PyLith Modeling Tutorial - Computational Infrastructure for
Contents
1. ds TimeD ma SimpleDB db initial Q5 db initial db be te COMPUTATIONAL PyLith Architecture INFRASTRUCTURE for GEODYNAMICS Unit and Regression Testing Automatically run more than 1800 tests on multiple platforms whenever code is checked into the source repository Create tests for nearly every function in code during development e Remove most bugs during initial implementation e Isolate and expose bugs at origin 9 Create new tests to expose reported bugs e Prevent bugs from reoccurring Rerun tests whenever code is changed e Code continually improves permits optimization with quality control e Binary packages generated automatically upon successful completion of tests e Additional full scale parallel regression tests are run before releases COMPUTATIONAL PyLith Testing INFRASTRUCTURE for GEODYNAMICS Mesh Generation Tips There is no silver bullet in finite element mesh generation e Hex Quad versus Tet Tri e Hex Quad are slightly more accurate and faster e Tet Tri easily handle complex geometry e Easy to vary discretization size with Tet Tri and Quad cells e There is no easy answer For a given accuracy a finer resolution Tet mesh that varies the discretization size in a more optimal way might run faster than a Hex mesh Check and double check your mesh e Were there any errors when running the mesher e Are the bou2. 1 on Tj on Sr 2 uj u on Sy and 3 Ryu on S 4 Multiply by weighting function and integrate over the volume f eii 0 plies aV 0 5 After some algebra f 8 puo av 6 V S V V COMPUTATIONAL PyLith Governing Equations INFRASTRUCTURE for GEODYNAMICS Discretize Domain Using Finite Elements PyLith v2 0 0 and later uses interpolated meshes Interpolated ee mesh Interpolated quadrilateral mesh qb di 5 108 d 2 0 5 1 8 10 15 914 id regs Cells eo e oO o Optimized triangular mesh Optimized quadrilateral mesh 3 ee LUN MS COMPUTATIONAL Governing INFRASTRUCTURE for GEODYNAMICS Governing Equations Using numerical quadrature we convert the integrals to sums over the cells and quadrature points 2 ci N Wa Jcen gt TiN wa vol cells quad pts surf cells quad pts 27 Wa Jcei vol cells quad pts MX aPN N wdea 0 7 vol cells quad pts COMPUTATIONAL INFRASTRUCTURE for GEODYNAMICS Quasi static Solution Neglect inertial terms Form system of algebraic equations A t t b t 8 where NRN Nr Walden 9 vol cells quad pts 600 gt N b gt Joe surf cells quad pts vol cells quad pts 10 and solve for u t COMPUTATIONAL
3. formulation prestep dt formulation step dt formulation poststep dt Architecture Implicit Formulation initialize prestep set values of constraints step compute residual solve for disp incr poststep update disp field write output COMPUTATIONAL INFRASTRUCTURE for GEODYNAMICS PyLith as a Hierarchy of Components Components are the basic building blocks Component n COMPUTATIONAL PyLith Architecture INFRASTRUCTURE for GEODYNAMICS PyLith as a Hierarchy of Components PyLith Application and Time Dependent Problem PyLithApp TimeDependent a b Y properties properties none dimension facilities facilities mesh generator normalizer problem materials petsc be interfaces gravity field formulation COMPUTATIONAL INFRASTRUCTURE for GEODYNAMICS PyLith as a Hierarchy of Components Fault with kinematic prescribed slip earthquake rupture FaultCohesiveKin properties id name up dir normal_dir facilities quadrature eq srcs output EqKinSrc properties origin time facilities slip function COMPUTATIONAL INFRASTRUCTURE for GEODYNAMICS PyLith as a Hierarchy of Components Diagram of simple toy problem COMPUTATIONAL PyLith Architecture bmg INFRASTRUCTURE for GEODYNAMICS PyLith as a Hierarchy of Components LJ L1 EN
4. NFRASTRUCTURE for GEODYNAMICS Crustal Deformation Modeling Elasticity problems where geometry does not change significantly Volcanic deformation associated with magma chambers and or dikes Inflation e What is the geometry of the magma chamber e What is the potential for an eruption e Eruption e Where is the deformation occurring e What is the ongoing potential for an eruption Dike intrusions e What is the geometry of the intrusion e What is the pressure change and or amount of opening dilatation COMPUTATIONAL PyLith Overview INFRASTRUCTURE for GEODYNAMICS Crustal Deformation Modeling Overview of workflow for typical research problem Geologic Mesh Physics Structure Generation Code Visualization Gocad CUBIT Trelis PyLith Earth Vision Relax Available Commercial Planned COMPUTATIONAL PyLith Overview mg INFRASTRUCTURE for GEODYNAMICS PyLith 9 Developers e Brad Aagaard USGS lead developer e Charles Williams GNS Science formerly at RPI e Matthew Knepley Rice Univ formerly Univ of Chicago Combined dynamic modeling capabilities of EqSim Aagaard with the quasi static modeling capabilities of Tecton Williams 9 Use modern software engineering modular design testing documentation distribution to develop an open source community code 7 COMPUTATIONAL PyLith Overview INFRASTRUCTURE for GEODYNAMICS Governing Equations Elasticity equation Gij f p in V
