# Step 1: Static Coseismic Slip % Metadata extracted from parameter files. ```{include} step01a_slip-synopsis.md ``` This example involves a static simulation that solves for the deformation from prescribed coseismic slip on the fault. {numref}`fig:example:strikeslip:2d:step01:diagram` shows the boundary conditions on the domain. :::{figure-md} fig:example:strikeslip:2d:step01:diagram Boundary conditions for static coseismic slip. We set the x and y displacement to zero on the +x and -x boundaries and prescribe 2 meters of right-lateral slip. ::: ## Step 1a: Coarse Mesh :::{note} *New in v4.1.0.* We start with a coarse resolution mesh and increase the resolution of the simulation by using uniform refinement or increasing the basis order of the solution fields. ::: ### Simulation parameters The parameters specific to this example are in `step01a_slip.cfg`. ```{code-block} cfg --- caption: Prescribed slip parameters for Step 1. --- [pylithapp.problem.interfaces.fault.eq_ruptures.rupture] db_auxiliary_field = spatialdata.spatialdb.UniformDB db_auxiliary_field.description = Fault rupture auxiliary field spatial database db_auxiliary_field.values = [initiation_time, final_slip_left_lateral, final_slip_opening] db_auxiliary_field.data = [0.0*s, -2.0*m, 0.0*m] ``` ### Running the simulation ```{code-block} console --- caption: Run Step 1a simulation --- $ pylith step01a_slip.cfg # The output should look something like the following. >> software/pylith-debug/lib/python3.12/site-packages/pylith/apps/PyLithApp.py:79:main -- info (application-flow) -- Running on 1 process(es). >> src/cig/pylith/libsrc/pylith/utils/PetscOptions.cc:251:static void pylith::utils::_PetscOptions::write(pythia::journal::info_t &, const char *, const PetscOptions &) -- info (application-flow) -- Setting PETSc options: dm_reorder_section = true dm_reorder_section_type = cohesive ksp_atol = 1.0e-7 ksp_converged_reason = true ksp_error_if_not_converged = true ksp_gmres_restart = 100 ksp_guess_pod_size = 8 ksp_guess_type = pod ksp_rtol = 1.0e-14 mg_fine_ksp_max_it = 5 mg_fine_pc_type = vpbjacobi pc_type = gamg snes_atol = 5.0e-7 snes_converged_reason = true snes_error_if_not_converged = true snes_monitor = true snes_rtol = 1.0e-14 ts_error_if_step_fails = true ts_exact_final_time = matchstep ts_monitor = true ts_type = beuler viewer_hdf5_collective = true >> src/cig/pylith/libsrc/pylith/meshio/MeshIOCubit.cc:170:virtual void pylith::meshio::MeshIOCubit::_read() -- info (application-flow) -- Component 'meshiocubit.reader': Reading finite-element mesh from 'mesh_tri.exo'. >> src/cig/pylith/libsrc/pylith/meshio/MeshIOCubit.cc:207:virtual void pylith::meshio::MeshIOCubit::_read() -- info (application-flow) -- Component 'meshiocubit.reader': Read 378 cells and 213 vertices. >> src/cig/pylith/libsrc/pylith/meshio/MeshIO.cc:76:void pylith::meshio::MeshIO::read(pylith::topology::Mesh *, const bool) -- info (application-flow) -- Component 'meshiocubit.reader': Domain bounding box: (-50000, 50000) (-75000, 75000) >> src/cig/pylith/libsrc/pylith/problems/TimeDependent.cc:316:virtual void pylith::problems::TimeDependent::verifyConfiguration() const -- info (application-flow) -- Component 'timedependent.problem': Verifying problem configuration. >> software/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:238:_printInfo -- info (application-flow) -- Scales for nondimensionalization: Length scale: 8000*m Displacement scale: 1*m Time scale: 3.15576e+09*s Rigidity scale: 1e+10*m**-1*kg*s**-2 Temperature scale: 1*K >> src/cig/pylith/libsrc/pylith/problems/TimeDependent.cc:342:virtual void pylith::problems::TimeDependent::initialize() -- info (application-flow) -- Component 'timedependent.problem': Initializing problem. >> src/cig/pylith/libsrc/pylith/topology/MeshOps.cc:239:static pylith::topology::Mesh *pylith::topology::MeshOps::createLowerDimMesh(const pylith::topology::Mesh &, const char *, const int, const char *) -- warning (deprecation) -- Creating lower dimension mesh from label with vertices. This feature will be removed in v6.0. In the future, you will need to mark boundaries instead of vertices. >> src/cig/pylith/libsrc/pylith/topology/MeshOps.cc:239:static pylith::topology::Mesh *pylith::topology::MeshOps::createLowerDimMesh(const pylith::topology::Mesh &, const char *, const int, const char *) -- warning (deprecation) -- Creating lower dimension mesh from label with vertices. This feature will be removed in v6.0. In the future, you will need to mark boundaries instead of vertices. >> src/cig/pylith/libsrc/pylith/problems/TimeDependent.cc:473:void pylith::problems::TimeDependent::solve() -- info (application-flow) -- Component 'timedependent.problem': Solving equations. 0 TS dt 0.001 time 0. 0 SNES Function norm 8.489136776687e+00 Linear solve converged due to CONVERGED_ATOL iterations 9 1 SNES Function norm 3.930434823490e-08 Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1 >> src/cig/pylith/libsrc/pylith/topology/MeshOps.cc:239:static pylith::topology::Mesh *pylith::topology::MeshOps::createLowerDimMesh(const pylith::topology::Mesh &, const char *, const int, const char *) -- warning (deprecation) -- Creating lower dimension mesh from label with vertices. This feature will be removed in v6.0. In the future, you will need to mark boundaries instead of vertices. >> src/cig/pylith/libsrc/pylith/topology/MeshOps.cc:239:static pylith::topology::Mesh *pylith::topology::MeshOps::createLowerDimMesh(const pylith::topology::Mesh &, const char *, const int, const char *) -- warning (deprecation) -- Creating lower dimension mesh from label with vertices. This feature will be removed in v6.0. In the future, you will need to mark boundaries instead of vertices. 1 TS dt 0.001 time 0.001 >> software/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:222:finalize -- info (application-flow) -- Finalizing problem. ``` At the beginning of the output written to the terminal, we see that PyLith is reading the mesh using the `MeshIOPetsc` reader and that it found the domain to extend from -50,000 m to +50,000 m in the x direction and from -75,000 m to +75,000 m in the y direction. The scales for nondimensionalization remain the default values for a quasistatic problem. PyLith detects the presence of a fault based on the Lagrange multiplier for the fault in the solution field and selects appropriate preconditioning options as discussed in {ref}`sec-user-run-pylith-petsc-options`. At the end of the output written to the terminal, we see that the solver advanced the solution one time step (static simulation). The linear solve converged after 9 iterations and the norm of the residual met the absolute convergence tolerance (`ksp_atol`) . The nonlinear solve converged in 1 iteration, which we expect because this is a linear problem, and the residual met the absolute convergence tolerance (`snes_atol`). ### Visualizing the results The `output` directory contains the simulation output. Each "observer" writes its own set of files, so the solution over the domain is in one set of files, the boundary condition information is in another set of files, and the material information is in yet another set of files. The HDF5 (`.h5`) files contain the mesh geometry and topology information along with the solution fields. The Xdmf (`.xmf`) files contain metadata that allow visualization tools like ParaView to know where to find the information in the HDF5 files. To visualize the data using ParaView or Visit, load the Xdmf files. In {numref}`fig:example:strikeslip:2d:step01a:solution` and {numref}`fig:example:strikeslip:2d:step01a:stress` we use the `pylith_viz` utility to visualize the simulation results. ```{code-block} console --- caption: Visualize PyLith output using `pylith_viz`. --- pylith_viz --filename=output/step01a_slip-domain.h5 warp_grid --component=y pylith_viz --filename=output/step01a_slip-elastic_xneg.h5,output/step01a_slip-elastic_xpos.h5 plot_field --field=cauchy_stress --component=xy ``` :::{figure-md} fig:example:strikeslip:2d:step01a:solution Solution for Step 1a. The colors indicate the y displacement, and the deformation is exaggerated by a factor of 1000. Solution for Step 1a. The colors of the shaded surface indicate the y displacement, and the deformation is exaggerated by a factor of 1000. The undeformed configuration is shown by the gray wireframe. The contrast in material properties across