4C

Contents:

  • About 4C
    • Overview
    • Capabilities
    • History
  • 4C Community
    • Roles in the 4C community
      • 4C Open Source community
      • 4C Developer
      • 4C Maintainer
    • Developer life cycle model
      • Becoming a member of the developer group
      • Inactivity and removal
      • Rejoining the developer group
  • Installation
    • External dependencies
      • Build information
    • Download and install
      • Access the repository
      • Configure
      • Build
    • Set-up your IDE
      • CLion
      • Visual Studio Code
    • Build 4C with custom targets
      • Custom target specifiers
  • Tutorials
    • Creating a Geometry with Coreform Cubit®
    • Fluid Tutorial
      • Introduction
      • Preprocessing
        • Creating the Geometry with Cubit
      • Working with 4C
        • General Procedure of Creating a Valid 4C Input File
        • Setting the boundary conditions
        • Running a Simulation with 4C
      • Postprocessing
        • Filtering result data
        • Visualize your results in Paraview
    • FSI Tutorial 2D
      • Introduction
      • The FSI problem with a partitioned solver
        • Geometry description
        • General parameters
        • Boundary conditions
        • Running the Simulation
      • Postprocessing
      • The FSI problem with a monolithic solver
        • Fluid split
        • Structure split
    • FSI Tutorial 3D
      • Introduction
      • Creating the Geometry with Cubit
      • Creating the 4C input file
        • Geometry description
        • General parameters
        • Running the simulation
      • Postprocessing
    • 3D Solid Tutorial with Coreform Cubit®
      • Introduction
      • Preprocessing
      • Simulation
      • Post processing
    • 3D Contact Tutorial
      • Overview
      • Problem description
      • Create files
        • Define Geometry
        • Define Boundary Conditions
        • Specify Simulation Settings
      • Run Simulation
    • 3D Solid-State Battery Tutorial
      • Overview
      • Problem description
      • Input files
        • Definition of the geometry
        • Definition of the materials
        • Definition of the boundary conditions
        • Definition of the interface conditions
        • Specification of the simulation settings
      • Run Simulation
  • Analysis Guide
    • Workflow
      • 4C Simulation
        • Running examples
        • Restarting an analysis
      • Preprocessing
        • Generating Exodus II files
        • Other ways to create a 4C input directly
        • Modify 4C input files
      • Postprocessing
        • Direct VTK output
        • Conversion to readable formats
        • post_monitor
        • ParaView
        • Animations
    • Problem types
      • Single field problems:
        • Ale
        • ArterialNetwork
        • Cardiac_Monodomain
        • Fluid
        • Electrochemistry
        • Fluid_Top_Opt
        • Fluid_XFEM
        • Level_Set
        • Particle
        • Polymer_Network
        • ReducedDimensionalAirWays
        • Scalar_Transport
        • Structure
        • Thermo
      • Multi field problems:
        • Biofilm_Fluid_Structure_Interaction
        • Elastohydrodynamic_Lubrication
        • Fluid_Ale
        • Fluid_Beam_Interaction
        • Fluid_Freesurface
        • Fluid_Poro_Structure_Interaction_XFEM
        • Fluid_Porous_Structure_Interaction
        • Fluid_Porous_Structure_Scalar_Scalar_Interaction
        • Fluid_RedModels
        • Fluid_Structure_Interaction
        • Fluid_Structure_Interaction_RedModels
        • Fluid_Structure_Interaction_XFEM
        • Fluid_XFEM_LevelSet
        • Gas_Fluid_Structure_Interaction
        • Low_Mach_Number_Flow
        • Lubrication
        • Multiphase_Poroelasticity
        • Multiphase_Poroelasticity_ScaTra
        • Multiphase_Porous_Flow
        • NP_Supporting_Procs
        • Particle_Structure_Interaction
        • Poroelastic_scalar_transport
        • Poroelasticity
        • Scalar_Thermo_Interaction
        • Structure_Ale
        • Structure_Scalar_Interaction
        • Structure_Scalar_Thermo_Interaction
        • Thermo_Fluid_Structure_Interaction
        • Thermo_Structure_Interaction
        • Tutorial
    • Geometry Discretization
      • Finite Element Discretization
        • Domain definition
        • Node definition
        • Element definition
        • Geometry sets
      • Particle Discretization
    • Elements
      • Structure Elements
      • Fluid Elements
      • Lubrication Elements
      • Transport Elements
      • Transport2 Elements
      • ALE Elements
      • Thermo Elements
      • Artery Elements
      • Reduced D Airways Elements
    • Function definitions
    • Boundary Conditions
      • Local Coordinate System
      • Dirichlet Boundary Conditions
      • Neumann Boundary Conditions
      • Robin (Spring-Dashpot) conditions
      • Constraint conditions
        • Several nodes coupled for specific degrees of freedom
        • Surface coupled to a node in a given direction
        • Node displacement relative to a given surface or line
        • Periodic boundary conditions
      • Contact conditions
      • Defining boundary conditions for geometries from EXODUS files
    • Contact and Mesh tying
      • Contact
        • Contact and symmetry conditions
        • Contact at edges/corners
      • Mesh Tying
    • Materials
      • General information
      • Structural Material Models
      • Fluid Material Models
      • Other Material Models
      • Coupling Material Models for Various Physics on a Single Discretization
    • Solving nonlinear systems in structural simulations
      • Time stepping in dynamic simulations
        • Explicit time stepping procedure
        • Implicit time stepping procedure
        • Iterative solution
      • Theory
        • Order of accuracy
        • Generalised-alpha time-stepping procedure
      • Time adaptivity
        • Based on indication of the local discretisation error
        • Zienkiewicz and Xie indicator
    • Linear solver
      • Solvers for single-field problems
      • Solvers for coupled problems (aka multiphysics)
        • Partitioned solution using a staggered or iterative coupling scheme:
        • Monolithic solution:
        • Special case: Contact
      • Solver Interfaces
        • Direct solver
        • Iterative solver
        • Preconditioners
  • Developer guide
    • Coding Guidelines
      • General Guidelines regarding Coding in C++
      • 4C-specific coding guidelines
        • Avoid define flags
        • Avoid header-in-header inclusion
        • Use of smart pointers
        • Use of Teuchos::ParameterList
        • Const-correctness
        • Enums
      • 4C-specific Naming Conventions
      • Directory structure
        • Details of the src directory
    • Testing
      • Overview on testing mechanisms
        • Guidelines for 4C input files
        • Executing 4C unit tests
        • How to add unit tests to 4C
    • CMake
      • Configuration from a terminal
      • Defining your own CMake presets
      • Reference of all CMake variables
      • Configuration from the IDE
      • For CMake maintainers
        • Conventions
        • General
        • Configuring dependencies
        • Internal dependency management
    • Debugging and Profiling Tools
      • Overview of debugging and profiling tools
      • Useful options for Debugging with gdb (or your IDE)
        • Build debug version
        • Pretty printing of the Standard Library
        • Useful settings for MPI Debugging
      • Code profiling with callgrind
      • Configure and build for profiling
      • Run simulation with valgrind
      • Examine results with kcachegrind
      • Teuchos Time Monitor
      • Add a timer for a method in 4C
      • How to interpret the output of the TimeMonitor
    • Documenting the code with Doxygen
      • What is Doxygen and why does 4C rely on it?
      • 4C’s Policy
      • How to write useful Doxygen documentation
      • What needs to be documented?