5. PyLith Governing Equations INFRASTRUCTURE for GEODYNAMICS Fault Interface Fault tractions couple deformation across interface COMPUTATIONAL PyLith Fault Implementation INFRASTRUCTURE for GEODYNAMICS Implementation Fault Interfaces Use cohesive cells to control fault behavior d Classify cells and iai b Add colocated c Update cells with rhe a Original mesh vertices fault faces remaining e e Sj 8r fault vertex Sede com es Original fault vertex negative side Cell on Cell on negative positive side side Add Lagrange multiplier edge fault edge vertex Add vertex on positive side COMPUTATIONAL PyLith Fault Implementation INFRASTRUCTURE for GEODYNAMICS Fault Implementation Governing Equations Terms in governing equation associated with fault Tractions on fault surface are analogous to boundary tractions j Tas ids j dS 0 Sr om S Fault Fault e Constraint equation relates slip to relative displacement 0 Sr Slip Relative Disp COMPUTATIONAL PyLith Fault Implementation INFRASTRUCTURE for GEODYNAMICS Fault Slip Implementation Use Lagrange multipliers to specify slip System without cohesive cells e Conventional finite element elasticity formulation Ai b e Fault slip associated with relative displacements across fault C d System with Lagrange mul
6. PyLith Modeling Tutorial Overview of CUBIT Trelis PyLith and ParaView Brad Aagaard Charles Williams Matthew Knepley COMPUTATIONAL INFRASTRUCTURE for GEODYNAMICS August 24 2015 Crustal Deformation Modeling Elasticity problems where geometry does not change significantly Quasi static modeling associated with earthquakes e Strain accumulation associated with interseismic deformation e What is the stressing rate on faults X and Y e Where is strain accumulating in the crust Coseismic stress changes and fault slip e What was the slip distribution in earthquake A e How did earthquake A change the stresses on faults X and Y Postseismic relaxation of the crust e What rheology is consistent with observed postseismic deformation e Can aseismic creep or afterslip explain the deformation 7 COMPUTATIONAL PyLith Overview INFRASTRUCTURE for GEODYNAMICS Crustal Deformation Modeling Elasticity problems where geometry does not change significantly Dynamic modeling associated with earthquakes e Modeling of strong ground motions e Forecasting the amplitude and spatial variation in ground motion for scenario earthquakes 9 Coseismic stress changes and fault slip e How did earthquake A change the stresses on faults X and Y e Earthquake rupture behavior e What fault constitutive models parameters are consistent with the observed rupture propagation in earthquake A 7 COMPUTATIONAL PyLith Overview I
7. bugger run in xterm nodes N to run on N processors on local machine e Journal info flags turn on writing progress pylithapp journal info timedependent 1 e Turns on off info for each type of component independently e Examples turn on writing lots of info to stdout using journal flags COMPUTATIONAL Troubleshooting PyLith INFRASTRUCTURE for GEODYNAMICS Getting Started e Read the PyLith User Manual Work through the examples e Chapter 7 of the PyLith manual e Input files are provided with the PyLith binary src pylith 2 1 0 examples e Input files are provided with the PyLith source tarball src examples e Modify an example to look like a problem of interest COMPUTATIONAL Troubleshooting PyLith INFRASTRUCTURE for GEODYNAMICS
