Browsing by Author "Madden, Niall"
Now showing items 1-13 of 13
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A parameter-robust numerical method for a system of reaction–diffusion equations in two dimensions
Kellogg, R.B.; Madden, Niall; Stynes, Martin (Wiley-Blackwell, 2007-01-01) -
A parameter-uniform schwarz method for a coupled system of reaction–diffusion equations
Stephens, Meghan; Madden, Niall (Elsevier BV, 2009-08-01) -
Algorithms for the accurate and efficient solution of fourth order boundary-layer problems
Alssaedi, Faiza (NUI Galway, 2022-06-10)In this thesis, we study the analysis and numerical solution of second-order complex-valued reactiondiffusion equations, and two families of fourth-order singularly perturbed problems. The problems are all singularly ... -
An introduction to the analysis and implementation of sparse grid finite element methods
Russell, Stephen; Madden, Niall (Walter de Gruyter GmbH, 2017-01-01)Our goal is to present an elementary approach to the analysis and programming of sparse grid finite element methods. This family of schemes can compute accurate solutions to partial differential equations, but using far ... -
Bayesian networks for mathematical models: techniques for automatic construction and efficient inference
Enright, Catherine G.; Madden, Michael G.; Madden, Niall (Elsevier BV, 2013-02-01) -
Improved mathematical and numerical modelling of dispersion of a solute from a continuous source
Madden, Niall (2011)We present a refinement of a model due to Mondal and Mazumder [7] for dispersion of fine particles in an oscillatory turbulent flow. The model is based on the time-dependent advection-diffusion equation posed on a ... -
Moving mesh methods for problems with layer phenomena
Hill, Róisín (NUI Galway, 2022-06-10)This thesis is concerned with developing, implementing, testing and refining novel algorithms for generating layer-adapted meshes for the numerical solution of singularly perturbed differential equations (SPDEs). We consider ... -
On the application of robust numerical methods to a complete flow wave-current model. Boundary and Interior Layers ONERA
Madden, Niall (2004)We aim to show how parameter-robust numerical method may be employed to solve equations arising in the modelling of wave-current interactions.We present two such models: a complete flow model for wave-current interaction ... -
Preconditioning techniques for singularly perturbed differential equations
Nhan, Anh Thai (2015-09-23)This thesis considers computer methods for solving singularly perturbed differential equations. Standard algorithms are very inefficient when applied to these problems, although the exact reasons for this have not ... -
Robust solution of singularly perturbed problems using multigrid methods
MacLachlan, Scott; Madden, Niall (Society for Industrial & Applied Mathematics (SIAM), 2013-01-01)We consider the problem of solving linear systems of equations that arise in the numerical solution of singularly perturbed ordinary and partial differential equations of reaction-diffusion type. Standard discretization ... -
Robust solution of singularly perturbed problems using multigrid methods: analysis and results in one and two dimensions
Madden, Niall (2012)We consider the problem of solving linear systems of equations that arise in the numerical solution of singularly perturbed ordinary and partial differential equations of reaction-diffusion type. Standard discretization ... -
Sparse grid methods for singularly perturbed problems
Russell, Stephen (2016-05-09)This thesis is concerned with the design, analysis and implementation of sparse grid finite element methods applied to singularly perturbed partial differential equations, in two and three dimensions. Typically, sparse ... -
A two-weight scheme for a time-dependent advection-diffusion problem
Chadha, Naresh M.; Madden, Niall (2011)We consider a family of two-weight finite difference schemes for a time-dependent advection-diffusion problem. For a given uniform grid-spacing in time and space, and for a fixed value of advection and diffusion parameters, ...