PETSc Options#

PyLith relies on PETSc for finite-element data structures, linear and nonlinear solvers, and time-stepping algorithms. PETSc has its own object-oriented interface for specifying runtime options. PyLith provides two mechanisms for passing options to PETSc:

  1. Default values that are controlled by a few flags in the PyLith Problem petsc_defaults facility, and

  2. PyLith petsc facility which passes options directly to PETSc.

When using the default values, PyLith selects solver and preconditioner options based on the governing equations. In most cases these default values will give good performance and you do not need to specify any PETSc options. The user-specified values always take precedence over the default values.

Default PETSc Options#

Note

New in v3.0.0

We separate the defaults into a few categories to make it easy to select desired options.

solver:

Options for the preconditioner and solver;

parallel:

Options used when running in parallel (can be used in serial as well);

monitors:

Options for basic monitoring of the solver;

collective_io:

Options for collective input/output; and

testing:

Options used in testing.

Tip

You can see which options PyLith sets using the petscoptions Pyre Journal. Either use the --journal.info.petscoptions command line argument or in your .cfg file include

[journal.info]
petscoptions = 1

See also

See PetscDefaults Component for more information about the the Pyre interface for specifying default PETSc options.

Solver Options#

The solver options are enabled by default. PyLith selects options based on the governing equation, formulation, presence of a fault, and whether the simulation is running in parallel. In some cases the solver settings for running in parallel are different than those for running in serial; in such cases, the settings for running in parallel often given give comparable or better performance. If you have a moderate or large simulation, you should enable the parallel settings. Additionally, PyLith specifies general options related to the solver tolerances and triggering errors if the linear or nonlinear solver fails to converge. The different sets of defaults are detailed in the following code blocks.

Warning

When running in parallel in cases where a fault face is split across processes, the current solver settings will result in a diverged solution. We attempt to prevent this from happening by specifying a penalty for splitting across the fault. In cases where these settings fail and the solver diverges, you can fall back to the previous settings by using the field split preconditioner in share/settings/solver_fault_fieldsplit.cfg. Simply add this .cfg file to your command line options.

This issue will go away once we implement parallel mesh loading.

Warning

If you do use the field split fall back, you need to be aware that it also has deficiencies. The split fields and algebraic multigrid preconditioning currently fails in problems with a nonzero null space. This most often occurs when a problem contains multiple faults that extend through the entire domain and create subdomains without any Dirichlet boundary conditions. The workaround is to use the ilu preconditioner. However, it only works in serial. An alternative is to use the asm preconditioner (Additive Schwarz) which works in parallel and serial.

Listing 3 PETSc options set whenever the solver defaults are enabled.#
[pylithapp.petsc]
ksp_rtol = 1.0e-12
ksp_atol = 1.0e-12
ksp_error_if_not_converged = true

snes_rtol = 1.0e-12
snes_atol = 1.0e-9
snes_error_if_not_converged = true

Quasistatic Elasticity#

Listing 4 PETSc options used for quasistatic elasticity in serial without a fault.#
[pylithapp.petsc]
ts_type = beuler
pc_type = lu
Listing 5 PETSc options used for quasistatic elasticity in parallel without a fault.#
[pylithapp.petsc]
ts_type = beuler
pc_type = gamg

The Lagrange multiplier corresponding to the tractions on the fault introduces a saddle point in the system of equations. We could use a Schur complement approach, but we have found that grouping the degrees of freedom on each side of the fault into blocks and using a variable point-block Jacobi preconditioner provides better results; the number of iterations remains nearly constant with increased problem size and the overall solution time is low.

Listing 6 PETSc options used for quasistatic elasticity with a fault.#
[pylithapp.petsc]
dm_reorder_section = True
dm_reorder_section_type = cohesive

pc_type = gamg
mg_fine_pc_type = vpbjacobi

Quasistatic Incompressible Elasticity#

The pressure field introduces a saddle point in the system of equations, so we use a Schur complement approach.

Listing 7 PETSc options used for quasistatic incompressible elasticity in serial.#
[pylithapp.petsc]
ts_type = beuler
pc_type = fieldsplit
pc_fieldsplit_type = schur

pc_fieldsplit_schur_factorization_type = full
pc_fieldsplit_schur_precondition = full

fieldsplit_displacement_pc_type = lu
fieldsplit_pressure_pc_type = lu
Listing 8 PETSc options used for quasistatic incompressible elasticity in parallel.#
[pylithapp.petsc]
ts_type = beuler
pc_type = fieldsplit
pc_fieldsplit_type = schur

pc_fieldsplit_schur_factorization_type = full
pc_fieldsplit_schur_precondition = full

fieldsplit_displacement_pc_type = gamg
fieldsplit_displacement_mg_levels_pc_type = sor
fieldsplit_displacement_mg_levels_ksp_type = richardson
fieldsplit_pressure_pc_type = gamg
fieldsplit_pressure_mg_levels_pc_type = sor
fieldsplit_pressure_mg_levels_ksp_type = richardson

