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Example Programs

This directory contains example programs that illustrate the use of the index_map_type Fortran module.

The compiled executables require no input. The serial executables are run like any normal executable. Running the parallel executables varies. For example:

  • MPI version: 
    $ mpirun -np <N> ./disk-fv-parallel
  • Coarray version:

    • NAG:

      $ NAGFORTRAN_NUM_IMAGES=<N> ./disk-fv-parallel

    • Intel:

      $ FOR_COARRAY_NUM_IMAGES=<N> ./disk-fv-parallel

      NOTE: When running on a single shared memory machine, it may be necessary to set the environment variable I_MPI_FABRICS=shm:ofi to force Intel's MPI to use shared memory transport. Otherwise performance may be significantly poorer.

    • GFortran:

      $ cafrun -n <N> ./disk-fv-parallel

Finite Volume Solution of the Heat Equation on a Unit Disk

The program disk-fv-parallel.F90 solves the heat equation $u_t = \Delta u$ on the unit disk subject to zero boundary conditions. It uses a simple finite volume discretization on a regular 2D Cartesian mesh that covers the unit disk. Only those cells whose center is contained in the unit disk are included in the problem. The unknowns are cell-centered values of $u$. Simple first-order forward Euler time stepping is used to solve from a uniform initial condition to a final time. Domain decomposition is used to parallelize the computation. The cells are numbered according to the usual order of the elements of a rank-2 array (but only for those included in the problem) and then partitioned into approximately equal blocks, one per process (i.e., MPI rank or coarray image). There is a single indirect indexing array that maps a cell index to the cell indices of its neighboring cells. For comparison, the program disk-fv-serial.F90 is a serial version of the solver. Aside from the initial setup of the parallel decomposition of the problem, the only difference between the parallel solver and the serial solver is a single call to index_map%gather_offp to update the off-process elements of the local unknown array with values from their corresponding on-process elements on neighboring processes -- a parallel halo exchange operation.

The size of the problem is easily changed by setting the NZ parameter at the top of the programs to the desired value.

Finite Element Solution of the Heat Equation on a Unit Disk

The program disk-fem-parallel.F90 solves the heat equation $u_t = \Delta u$ on the unit disk subject to zero boundary conditions. It uses a Galerkin finite element discretization with bilinear elements on a regular 2D Cartesian mesh that covers the unit disk. Only those cells with at least one node contained in the interior of the unit disk are included in the problem. The unknowns are nodal values of $u$ for nodes contained in the interior of the unit disk. In order to avoid complexities associated with the need to solve a linear system, a lumped mass matrix and simple first-order forward Euler time stepping are used to solve from a uniform initial condition to a final time. Domain decomposition is used to parallelize the computation. The cells are numbered according to the usual order of the elements of a rank-2 array (but only for those included in the problem) and then partitioned into approximately equal blocks, one per process (i.e., MPI rank or coarray image). The nodes are similarly numbered, and are partitioned compatibly with the cells: a node is assigned to a partition of one of its adjacent cells. There is a single indirect indexing array that maps a cell index to the indices of its adjacent nodes. For comparison, the program disk-fem-serial.F90 is a serial version of the solver. Aside from the initial setup of the parallel decomposition of the problem, the only difference in the parallel solver are two parallel halo exchange calls: a call to index_map%gather_offp at the beginning of each time step to update the off-process elements of the local unknown array, and a later call to index_map%scatter_offp_sum to complete the FE assembly of the right-hand-side Laplacian term.

The size of the problem is easily changed by setting the NZ parameter at the top of the programs to the desired value.

Redistribution of a Distributed Array

The program redistribute.F90 illustrates how the index_map type can be used to redistribute the elements of an array distributed according to one partitioning of its index set to another array that is distributed according to another partitioning of the index set.