      • Building the Doxygen Documentation
        • Local build using CMake
        • Pipeline build
      • Choosing good names to simplify documentation
        • Use Intention-Revealing Names
        • Use Searchable Names
        • Use Pronounceable Names
    • Coverage report
      • Best practices
        • 1. Coverage comes after good tests
        • 1. Coverage should increase over time
      • Code coverage
      • Some technical details
    • Speed up recompilation using ccache
      • Enforce a complete recompilation
    • Cloning 4C on a cluster
      • Method 1: Clone 4C repository from GitHub
      • Method 2: Clone 4C from local workstation
      • Method 3: Clone 4C from local workstation via reverse ssh tunnel
    • Distributed computations with the Petra Object Model
      • Petra Object Model
      • Types of Maps – a linear algebra point of view
      • Types of Maps – a finite element point of view
    • Development of specific code blocks
      • Development of material models
        • Input reader for the material model
        • Definition of the material model as an enumeration item
        • Definition of the classes needed for the new material
        • Selection of the material model
        • Unit test of the material model
        • Remark on the dimensionality of the material model
    • How to release 4C
  • Input Parameter Reference
    • General
      • Sections
      • Comments
      • Extended Backus–Naur formalism
    • Element reference
      • Element types
        • STRUCTURE ELEMENTS
        • FLUID ELEMENTS
        • LUBRICATION ELEMENTS
        • TRANSPORT ELEMENTS
        • TRANSPORT2 ELEMENTS
        • ALE ELEMENTS
        • THERMO ELEMENTS
        • ARTERY ELEMENTS
        • REDUCED D AIRWAYS ELEMENTS
        • ACOUSTIC ELEMENTS
      • Cell types
        • 0D cell types
        • 1D cell types
        • 2D cell types
        • 3D cell types
    • Material reference
      • MAT_LinElast1DGrowth
      • MAT_LinElast1D
      • MAT_crystal_plasticity
      • MIX_GrowthRemodelMixtureRule
      • MIX_Rule_Simple
      • MIX_Rule_Map
      • MIX_Rule_Function
      • MIX_Constituent_RemodelFiber_Material_Exponential_Active
      • MIX_Constituent_RemodelFiber_Material_Exponential
      • MIX_Constituent_ImplicitRemodelFiber
      • MIX_Constituent_ExplicitRemodelFiber
      • MIX_Constituent_FullConstrainedMixtureFiber
      • MIX_Prestress_Strategy_Iterative
      • MIX_Prestress_Strategy_Cylinder
      • MIX_Prestress_Strategy_Constant
      • MAT_IterativePrestress
      • MIX_GrowthStrategy_Stiffness
      • MIX_GrowthStrategy_Anisotropic
      • MIX_GrowthStrategy_Isotropic
      • MIX_Constituent_SolidMaterial
      • MIX_Constituent_ElastHyper_ElastinMembrane
      • MIX_Constituent_ElastHyper_Damage
      • MIX_Constituent_ElastHyper
      • MAT_Mixture
      • MAT_ParticleWallDEM
      • MAT_ParticleDEM
      • MAT_ParticleSPHBoundary
      • MAT_ParticleSPHFluid
      • MAT_0D_MAXWELL_ACINUS_OGDEN
      • MAT_0D_MAXWELL_ACINUS_DOUBLEEXPONENTIAL
      • MAT_0D_MAXWELL_ACINUS_EXPONENTIAL
      • MAT_0D_MAXWELL_ACINUS_NEOHOOKEAN
      • MAT_0D_MAXWELL_ACINUS
      • MAT_Crosslinker
      • MAT_Kirchhoff_Love_shell
      • MAT_BeamKirchhoffTorsionFreeElastHyper_ByModes
      • MAT_BeamKirchhoffTorsionFreeElastHyper
      • MAT_BeamKirchhoffElastHyper_ByModes
      • MAT_BeamKirchhoffElastHyper
      • MAT_BeamReissnerElastHyper_ByModes
      • MAT_BeamReissnerElastPlastic
      • MAT_BeamReissnerElastHyper
      • MAT_Struct_Spring
      • MAT_PhaseLawByFunction
      • MAT_PhaseLawConstraint
      • MAT_PhaseLawTangent
      • MAT_PhaseLawLinear
      • MAT_FluidPoroSinglePhaseDofSaturation
