poissbox

Testing solving the Poisson equation using iterative solvers

Building poissbox

poissbox is written in modern Fortran and depends on MPI and PETSc. A CMake build system is used, this should pick up your MPI compilers automatically, however to find PETSc you should set PKG_CONFIG_PATH to point to the PETSc package configuration directory, e.g.

export PKG_CONFIG_PATH=${PETSC_DIR}/lib/pkgconfig:${PKG_CONFIG_PATH}

The poissbox build can then be configured and run by executing

cmake -B build .
cmake --build build/

which should build the executable build/bin/poissbox.

The executable should run, printing how many ranks it is running on, followed by a "Hello world!" message from each rank, and the distribution of DoF between ranks (currently hardcoded as 64x64x64) e.g.

$ mpirun -np 3 ./build/bin/poissbox
 Running poissbox on            3  ranks
 Hello from            0
 Hello from            1
 Hello from            2
 Rank            0  has        90112  of       262144  expected:       262144
 Rank            1  has        86016  of       262144  expected:       262144
 Rank            2  has        86016  of       262144  expected:       262144

this confirms that no errors occur when initialising the PETSc data structures.

Running poissbox

Running the poissbox_demo executable as above will run with the PETSc default linear solver/preconditioner combination. A better solver and preconditioner for Poisson problems is multigrid-preconditioned conjugate gradient, this can be selected at runtime

$ mpirun -np 4 ./build/bin/poissbox_demo -ksp_type cg -pc_type gamg -mg_coarse_sub_pc_type svd \
    -mg_levels_ksp_rtol 1.0e-4 -mg_levels_ksp_type richardson -mg_levels_pc_type sor

where the first 2 options set the linear solver and preconditioner, the rest are recommended customisations of the multigrid preconditioner from PETSc that have also been found effective here. The tolerance can be controlled by setting -ksp_rtol, additional information on the linear solver can be printed by adding -ksp_monitor -ksp_converged_reason.