Reaction-diffusion(RD) systems form a class of PDEs used to model pattern-formation. In their most basic form, they involve an interplay between a linear model of diffusion and non-linear model of reaction between multiple species, which can result in a heterogeneous solution(pattern) under seemingly inconspicuous initial conditions. They arose in the then nascent field of mathematical biology with the foundational work of Alan Turing, and since then, have been applied to a wide range of scenarios.
This repository is intended to be a collection of C++ codes to model different RD systems. The numerical implementation constitutes a Finite Element(FE) approximation to the system of PDEs and the codes are built on the deal.II open source FE library.
FE Package : deal.II(version 9.2)
deal.II prerequisites : MPI, P4EST(version 2.2), BLAS/LAPACK, Trilinos(version 13.0.1)
- MPI : On an HPC platform there will most likely be an MPI implementation which can be loaded as a module. On the desktop the appropriate package manager can be used to install the required libraries. For example, an OpenMPI distribution can be installed in ubuntu as follows :
sudo apt-get install libopenmpi-dev openmpi-bin
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P4EST : Installation instructions can be found here.
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BLAS/LAPACK : On an HPC platform, there will most likely be some BLAS/LAPACK implementation which can be loaded as a module. On the desktop the appropriate package manager can be used to install the relevant libraries. For example, one can install BLAS/LAPACK in ubuntu as follows :
sudo apt-get install libblas3
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Trilinos : Installation instructions can be found here.
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deal.II : Once the prerequisites have installed successfully, deal.II version 9.2.0 can be cloned an installed following the instructions here.
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After installing deal.II make sure to initialize the environment variable DEAL_II_DIR as the absolute path to the deal.II installation.
The code can be compiled as :
cmake . ; make
and run as :
mpirun -np $NPROCS $EXECUTABLE $INPUTFILE
where $NPROCS refers to the number of processors, $EXECUTABLE refers to the problem executable created after compilation, and $INPUTFILE is the input file supplied by the user. For example, in the Schnakenberg folder the executable is RD_PBC which is generated after compiling RD_PBC.cc. The file testinp.prm is the input file which is typically modified by the user to provide the required inputs to the problem.