PaReDiSo: A reaction-diffusion solver coupled with OpenMPI and CVODE

Reaction-diffusion systems are ubiquitous in nature, therefore they are widely studied both experimentally and theoretically. The driving force behind reaction-diffusion phenomena can be investigated via numerical modeling. However, in many cases the differential equations describing the systems are stiff, thus small temporal time step and high spatial resolution are required. These conditions result in expensive calculations, which hinders the exploration of such systems.PaReDiSo, is an open source program, developed to solve any kind of reaction-diffusion systems in two spatial dimensions. The kinetic equations with rate coefficients, the initial and boundary conditions specific to the system have to be provided in a user-friendly manner. Moreover, the frequently used boundary conditions, such as the Neumanm, Dirichlet and periodic boundaries, are built in the software. Due to the utilized CVODE integrator module both stiff and non-stiff equations can be solved. The software enables the user to run the calculations in parallel mode, using multiple CPU threads, since OpenMPI libraries are implemented. Thus, significant decrease in the required calculation time can be achieved.In this article the algorithm and the usage of the program is presented. The capabilities of the solver are tested on three commonly known reaction-diffusion phenomena: Turing pattern formation, Belousov-Zhabotinsky waves propagation, and diffusive fingering by autocatalysis. The results are validated on experimental end theoretical data found in the literature. Moreover, a performance test was executed, to investigate the extent of acceleration by the parallelization. Program summary Program Title: PaReDiSoCPC Library link to program files: https://doi.org/10.17632/4ttyd4zxst.1Licensing provisions: MITProgramming language: C and MPISupplementary material: User ManualExternal routines/libraries: MPI, SUNDIALSNature of problem: The modeling of reaction-diffusion systems in two spatial dimensions can be a challenging task. In many cases fine spatial discretization is needed which hugely increases the calculation time. Moreover, the kinetic differential equations describing the system tend to be stiff, which require small time steps and advanced numerical methods.Solution method: PaReDiSo can be customized for the users' needs (unique reaction equation, mesh, grid, boundary and initial conditions) in a user friendly manner. The code can be run in parallel mode, dramatically decreasing the required computational time. In order to deal with the stiff differential equations, the CVODE library of SUNDIALS software package is used by the source code.