Common Information

In addition to the finite-element mesh, PyLith requires files to specify the simulation parameters. We specify parameters common to all simulations in a directory in pylithapp.cfg, which contains numerous comments, so we only summarize the parameters here.

Metadata, Mesh, and Output

The pylithapp.metadata section specifies metadata common to all simulations in the directory. We control the verbosity of the output written to stdout using journal.info. We set the parameters for importing the finite-element mesh in pylithapp.mesh_generator.

Physics

These quasi-static simulations solve the elasticity equation and include a fault, so we have a solution field with both displacement and Lagrange multiplier subfields.

(171)\[\begin{gather} \vec{s} = \left(\begin{array}{c} \vec{u} \quad \vec{\lambda} \end{array}\right)^T \\ \boldsymbol{\nabla} \cdot \boldsymbol{\sigma}(\vec{u}) = \vec{0} \end{gather}\]

We use the default TimeDependent problem and solution field with a single displacement subfield of basis order 1. In addition to output of the solution over the domain, we output the solution over the -y and +y boundaries.

Listing 69 Parameters for the solution and output of the solution on the -y and +y boundaries.

[pylithapp.problem]
solution = pylith.problems.SolnDispLagrange

[pylithapp.problem]
solution_observers = [domain, top_boundary, bot_boundary]
solution_observers.top_boundary = pylith.meshio.OutputSolnBoundary
solution_observers.bot_boundary = pylith.meshio.OutputSolnBoundary

[pylithapp.problem.solution_observers.top_boundary]
label = boundary_ypos
label_value = 13

[pylithapp.problem.solution_observers.bot_boundary]
label = boundary_yneg
label_value = 12

We use the same material properties in all of the simulations in this directory, so we specify them in pylithapp.cfg to avoid repeating the information in the file with parameters for each simulation. We have two materials with a contrast in the shear modulus across the fault.

Listing 70 Material parameters common to all simulations in this directory.

[pylithapp.problem]
materials = [elastic_xneg, elastic_xpos]

[pylithapp.problem.materials.elastic_xneg]
description = Material to on the -x side of the fault
label_value = 1

db_auxiliary_field = spatialdata.spatialdb.UniformDB
db_auxiliary_field.description = Elastic properties xneg
db_auxiliary_field.values = [density, vs, vp]
db_auxiliary_field.data = [2500.0*kg/m**3, 3.00*km/s, 5.29*km/s]

auxiliary_subfields.density.basis_order = 0
bulk_rheology.auxiliary_subfields.bulk_modulus.basis_order = 0
bulk_rheology.auxiliary_subfields.shear_modulus.basis_order = 0

derived_subfields.cauchy_strain.basis_order = 0
derived_subfields.cauchy_stress.basis_order = 0

[pylithapp.problem.materials.elastic_xpos]
description = Material to on the +x side of the fault
label_value = 2

db_auxiliary_field = spatialdata.spatialdb.UniformDB
db_auxiliary_field.description = Elastic properties xpos
db_auxiliary_field.values = [density, vs, vp]
db_auxiliary_field.data = [2500.0*kg/m**3, 4.24*km/s, 5.29*km/s]

auxiliary_subfields.density.basis_order = 0
bulk_rheology.auxiliary_subfields.bulk_modulus.basis_order = 0
bulk_rheology.auxiliary_subfields.shear_modulus.basis_order = 0

derived_subfields.cauchy_strain.basis_order = 0
derived_subfields.cauchy_stress.basis_order = 0

Similarly, we set the general fault parameters common to all simulations in the directory.

Listing 71 General fault parameters common to all simulations in this directory.

[pylithapp.problem]
interfaces = [fault]

[pylithapp.problem.interfaces.fault]
label = fault
label_value = 20

# Output `slip` on the fault.
observers.observer.data_fields = [slip]

All simulations in this directory use Dirichlet boundary conditions on the -x and +x boundaries with zero displacements,

(172)\[\begin{gather} u_x(-50km,y) = 0,\\ u_y(-50km,y) = 0,\\ u_x(+50km,y) = 0,\\ u_y(+50km,y) = 0. \end{gather}\]

Listing 72 Dirichlet boundary conditions common to all simulations in this directory.

[pylithapp.problem]
bc = [bc_xneg, bc_xpos]
bc.bc_xneg = pylith.bc.DirichletTimeDependent
bc.bc_xpos = pylith.bc.DirichletTimeDependent

[pylithapp.problem.bc.bc_xpos]
label = boundary_xpos
label_value = 11
constrained_dof = [0, 1]
db_auxiliary_field = pylith.bc.ZeroDB
db_auxiliary_field.description = Dirichlet BC +x boundary

[pylithapp.problem.bc.bc_xneg]
label = boundary_xneg
label_value = 10
constrained_dof = [0, 1]
db_auxiliary_field = pylith.bc.ZeroDB
db_auxiliary_field.description = Dirichlet BC -x boundary