Quasistatic Poroelasticity#

Listing 9 PETSc options used for quasistatic poroelasticity in serial.#
[pylithapp.petsc]
ts_type = beuler
pc_type = fieldsplit
pc_fieldsplit_type = multiplicative
pc_fieldsplit_0_fields = 2
pc_fieldsplit_1_fields = 1
pc_fieldsplit_2_fields = 0
fieldsplit_trace_strain_pc_type = bjacobi
fieldsplit_pressure_pc_type = bjacobi
fieldsplit_displacement_pc_type = lu
Listing 10 PETSc options used for quasistatic poroelasticity in parallel.#
[pylithapp.petsc]
pc_type = fieldsplit
pc_fieldsplit_type = multiplicative
pc_fieldsplit_0_fields = 2
pc_fieldsplit_1_fields = 1
pc_fieldsplit_2_fields = 0
fieldsplit_trace_strain_pc_type = bjacobi
fieldsplit_pressure_pc_type = bjacobi
fieldsplit_displacement_pc_type = ml
fieldsplit_displacement_ksp_type = gmres
Listing 11 PETSc options used for quasistatic poroelasticity with a porosity state variable in serial. The second set of parameters are the additional parameters needed for the additional solution subfields.#
[pylithapp.petsc]
ts_type = beuler
pc_type = fieldsplit
pc_fieldsplit_type = multiplicative
pc_fieldsplit_0_fields = 2
pc_fieldsplit_1_fields = 1
pc_fieldsplit_2_fields = 0
fieldsplit_trace_strain_pc_type = bjacobi
fieldsplit_pressure_pc_type = bjacobi
fieldsplit_displacement_pc_type = lu

pc_fieldsplit_3_fields = 3
pc_fieldsplit_4_fields = 4
pc_fieldsplit_5_fields = 5
fieldsplit_velocity_pc_type = bjacobi
fieldsplit_pressure_t_pc_type = bjacobi
fieldsplit_trace_strain_t_pc_type = bjacobi
Listing 12 PETSc options used for quasistatic poroelasticity with a porosity state variable in parallel. The second set of parameters are the additional parameters needed for the additional solution subfields.#
[pylithapp.petsc]
pc_type = fieldsplit
pc_fieldsplit_type = multiplicative
pc_fieldsplit_0_fields = 2
pc_fieldsplit_1_fields = 1
pc_fieldsplit_2_fields = 0
fieldsplit_trace_strain_pc_type = bjacobi
fieldsplit_pressure_pc_type = bjacobi
fieldsplit_displacement_pc_type = ml
fieldsplit_displacement_ksp_type = gmres

pc_fieldsplit_3_fields = 3
pc_fieldsplit_4_fields = 4
pc_fieldsplit_5_fields = 5
fieldsplit_velocity_pc_type = bjacobi
fieldsplit_pressure_t_pc_type = bjacobi
fieldsplit_trace_strain_t_pc_type = bjacobi

Monitoring#

The monitoring options are enabled by default and provide a few lines of output per time step summarizing the operation of the linear and nonlinear solvers and time stepping. Additional monitoring can be turned on using the user-specified options.

Listing 13 Default PETSc options for monitoring.#
# Turn off monitoring options (enabled by default).
[pylithapp.problem.petsc_defaults]
monitoring = False

# Corresponding PETSc options
[pylithapp.petsc]
ksp_converged_reason = true

snes_converged_reason = true
snes_monitor = true

ts_monitor = true
ts_error_if_step_fails = true

Collective I/O#

The collective input and output options are enabled by default and turn on HDF5 collective output. We use parallel HDF5 implementation, which in turn relies on MPI IO. Many MPI IO implementations require collective input and output to be enabled for parallel HDF5 output even if only one process is being used.

Listing 14 Default PETSc options for collective input and output.#
[pylithapp.problem.petsc_defaults]
collective_io = True

# Corresponding PETSc options
[pylithapp.petsc]
viewer_hdf5_collective = true

Testing#

The options in the testing category are intended for use in internal testing. These options help identify memory leaks in PETSc data structures and inconsistent back traces.

Listing 15 Default PETSc options for testing.#
# Turn on testing options (turned off by default).
[pylithapp.problem.petsc_defaults]
testing = True

# Corresponding PETSc options
[pylithapp.petsc]
malloc_dump = true

User-Specified PETSc Options#

Table 8 shows the main monitoring options offered by PETSc. When optimizing and troubleshooting solver options, we usually turn on all the monitoring.

Table 8 Description of PETSc monitoring options#

Option

Description

log_view

Show logging objects and events.

ts_monitor

Show time-stepping progress.

ksp_monitor

Show preconditioned residual norm.

ksp_view

Show linear solver parameters.

ksp_error_if_not_converged

Generate an error if linear solver does not converge.

ksp_converged_reason

Indicate why iterating stopped in linear solve.

snes_monitor

Show residual norm for each nonlinear solve iteration.

snes_view

Show nonlinear solver parameters.

snes_error_if_not_converged

Generate an error if nonlinear solver does not converge.

snes_converged_reason

Indicate why iterating stopped in nonlinear solve.

snes_linesearch_monitor

Show line search information in nonlinear solve.

Solver Options#

For most problems we use the GMRES method from Saad and Schultz [1986] for the linear solver; this is the linear solver PETSc uses as the default. See PETSc linear solver table for a list of PETSc options for linear solvers and preconditioners.

Tip

It is important to keep in mind the resolution of the model and observations when setting solver tolerances. For example, matching observations with an accuracy of 1.0 mm does not require solving the equations to an accuracy of 0.0001 mm.

Table 9 Summary of PETSc solver tolerances.#

Option

Description

ksp_rtol

Stop iterating when the preconditioned KSP residual norm has this amount relative to its starting value.

ksp_atol

Stop iterating when the preconditioned KSP residual normal is smaller than this value.

snes_rtol

Stop iterating when the SNES residual norm has this amount relative to its starting value.

snes_atol

Stop iterating when the SNES residual normal is smaller than this value.