8. e of UniformDB COMPUTATIONAL PyLith Running PyLith IG INFRASTRUCTURE for GEODYNAMICS Features in PyLith v2 1 Bugfix release for v2 0 plus some minor new features e Time integration schemes and elasticity formulations e Implicit for quasistatic problems neglect inertial terms Infinitesimal strains e Small strains e Explicit for dynamic problems 9 Infinitesimal strains e Small strains Numerical damping via viscosity e Bulk constitutive models 2 D and 3 D Elastic model Linear Maxwell viscoelastic models Generalized Maxwell viscoelastic models Power law viscoelastic model Drucker Prager elastoplastic model COMPUTATIONAL PyLith Features INFRASTRUCTURE for GEODYNAMICS Features in PyLith v2 1 cont e Boundary and interface conditions e Time dependent Dirichlet boundary conditions Time dependent Neumann traction boundary conditions Absorbing boundary conditions Kinematic prescribed slip fault interfaces w multiple ruptures Dynamic friction fault interfaces Fault interfaces with T intersections Time dependent point forces e Gravitational body forces e Fault constitutive models e Static friction e Linear slip weakening e Linear time weakening e Dieterich Ruina rate and state friction w ageing law COMPUTATIONAL PyLith Features INFRASTRUCTURE for GEODYNAMICS Features in PyLith v2 1 cont Automatic and user controlled time stepping Ability to specify initial stress strain state e Im
9. ndaries etc marked correctly for your BC e Check mesh quality aspect ratio should be close to 1 COMPUTATIONAL CUBIT Trelis General INFRASTRUCTURE for GEODYNAMICS CUBIT Workflow Create geometry Consiruct surfaces from points curves etc or basic shapes Create domain and subdivide to create any interior surfaces e Fault surfaces must be interior surfaces or a subset that completely divide domain Need separate volumes for different constitutive models not parameters Q Create finite element mesh Q Specify meshing scheme Q Specify mesh sizing information Q Generate mesh Q Smooth to fix any poor quality cells Q Create nodesets and blocks Q Create block for each constitutive model Q Create nodeset for each BC and fault Create nodeset for buried fault edges Q Create nodeset for ground surface for output optional Export mesh in Exodus II format exo files COMPUTATIONAL CUBIT Trelis General INFRASTRUCTURE for GEODYNAMICS CUBIT Trelis Issues Keep in mind the scales of the observations you are modeling Topography bathymetry e Ignore topography bathymetry unless you know it matters e For rectilinear grid create UV net surface e Convert triangular facets to UV net surface via mapped mesh Fault surfaces e Building surfaces from contours is usually easiest e Include features at the resolution that matters e Performance e Number of points in spline curves surfaces has huge affect on mesh generation r
10. porting meshes e LaGriT GMV Pset e CUBIT Exodus II e ASCII PyLith mesh ASCII format intended for toy problems only 9 Output VTK and HDF5 files Solution over volume e Solution over surface boundary e Solution interpolated to user specified points w station names e State variables e g stress and strain for each material e Fault information e g slip and tractions COMPUTATIONAL PyLith Features INFRASTRUCTURE for GEODYNAMICS Features in PyLith v2 1 cont 9 Automatic conversion of units for all parameters e Parallel uniform global refinement PETSc linear and nonlinear solvers e Custom preconditioner with algebraic multigrid solver 9 Output of simulation progress estimates runtime COMPUTATIONAL PyLith Features INFRASTRUCTURE for GEODYNAMICS PyLith Development See PyLith User Resources for detailed development plan 9 Immediate priorities in progress e New fault implementation for spontaneous rupture Much faster convergence for quasi static simulations e Support higher order basis functions Provides much higher resolution for a given mesh e Adaptive time stepping e Prepare for multi physics e Scaling to 1000 cores Short term priorities e Multiphysics Elasticity Fluid flow Heat flow e Multigrid nonlinear solver Multi cycle earthquake modeling Resolve interseismic coseismic and postseismic deformation e Coupling solvers for quasistatic and dynamic deformation COMPUTATIONAL PyLith Feat
11. r problems gt much faster turnaround e Start with an exact solver e Experiment with meshing boundary conditions solvers etc e Increase resolution until solution resolves features of interest e Resolution will depend on spatial scales in BC initial conditions deformation and geologic structure 9 s geometry of domain important At what resolution e Displacement field is integral of strains stresses e Resolving stresses strains requires fine resolution simulations Use your intuition and analogous solutions to check your results COMPUTATIONAL Troubleshooting General INFRASTRUCTURE for GEODYNAMICS PyLith Tips e Read the PyLith User Manual e Do not ignore error messages and warnings Use an example benchmark as a starting point Quasi static simulations e Start with a static simulation and then add time dependence e Check that the solution converges at every time step e Dynamic simulations e Start with a static simulation e Shortest wavelength seismic waves control cell size CIG Short Term Crustal Dynamics mailing list cig short geodynamics org e PyLith User Resources http wiki geodynamics org software pylith start z COMPUTATIONAL Troubleshooting PyLith INFRASTRUCTURE for GEODYNAMICS PyLith Debugging Tools 9 pylithinfo verbose PyLith args Dumps all parameters with their current values to text file Command line arguments 9 help 9 help components 9 help properties 9 petsc start in de
