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Heat equation decomposed in two dimensions

Note: this is very advanced exercise. It is meant more for illustration what can be done with derived datatypes, and as something one might want to study after the course, rather than completing during the course.

If you are not familiar with the two dimensional heat equation, please have a look for basic description in "Parallel programming with MPI" exercise material.

Here, starting point is a working code parallelized over columns (in Fortran) or rows (in C/C++).

Before starting with this exercise, it is recommended that you have the usage of Cartesian communicator implemented.

  1. Modify the creation of Cartesian communicator so that the decomposition is done in two dimensions, and determine all four neighbors (up, down, left, right).

  2. As the rows (in Fortran) or columns (in C/C++) are not contiguous in the computer memory, one needs to use user-defined datatypes when communicating in the exchange() routine in cpp/core.cpp or fortran/core.F90. In order to make code more symmetric, one can utilize derived type also for the contiguous dimension. Create required datatypes (it is recommended to store them as attributes in "parallel" data structure).

  3. Perform the halo exchange with MPI_Neighbor_alltoallw. Together with the user defined datatypes, no temporary buffers are needed in the user code. In order to use MPI_Neighbor_alltoallw, you need to determine the correct displacements both in sending and receiving.

  4. In the base version, the I/O routines write_field and read_field (in cpp/core.cpp or fortran/core.F90) use temporary buffers for communication. Create appropriate datatype and utilize it in I/O related communication. Note that you need also the coordinates of processes in the cartesian grid in order to read from / write to the correct part of the global temperature field.