Experiences with algebraic multigrid for a 2D and 3D biological respiration-diffusion model

Dominik Smits, Stefan Vandewalle
Katholieke Universiteit Leuven, Department of Computerscience, Celestijnenlaan 200A, B-3001 Leuven, Belgium

Nico Scheerlinck, Bart Nicolaï
Katholieke Universiteit Leuven, Laboratory for PostHarvest Technology, De Croylaan 42, B-3001 Leuven, Belgium


At the Laboratory of PostHarvest Technology of the 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 Conférence 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 consist 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 using 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 Stüben, at the Fraunhofer Institute for Algorithms and Scientific Computing, Sankt Augustin, Germany. 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. The AMG-results will be compared with the results obtained with classical, single-level solvers.