the faults causes the asymmetry in the y displacement field. ::: :::{figure-md} fig:example:strikeslip:2d:step01a:stress Cauchy stress component xy for Step 1a. The colors indicate the xy stress component. Cauchy stress component xy for for Step 1a. The colors of the shaded surface indicate the xy stress component. The stress field is uniform within each cell, and the coarse resolution shows a checkerboard pattern near the top and bottom boundaries, which is indicative of poor resolution of the stress field in those regions. ::: ### Step 1a with Cubit Mesh Using the Cubit mesh rather than the Gmsh mesh involves two changes: 1. Use the `MeshIOCubit` reader instead of the `MeshIOPetsc` reader and change the filename of the mesh file. 2. Set the `label_value` to 1 for boundary conditions and faults.\ We must override the nondefault `label_value` settings in `pylithapp.cfg` that were appropriate for our Gmsh reader but are incorrect for the Cubit reader. The file `step01_slip_cubit.cfg` provides these changes and updates the names for output. ```{code-block} console --- caption: Run Step 1 simulation with the Cubit mesh --- $ pylith step01_slip_cubit.cfg # The output should look something like the following. >> software/pylith-debug/lib/python3.12/site-packages/pylith/apps/PyLithApp.py:79:main -- info (application-flow) -- Running on 1 process(es). >> src/cig/pylith/libsrc/pylith/utils/PetscOptions.cc:251:static void pylith::utils::_PetscOptions::write(pythia::journal::info_t &, const char *, const PetscOptions &) -- info (application-flow) -- Setting PETSc options: dm_reorder_section = true dm_reorder_section_type = cohesive ksp_atol = 1.0e-7 ksp_converged_reason = true ksp_error_if_not_converged = true ksp_gmres_restart = 100 ksp_guess_pod_size = 8 ksp_guess_type = pod ksp_rtol = 1.0e-14 mg_fine_ksp_max_it = 5 mg_fine_pc_type = vpbjacobi pc_type = gamg snes_atol = 5.0e-7 snes_converged_reason = true snes_error_if_not_converged = true snes_monitor = true snes_rtol = 1.0e-14 ts_error_if_step_fails = true ts_exact_final_time = matchstep ts_monitor = true ts_type = beuler viewer_hdf5_collective = true >> src/cig/pylith/libsrc/pylith/meshio/MeshIOCubit.cc:170:virtual void pylith::meshio::MeshIOCubit::_read() -- info (application-flow) -- Component 'meshiocubit.reader': Reading finite-element mesh from 'mesh_tri.exo'. >> src/cig/pylith/libsrc/pylith/meshio/MeshIOCubit.cc:207:virtual void pylith::meshio::MeshIOCubit::_read() -- info (application-flow) -- Component 'meshiocubit.reader': Read 378 cells and 213 vertices. >> src/cig/pylith/libsrc/pylith/meshio/MeshIO.cc:76:void pylith::meshio::MeshIO::read(pylith::topology::Mesh *, const bool) -- info (application-flow) -- Component 'meshiocubit.reader': Domain bounding box: (-50000, 50000) (-75000, 75000) >> src/cig/pylith/libsrc/pylith/problems/TimeDependent.cc:316:virtual void pylith::problems::TimeDependent::verifyConfiguration() const -- info (application-flow) -- Component 'timedependent.problem': Verifying problem configuration. >> software/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:238:_printInfo -- info (application-flow) -- Scales for nondimensionalization: Length scale: 8000*m Displacement scale: 1*m Time scale: 3.15576e+09*s Rigidity scale: 1e+10*m**-1*kg*s**-2 Temperature scale: 1*K >> src/cig/pylith/libsrc/pylith/problems/TimeDependent.cc:342:virtual void pylith::problems::TimeDependent::initialize() -- info (application-flow) -- Component 'timedependent.problem': Initializing problem. >> src/cig/pylith/libsrc/pylith/topology/MeshOps.cc:239:static pylith::topology::Mesh *pylith::topology::MeshOps::createLowerDimMesh(const pylith::topology::Mesh &, const char *, const int, const char *) -- warning (deprecation) -- Creating lower dimension mesh from label with vertices. This feature will be removed in v6.0. In the future, you will need to mark boundaries instead of vertices. >> src/cig/pylith/libsrc/pylith/topology/MeshOps.cc:239:static pylith::topology::Mesh *pylith::topology::MeshOps::createLowerDimMesh(const pylith::topology::Mesh &, const char *, const int, const char *) -- warning (deprecation) -- Creating lower dimension mesh from label with vertices. This feature will be removed in v6.0. In the future, you will need to mark boundaries instead of vertices. >> src/cig/pylith/libsrc/pylith/problems/TimeDependent.cc:473:void pylith::problems::TimeDependent::solve() -- info (application-flow) -- Component 'timedependent.problem': Solving equations. 