a computational simulation. Royal Society Open Science, 4, https://doi.org/10.1098/rsos.170014

The tumour vasculature and microenvironment is complex and heterogeneous, contributing to reduced delivery of cancer drugs to the tumour. We have developed an in silico model of drug transport in a tumour cord to explore the effect of different drug... Read More about Drug delivery in a tumour cord model: a computational simulation.

Bayesian calibration, validation and uncertainty quantification for predictive modelling of tumour growth: a tutorial (2017)
Journal Article
Collis, J., Connor, A. J., Paczkowski, M., Kannan, P., Pitt-Francis, J., Byrne, H. M., & Hubbard, M. E. (2017). Bayesian calibration, validation and uncertainty quantification for predictive modelling of tumour growth: a tutorial. Bulletin of Mathematical Biology, 79(4), 939-974. https://doi.org/10.1007/s11538-017-0258-5

In this work we present a pedagogical tumour growth example, in which we apply calibration and validation techniques to an uncertain, Gompertzian model of tumour spheroid growth. The key contribution of this article is the discussion and application... Read More about Bayesian calibration, validation and uncertainty quantification for predictive modelling of tumour growth: a tutorial.

Effective equations governing an active poroelastic medium (2017)
Journal Article
Collis, J., Brown, D., Hubbard, M. E., & O'Dea, R. D. (2017). Effective equations governing an active poroelastic medium. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2198), https://doi.org/10.1098/rspa.2016.0755

In this work we consider the spatial homogenization of a coupled transport and fluid-structure interaction model, to the end of deriving a system of effective equations describing the flow, elastic deformation, and transport in an active poroelastic... Read More about Effective equations governing an active poroelastic medium.

The impact of electrode resistance on the biogalvanic characterisation technique (2016)
Journal Article
Chandler, J., Head, D., Hubbard, M. E., Neville, A., Jayne, D., & Culmer, P. (2016). The impact of electrode resistance on the biogalvanic characterisation technique. Physiological Measurement, 38(2), https://doi.org/10.1088/1361-6579/38/2/101

Measurement of a tissue-specific electrical resistance may offer a discriminatory metric for evaluation of tissue health during cancer surgery. With a move toward minimally-invasive procedures, applicable contact sensing modalities must be scalable,... Read More about The impact of electrode resistance on the biogalvanic characterisation technique.

A multiscale analysis of drug transport and response for a multiphase tumor model (2016)
Journal Article
Collis, J., Hubbard, M. E., & O'Dea, R. D. (in press). A multiscale analysis of drug transport and response for a multiphase tumor model. European Journal of Applied Mathematics, https://doi.org/10.1017/S0956792516000413

In this article we consider the spatial homogenization of a multi- phase model for avascular tumour growth and response to chemother- apeutic treatment. The key contribution of this work is the derivation of a system of homogenized partial differenti... Read More about A multiscale analysis of drug transport and response for a multiphase tumor model.

Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth (2016)
Journal Article
Collis, J., Hubbard, M. E., & O'Dea, R. D. (2016). Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth. Computer Methods in Applied Mechanics and Engineering, 309, https://doi.org/10.1016/j.cma.2016.06.015

In this work we consider the discretization of a recently formulated (Collis et al., [22]) multiscale model for drug- and nutrient-limited tumour growth. The key contribution of this work is the proposal of a discontinuous Galerkin finite element sch... Read More about Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth.

An optimally efficient technique for the solution of systems of nonlinear parabolic partial differential equations (2016)
Journal Article
Yang, F.-W., Goodyer, C. E., Hubbard, M. E., & Jimack, P. K. (2017). An optimally efficient technique for the solution of systems of nonlinear parabolic partial differential equations. Advances in Engineering Software, 103, https://doi.org/10.1016/j.advengsoft.2016.06.003

This paper describes a new software tool that has been developed for the efficient solution of systems of linear and nonlinear partial differential equations (PDEs) of parabolic type. Specifically, the software is designed to provide optimal computat... Read More about An optimally efficient technique for the solution of systems of nonlinear parabolic partial differential equations.

Inertial effects on thin-film wave structures with imposed surface shear on an inclined plane (2016)
Journal Article
Sivapuratharasu, M., Hibberd, S., Hubbard, M. E., & Power, H. (2016). Inertial effects on thin-film wave structures with imposed surface shear on an inclined plane. Physica D: Nonlinear Phenomena, 325, 86-97. https://doi.org/10.1016/j.physd.2016.03.008

This study provides an extended approach to the mathematical simulation of thin-film flow on a flat inclined plane relevant to flows subject to high surface shear. Motivated by modelling thin-film structures within an industrial context, wave structu... Read More about Inertial effects on thin-film wave structures with imposed surface shear on an inclined plane.

Nonlinear multigrid methods for second order differential operators with nonlinear diffusion coefficient (2014)
Journal Article
Brabazon, K. J., Hubbard, M. E., & Jimack, P. K. (2014). Nonlinear multigrid methods for second order differential operators with nonlinear diffusion coefficient. Computers and Mathematics with Applications, 68(12A), https://doi.org/10.1016/j.camwa.2014.11.002

Nonlinear multigrid methods such as the Full Approximation Scheme (FAS) and Newton-multigrid (Newton-MG) are well established as fast solvers for nonlinear PDEs of elliptic and parabolic type. In this paper we consider Newton-MG and FAS iterations ap... Read More about Nonlinear multigrid methods for second order differential operators with nonlinear diffusion coefficient.

Runge-Kutta residual distribution schemes (2014)
Journal Article
Warzynski, A., Hubbard, M. E., & Ricchiuto, M. (2015). Runge-Kutta residual distribution schemes. Journal of Scientific Computing, 62(3), https://doi.org/10.1007/s10915-014-9879-0

We are concerned with the solution of time-dependent non-linear hyperbolic partial differential equations. We investigate the combination of residual distribution methods with a consistent mass matrix (discretisation in space) and a Runge–Kutta-type... Read More about Runge-Kutta residual distribution schemes.

Mathematical and computational models of drug transport in tumours (2014)
Journal Article
Groh, C., Hubbard, M. E., Jones, P., Loadman, P., Periasamy, N., Sleeman, B., Smye, S., Twelves, C., & Phillips, R. (2014). Mathematical and computational models of drug transport in tumours. Interface, 11(94), Article 20131173. https://doi.org/10.1098/rsif.2013.1173

The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and sched... Read More about Mathematical and computational models of drug transport in tumours.