International Congress on Computational and Applied Mathematics edition:15 location:Leuven, Belgium date:5-9 July 2010
We present a simulation procedure to compute the concentration of chemical particles in a growing apple. This simulation can be used to gain insight into the growth and ripening process of apple fruit. These processes are modelled by a set of time-dependent, nonlinear reaction-diffusion partial differential equations. A stochastic Galerkin finite element approach is applied to quantify the impact of uncertainty on the simulation outcomes. This method converts the problem into a large coupled set of deterministic problems. It is combined with a Newton linearization of the nonlinear reaction terms. An algebraic multigrid solver is presented to solve the resulting algebraic systems. This solver is shown to possess very good convergence properties with respect to the spatial, stochastic and time discretization parameters. A point-based smoothing approach is key to its performance.