0 TS dt 0.001 time 0. 0 SNES Function norm 8.489136776687e+00 Linear solve converged due to CONVERGED_ATOL iterations 9 1 SNES Function norm 3.930434823490e-08 Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1 >> src/cig/pylith/libsrc/pylith/topology/MeshOps.cc:239:static pylith::topology::Mesh *pylith::topology::MeshOps::createLowerDimMesh(const pylith::topology::Mesh &, const char *, const int, const char *) -- warning (deprecation) -- Creating lower dimension mesh from label with vertices. This feature will be removed in v6.0. In the future, you will need to mark boundaries instead of vertices. >> src/cig/pylith/libsrc/pylith/topology/MeshOps.cc:239:static pylith::topology::Mesh *pylith::topology::MeshOps::createLowerDimMesh(const pylith::topology::Mesh &, const char *, const int, const char *) -- warning (deprecation) -- Creating lower dimension mesh from label with vertices. This feature will be removed in v6.0. In the future, you will need to mark boundaries instead of vertices. 1 TS dt 0.001 time 0.001 >> software/pylith-debug/lib/python3.12/site-packages/pylith/problems/Problem.py:222:finalize -- info (application-flow) -- Finalizing problem. ``` The `MeshIOCubit` reader includes diagnostic information in the journal output related to the sizes of the nodesets and material blocks. ## Step 1b: Refined Mesh The parameters specific to this example are in `step01b_slip.cfg`. ### Simulation parameters In an attempt to better resolve the stress field, we use the same coarse resolution input mesh but add uniform refinement after PyLith reads in the mesh to reduce the discretization size by a factor of 2 in the. During uniform refinement, each triangle is subdivided into four triangles. ```{code-block} cfg --- caption: Uniform refinement parameters added in Step 1b. --- [pylithapp.mesh_generator] refiner = pylith.topology.RefineUniform ``` ### Running the simulation ```{code-block} console --- caption: Run Step 1b simulation --- $ pylith step01b_slip.cfg # The output will look almost identical to Step 1a. ``` ### Visualizing the results In {numref}`fig:example:strikeslip:2d:step01b:solution` and {numref}`fig:example:strikeslip:2d:step01b:stress` we use the `pylith_viz` utility to visualize the simulation results. ```{code-block} console --- caption: Visualize PyLith output using `pylith_viz`. --- pylith_viz --filename=output/step01b_slip-domain.h5 warp_grid --component=y pylith_viz --filename=output/step01b_slip-elastic_xneg.h5,output/step01b_slip-elastic_xpos.h5 plot_field --field=cauchy_stress --component=xy ``` :::{figure-md} fig:example:strikeslip:2d:step01b:solution Solution for Step 1b. The colors indicate the y displacement, and the deformation is exaggerated by a factor of 1000. Solution for Step 1b. The colors of the shaded surface indicate the y displacement, and the deformation is exaggerated by a factor of 1000. The undeformed configuration is shown by the gray wireframe. Uniform refinement reduces the discretization size by a factor of 2. ::: :::{figure-md} fig:example:strikeslip:2d:step01b:stress Cauchy stress component xy for Step 1b. The colors indicate the xy stress component. Cauchy stress component xy for for Step 1b. The colors of the shaded surface indicate the xy stress component. The reduced discretization size results in better resolution of the stress changes near the top and bottom boundaries. However, the stress field is still uniform within each cell, so the checkerboard pattern still persists, albeit with less variation between cells. ::: ## Step 1c: Higher Order Discretization The parameters specific to this example are in `step01c_slip.cfg`. ### Simulation parameters Increasing the basis order of the solution subfields provides an alternative approach to increasing the resolution of the mesh using uniform refinement. The accuracy of the stress and strain will be 1 order lower than the basis order of the