This repository contains solvers for testing the parallel performance of DOLFINx and the underlying linear solvers. It tests elliptic equations

• Poisson equation and elasticity - in three dimensions.

Representative performance data is available at https://fenics.github.io/performance-test-results/.

The source of the tests is in src/ directory.

• FEniCSx/DOLFINx installation (development version of DOLFINx required)
• PETSc installation
• Boost Program Options

In the src/ directory, build the program:

    cmake .
    make

Options for the test are:

• Problem type (--problem_type): poisson or elasticity
• Scaling type (--scaling_type): strong (fixed problem size) or weak (fixed problem size per process)
• Number of degrees-of-freedom (--ndofs): total (in case of strong scaling) or per process (for weak scaling)
• Order (--order): polynomial order (1, 2, or 3) - only on cube mesh, defaults to 1.
• File output (--output): true or false (IO performance depends heavily on the underlying filesystem)
• Data output directory (--output_dir): directory to write solution data to

Linear solver options are configured via PETSc command line options, (single hyphen) as shown below.

Suggested options for running tests are listed below. The options include PETSc performance logging which is useful for assessing performance.

For elasticity, a conjugate gradient (CG) solver with a smoothed aggregation algebraic multigrid (GAMG) preconditioner is recommended. For a weak scaling test with 8 MPI processes and 500k degrees-of-freedom per process:

mpirun -np 8 ./dolfinx-scaling-test \
--problem_type elasticity \
--scaling_type weak \
--ndofs 500000 \
-log_view \
-ksp_view \
-ksp_type cg \
-ksp_rtol 1.0e-8 \
-pc_type gamg \
-pc_gamg_coarse_eq_limit 1000 \
-mg_levels_ksp_type chebyshev \
-mg_levels_pc_type jacobi \
-mg_levels_esteig_ksp_type cg \
-matptap_via scalable \
-options_left

For a strong scaling test, with 8 MPI processes and 10M degrees-of-freedom in total:

mpirun -np 8 ./dolfinx-scaling-test \
--problem_type elasticity \
--scaling_type strong \
--ndofs 10000000 \
-log_view \
-ksp_view \
-ksp_type cg \
-ksp_rtol 1.0e-8 \
-pc_type gamg \
-pc_gamg_coarse_eq_limit 1000 \
-mg_levels_ksp_type chebyshev \
-mg_levels_pc_type jacobi \
-mg_levels_esteig_ksp_type cg \
-matptap_via scalable \
-options_left

For the Poisson equation, a conjugate gradient (CG) solver with a classical algebraic multigrid (BoomerAMG) preconditioner is recommended. For a weak scaling test with 8 MPI processes and 500k degrees-of-freedom per process:

mpirun -np 8 ./dolfinx-scaling-test \
--problem_type poisson \
--scaling_type weak \
--ndofs 500000 \
-log_view \
-ksp_view \
-ksp_type cg \
-ksp_rtol 1.0e-8 \
-pc_type hypre \
-pc_hypre_type boomeramg \
-pc_hypre_boomeramg_strong_threshold 0.7 \
-pc_hypre_boomeramg_agg_nl 4 \
-pc_hypre_boomeramg_agg_num_paths 2 \
-options_left

For a strong scaling test, with 8 MPI processes and 10M degrees-of-freedom in total:

mpirun -np 8 ./dolfinx-scaling-test \
--problem_type poisson \
--scaling_type strong \
--ndofs 10000000 \
-log_view \
-ksp_view \
-ksp_type cg \
-ksp_rtol 1.0e-8 \
-pc_type hypre \
-pc_hypre_type boomeramg \
-pc_hypre_boomeramg_strong_threshold 0.7 \
-pc_hypre_boomeramg_agg_nl 4 \
-pc_hypre_boomeramg_agg_num_paths 2 \
-options_left

The default loglevel diagnostic messages from DOLFINx will be present, and if -log_view is specified, there will be a performance profile from PETSc. There's also a "Test problem summary" summarizing the test parameters and environment to aid with reproducibility. Finally, there's a table labeled "Summary of timings" that contains various times (in units of seconds) of interest, the parts that are explicit to this test are labeled ZZZ. We elaborate on some:

• ZZZ Create Mesh: Create the mesh to be used as the spatial discretisation of the domain in the FE problem
• ZZZ Create facets and facet->cell connectivity: Compute the topology connectivity of the mesh's graph, i.e. compute the relationship between which cells are connected to each facet.
• ZZZ FunctionSpace: Create the function space in which the finite element method solution will be sought along with appropriate index maps for each degree of freedom and their relationship with the mesh.
• ZZZ Assemble: Encompassing timer for:
  • ZZZ Create boundary conditions: Find the mesh’s topological indices and corresponding degree of freedom indices on which to impose boundary data in a strong Dirichlet sense.
  • ZZZ Create RHS function: This is the step computing the function $f$ in the cases where $\nabla^2u=-f$ (Poisson) and $\nabla\cdot u=-f$ (elasticity, i.e. elastostatics in this case).
  • ZZZ Assemble matrix: Assemble the finite element matrix $A$ underlying finite element formulation, such that we seek to later solve $A\vec{x}=\vec{b}$.
  • ZZZ Assemble vector: Assemble the right-hand-side vector $\vec{b}$.
• ZZZ Solve: Compute the solution of the linear system. This is typically the dominant stage taking the greatest computational effort.
• ZZZ Output: Postprocess and potentially output (with --output) results to disk.

Reference performance data is provided here to help in assessing performance on a given system.

The tests have been developed by Chris N. Richardson ([email protected]) and Garth N. Wells ([email protected]).

The code is covered by the MIT license. See LICENSE.md.