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math.NA2015
An introduction to the analysis and implementation of sparse grid finite element methods
Stephen Russell, Niall Madden
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 partia…
math.NA2015
Cholesky factorisation of linear systems coming from finite difference approximations of singularly perturbed problems
Thái Anh Nhan, Niall Madden
We consider the solution of large linear systems of equations that arise when two-dimensional singularly perturbed reaction-diffusion equations are discretized. Standard methods fo…