The impact of parameter selection on the performance of an automatic adaptive code for solving reaction–diffusion equations in three dimensions

Abstract

The performance of automatic codes for solving reaction–diffusion systems is controlled by a variety of parameters. Some of them are invisible to the user while others can be modified. For the latter default values are available. The effects of four such parameters are studied for a code that couples the method-of-lines in time with a high-order h-refinement finite element strategy in space. The key parameters considered are the ratio of the temporal error tolerance to the spatial error tolerance, two parameters governing convergence of the iterative methods for the linear and nonlinear systems, and the number of time steps between regridding. These parameters are typical in method-of-lines based codes. Computations on a model problem demonstrate that both small and large temporal to spatial error ratios lead to performance degradation as does less frequent regridding. They also show that insufficient convergence in the nonlinear solver can reduce the reliability of the spatial error estimates.