heat-equation

Heat equation solver in parallel with MPI

Parallelise our implementation of a two-dimensional heat equation solver using MPI. See Code description for some theory and more details about the code.

To parallelise the code, one needs to divide the grid into blocks of columns (in Fortran) or rows (in C/C++) and assign each block to one MPI task. Or in other words, share the work among the MPI tasks by doing a domain decomposition.

The MPI tasks are able to update the grid independently everywhere else than on the boundaries -- there the communication of a single column (or row) with the nearest neighbour is needed. This can be achieved by having additional ghost-layers that contain the boundary data of the neighbouring tasks. As the system is aperiodic, the outermost ranks communicate with only one neighbour, and the inner ranks with two neighbours.

Some parts of the code are already parallelized (e.g. input/output), complete the parallelization as follows (marked with TODOs in the source code):

1. Initialize and finalize MPI in the main routine (cpp/main.cpp or fortran/main.F90)
2. Determine the number of MPI processes, rank, as well as the left (or up) and right (or down) neighbours of a domain in the routine parallel_setup() (in fortran/heat_mod.F90) or in the ParallelData() constructor (in cpp/heat.hpp
3. Use MPI_Send and MPI_Recv for implementing the "halo exchange" operation in the exchange() routine in cpp/core.cpp or fortran/core.F90.

To build the code, please use the provided Makefile (by typing make). By default, Intel compiler is used, in order to use gcc type make COMP=gnu.