displacement field. Consequently, we use a basis order of 1 (rather than 0) for the output of the Cauchy stress and strain. We continue to output the solution fields using a basis order of 1, because many visualization tools do not know how to display fields with a basis order of 2. This means the solution subfields in the output are at a reduced resolution compared to the simulation and correspond to projection of each subfield from a basis order of 2 to a basis order of 1. ```{code-block} cfg --- caption: Parameters related to increasing the basis order of the solution subfields to 2. --- [pylithapp.problem] defaults.quadrature_order = 2 [pylithapp.problem.solution.subfields] displacement.basis_order = 2 lagrange_multiplier_fault.basis_order = 2 [pylithapp.problem.materials.elastic_xneg] derived_subfields.cauchy_strain.basis_order = 1 derived_subfields.cauchy_stress.basis_order = 1 [pylithapp.problem.materials.elastic_xpos] derived_subfields.cauchy_strain.basis_order = 1 derived_subfields.cauchy_stress.basis_order = 1 ``` ### Running the simulation ```{code-block} console --- caption: Run Step 1c simulation --- $ pylith step01c_slip.cfg # The output will look almost identical to Steps 1a and 1b. ``` ### Visualizing the results In {numref}`fig:example:strikeslip:2d:step01c:solution` and {numref}`fig:example:strikeslip:2d:step01c:stress` we use the `pylith_viz` utility to visualize the simulation results. ```{code-block} console --- caption: Visualize PyLith output using `pylith_viz`. --- pylith_viz --filename=output/step01c_slip-domain.h5 warp_grid --component=y pylith_viz --filename=output/step01c_slip-elastic_xneg.h5,output/step01c_slip-elastic_xpos.h5 plot_field --field=cauchy_stress --component=xy ``` :::{figure-md} fig:example:strikeslip:2d:step01c:solution Solution for Step 1a. The colors indicate the y displacement, and the deformation is exaggerated by a factor of 1000. Solution for Step 1a. The colors of the shaded surface indicate the y displacement, and the deformation is exaggerated by a factor of 1000. The undeformed configuration is shown by the gray wireframe. The displacement field shows little difference from Step 1a. ::: :::{figure-md} fig:example:strikeslip:2d:step01c:stress Cauchy stress component xy for Step 1a. The colors indicate the xy stress component. Cauchy stress component xy for for Step 1a. The colors of the shaded surface indicate the xy stress component. Output with a basis order of 1 shows much better resolution of the shear stress near the top and bottom of the domain with no noticeable checkboard pattern. ::: :::{note} We focus on the displacement field in the subsequent steps in the example, which has sufficient accuracy with a basis order of 1 if we use uniform refinement. Consequently, in the subsequent steps we adopt the uniform refinement parameters that we used in Step 1b. ::: ## Key Points 1. We can generate a mesh at coarse resolution that captures the geometry and use uniform refinement and high order discretizations of the solution subfields to achieve sufficient resolution. 2. Using uniform mesh refinement in PyLith requires only two parameter settings: enabling uniform refinement by setting the mesh generator `refiner` facility to `pylith.topology.RefineUniform` and setting the number of levels of refinement. 3. Using higher order discretizations of the solution subfields requires adjusting more parameters that uniform refinement. We adjust the default quadrature order, basis order of the solution fields, and basis order of relevant output fields. 4. Because uniform mesh refinement requires only a couple of additional parameters, we recommend first using uniform refinement to assess the sensitivity of the results to the discretization size before increasing the basis order of the solution subfields. However, if you know your results are sensitive to the stress field, then we recommend first increasing the basis order. 5. In some cases, you may find that uniform refinement and higher order discretizations indicate that some portions of the mesh need higher resolution that others, and you might need to adjust the spatial variation of the discretization size in the initial coarse mesh.