Dominik Smits , Stefan Vandewalle, Nico Scheerlinck, Bart Nicoai :
Algebraic multigrid for a 2D and 3D biological respiration-diffusion model
At the Laboratory of PostHarvest Technology (University of Leuven), a respiration-diffusion model is
being developed and studied for the oxygen consumption and carbon dioxyde production inside harvested
fruit (in particular for the Conference pear). The research aims at a better understanding of the
respiratory activity of fruit and the causes that affect the onset of certain fruit diseases
(e.g., the diseases 'brown and hollow' or 'core breakdown'). The current mathematical model consists
of a set of two coupled non-linear reaction diffusion equations, defined on a two- or three-dimensional
domain, with a mixed type of boundary condition.
In this talk, we will present our experiences with the use of an algebraic multigrid method for
solving the set of equations obtained after a finite element discretization of the mathematical model.
We have concentrated on the use of the recent version of the systems AMG code developed by
Klaus St¨ben, at the Fraunhofer Institute for Algorithms and Scientific Computing, Sankt Augustin.
We will consider its application for solving both the steady-state problem and the time-evolution
problem. For the latter case, we will discuss the use of different time-discretisation methods of
backward differentiation or implicit Runge-Kutta type. For the implicit Runge-Kutta method, we will
describe how to exploit the structure of the coefficient matrix by performing the AMG set-up phase
only for a submatrix. The AMG-results will be compared with the results obtained with
classical, single-level solvers.