Applying a patched mesh method to
efficiently solve a singularly perturbed reaction-diffusion
problem
José Luis
Gracia,
Niall Madden and
Thái Anh Nhan
Abstract
The solution of linear systems of equations that arise when
singularly perturbed partial differential equations
are discretized can be difficult:
direct solvers scale poorly, but are also known not to be robust
with respect to the perturbation parameter,
while the design of parameter robust preconditioners is not trivial,
primarily due to the specialised layer adapted meshes
used for such problems [MacLachlan and Madden, 2013].
Here we present a multigrid solver strategy
that circumvents this problem by using a robust patched mesh
method [de Falca and O'Riordan, 2009], as well as permitting
parallelization. Numerical results
demonstrate the efficiency of the method.