Professor Matthew Hubbard's Outputs (4)

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.

A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries (2014)
Journal Article
Morales-Hernandez, M., Hubbard, M. E., & Garcia-Navarro, P. (2014). A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries. Journal of Computational Physics, 263, https://doi.org/10.1016/j.jcp.2014.01.019

A 2D Large Time Step (LTS) explicit scheme on structured grids is presented in this work. It is first detailed and analysed for the 2D linear advection equation and then applied to the 2D shallow water equations. The dimensional splitting technique a... Read More about A 2D extension of a large time step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries.