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. This limits duplicate information in the parameter files for each simulation.

Metadata, Mesh, and Output

The pylithapp.metadata section specifies metadata common to all simulations in the directory. We set the parameters for importing the finite-element mesh in pylithapp.mesh_generator.

Physics

All of the simulations in this example suite solve the elasticity equation without inertia,

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

The default PyLith settings target solving the quasi-static elasticity equation, so we can use the default TimeDependent problem and solution field with a single displacement subfield of basis order 1.

Listing 32 Default PyLith problem and solution field settings appropriate for quasi-static elasticity. We do not include these in pylithapp.cfg.

[pylithapp]
# Default problem and solution field.
problem = pylith.problems.TimeDependent
problem.solution = pylith.problems.SolnDisp
        
[pylithapp.problem.solution.subfields]
# The default basis order for solution subfields is 1 (linear variation within cells).
displacement.basis_order = 1

[pylithapp.problem]
# Default output for the solution is over the domain.
solution_observers = [domain]

The default material and bulk rheology also target solving the quasi-static elasticity equation. The default bulk rheology is isotropic linear elasticity.

Listing 33 Default PyLith material and bulk rheology settings appropriate for quasi-static elasticity. We do not include these in pylithapp.cfg.

[pylithapp.problem]
materials = [elastic]
materials.elastic = pylith.materials.Elasticity

[pylithapp.problem.materials.elastic]
bulk_rheology = pylith.materials.IsotropicLinearElasticity

In this suite of examples we have a single material, and we must specify a description for the material and the label value. In this case the label value corresponds to the material-id in the finite-element mesh file. The physical properties for each material are specified in a spatial database. The material properties are uniform, so we use a single UniformDB to specify the material properties in pylithapp.cfg. When we have a spatial variation in the material properties, we specify them in a spatial database file. With uniform properties we use a basis order of 0 for the auxiliary subfields.

Listing 34 Material settings in pylithapp.cfg.

[pylithapp.problem]
materials = [elastic]

[pylithapp.problem.materials.elastic]
label_value = 0

# We will use uniform material properties, so we use the UniformDB
# spatial database.
db_auxiliary_field = spatialdata.spatialdb.UniformDB
db_auxiliary_field.description = Elastic properties
db_auxiliary_field.values = [density, vs, vp]
db_auxiliary_field.data = [2500*kg/m**3, 3.0*km/s, 5.2915026*km/s]

# Set the discretization of the material auxiliary fields (properties).
# We have uniform material properties, so we can use a basis order of 0.
auxiliary_subfields.density.basis_order = 0
bulk_rheology.auxiliary_subfields.bulk_modulus.basis_order = 0
bulk_rheology.auxiliary_subfields.shear_modulus.basis_order = 0