12. tiplier constraints for fault slip C V N 0 lj d e Prescribed kinematic slip _ Specify fault slip d and solve for Lagrange multipliers Spontaneous dynamic slip Adjust fault slip to be compatible with fault constitutive model 3 n COMPUTATIONAL PyLith Fault Implementation INFRASTRUCTURE for GEODYNAMICS Implementing Fault Slip with Lagrange multipliers 9 Advantages e Fault implementation is local to cohesive cell e Solution includes tractions generating slip Lagrange multipliers e Retains block structure of matrix including symmetry e Offsets in mesh mimic slip on natural faults Disadvantages e Cohesive cells require adjusting topology of finite element mesh e Scalable preconditioner solver is more complex COMPUTATIONAL PyLith Fault Implementation INFRASTRUCTURE for GEODYNAMICS Workflow for Running PyLith Mesh Generator Simulation Parameters Post processing COMPUTATIONAL PyLith Running PyLith INFRASTRUCTURE for GEODYNAMICS Spatial Databases User specified field value in space Examples e Uniform value for Dirichlet 0 D e Piecewise linear variation in tractions for Neumann BC 1 D e SCEC CVM H seismic velocity model 3 D e Generally independent of discretization for problem Available spatial databases UniformDB Optimized for uniform value SimpleDB Simple ASCII files 0 D 1 D 2 D or 3 D SCECCVMH SCEC CVM H seismic velocity model v5 3 ZeroDispDB Special cas
13. untime e CUBIT Trelis do not run in parallel e Use uniform global refinement in PyLith for large sims gt 10M cells COMPUTATIONAL CUBIT Trelis General INFRASTRUCTURE for GEODYNAMICS CUBIT Trelis Best Practices Issue Soln Issue Soln Issue Soln Issue Soln Issue Soln Issue Soln CUBIT Trelis Changes in geometry cause changes in object ids Name objects and use APREPRO or Python to eliminate hardwired ids wherever possible Splines with many points slows down operations Reduce the number of points per spline Surfaces meet in small angles creating distorted cells Trim geometry to eliminate features smaller than cell size Difficulty meshing complex geometry with Hex cells Use Tet cells even if it requires a finer mesh Hex mesh over samples parts of the domain Use Tet mesh and vary discretization within domain Extended surfaces create very complex geometry Subdivide geometry before webcutting to eliminate overly complex geometry COMPUTATIONAL General INFRASTRUCTURE for GEODYNAMICS General Numerical Modeling Tips Start simple and progressively add complexity and increase resolution Start in 2 D if possible and then go to 3 D e Much smaller problems gt much faster turnaround e Start with an exact solver e Experiment with meshing boundary conditions solvers etc e Keep in mind how physics differs from 3 D e Start with coarse resolution and then increase resolution e Much smalle
14. ures INFRASTRUCTURE for GEODYNAMICS PyLith Development Planned Releases v2 1 1 Sep 2015 e Bugfixes Restarting simulations for viscoelastic materials e Finite strain e Better examples for gravitational body forces initial conditions and finite strain 9 v3 0 Late 2015 e New fault implementation for spontaneous rupture e Support for higher order basis functions e Adaptive time stepping v3 1 Summer 2016 e Support for incompressible elasticity e Heat and fluid flow coupled to elastic deformation COMPUTATIONAL PyLith Features INFRASTRUCTURE for GEODYNAMICS Design Philosophy Modular extensible and smart e Code should be flexible and modular Users should be able to add new features without modifying code for example e Boundary conditions e Bulk constitutive models e Fault constitutive models Input output should be user friendly Top level code written in Python expressive dynamic typing 9 Low level code written in C modular fast 3 COMPUTATIONAL PyLith Architecture INFRASTRUCTURE for GEODYNAMICS PyLith Design Focus on Geodynamics Leverage packages developed by computational scientists COMPUTATIONAL PyLith Architecture INFRASTRUCTURE for GEODYNAMICS PyLith Application Flow PyLithApp main mesher create problem initialize problem run TimeDependent Problem initialize formulation initialize run while t lt tEnd dt formulation dt
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