      • MAT_FluidPoroSinglePhaseDofPressure
      • MAT_FluidPoroSinglePhaseDofDiffPressure
      • MAT_FluidPoroVolFracPressure
      • MAT_FluidPoroSingleVolFrac
      • MAT_FluidPoroSinglePhase
      • MAT_FluidPoroSingleReaction
      • MAT_FluidPoroMultiPhaseReactions
      • MAT_FluidPoroMultiPhase
      • MAT_FluidPoro
      • MAT_StructPoroReactionECM
      • MAT_StructPoroReaction
      • MAT_FluidPoroViscosityLawCellAdherence
      • MAT_FluidPoroViscosityLawConstant
      • MAT_FluidPoroRelPermeabilityLawExp
      • MAT_FluidPoroRelPermeabilityLawConstant
      • MAT_PoroDensityLawExp
      • MAT_PoroDensityLawConstant
      • MAT_PlasticElastHyper
      • MAT_PlasticElastHyperVCU
      • MAT_ElastHyper
      • ELAST_Iso1Pow
      • MAT_Struct_Multiscale
      • MAT_Struct_Damage
      • ELAST_IsoMooneyRivlin
      • MAT_Struct_SuperElastSMA
      • MAT_Struct_PlasticGTN
      • MAT_Struct_ThermoPlasticLinElast
      • ELAST_CoupLogNeoHooke
      • MAT_Struct_DruckerPrager
      • MAT_Struct_ThermoStVenantK
      • MAT_Struct_StVenantKirchhoff
      • ELAST_CoupSimoPister
      • MAT_Struct_PlasticNlnLogNeoHooke
      • MAT_elchphase
      • ELAST_IsoAnisoExpo
      • ELAST_CoupSVK
      • MAT_Struct_PlasticLinElast
      • MAT_elchmat
      • ELAST_Iso2Pow
      • MAT_matlist_chemo_reac
      • MAT_matlist_chemotaxis
      • MAT_matlist_reactions
      • MAT_Struct_Robinson
      • MAT_matlist
      • MAT_electrode
      • ELAST_IsoExpoPow
      • MAT_scatra_reaction_poro
      • MAT_Muscle_Weickenmeier
      • MAT_Struct_Viscoplastic_No_Yield_Surface
      • MAT_lubrication_law_roeland
      • MAT_VISCONEOHOOKE
      • MAT_lubrication_law_barus
      • MAT_fluid_weakly_compressible
      • VISCO_IsoRateDep
      • MAT_ViscoElastHyper
      • MAT_lubrication_law_constant
      • MAT_fluid_murnaghantait
      • ELAST_IsoOgden
      • MAT_VISCOANISO
      • MAT_lubrication
      • MAT_fluid_linear_density_viscosity
      • ELAST_IsoNeoHooke
      • MAT_carreauyasuda
      • VISCO_GenMax
      • MAT_scatra
      • MAT_herschelbulkley
      • MAT_sutherland
      • MAT_Struct_AAANeoHooke
      • ELAST_CoupBlatzKo
      • MAT_modpowerlaw
      • MAT_scatra_multiporo_volfrac
      • MAT_fluid
      • ELAST_IsoMuscle_Blemker
      • MAT_scatra_reaction
      • MAT_myocard
      • MAT_scatra_multiporo_fluid
      • MAT_scatra_multiporo_solid
      • MAT_scatra_multiporo_temperature
      • MAT_Muscle_Combo
      • MAT_scatra_chemotaxis
      • MAT_newman
      • MAT_scatra_multiscale
      • MAT_Muscle_Giantesio
      • MAT_Struct_ThermoPlasticHyperElast
      • MAT_ion
      • MAT_newman_multiscale
      • MAT_scl
      • ELAST_CoupLogMixNeoHooke
      • ELAST_CoupExpPol
      • ELAST_CoupNeoHooke
      • ELAST_CoupMooneyRivlin
      • ELAST_IsoYeoh
      • ELAST_Coup1Pow
      • ELAST_Coup2Pow
      • ELAST_Coup3Pow
      • ELAST_Coup13aPow
      • ELAST_IsoTestMaterial
      • ELAST_RemodelFiber
      • ELAST_VolSussmanBathe
      • ELAST_VolPenalty
      • ELAST_VolOgden
      • ELAST_VolPow
      • ELAST_CoupAnisoExpoActive
      • ELAST_CoupAnisoExpo
      • ELAST_CoupAnisoExpoShear
      • ELAST_CoupAnisoPow
      • ELAST_CoupAnisoExpoTwoCoup
      • ELAST_CoupAnisoNeoHooke
      • ELAST_AnisoActiveStress_Evolution
      • ELAST_CoupAnisoNeoHooke_VarProp
      • ELAST_StructuralTensor
      • ELAST_CoupTransverselyIsotropic
      • ELAST_CoupVarga
      • ELAST_IsoVarga
      • VISCO_CoupMyocard
      • VISCO_Fract
      • MAT_ConstraintMixture
      • VISCO_PART
      • VISCO_GeneralizedGenMax
      • MAT_CNST_ART
      • VISCO_BRANCH
      • MAT_Fourier
      • MAT_soret
      • MAT_Membrane_ElastHyper
      • MAT_Membrane_ActiveStrain
      • MAT_GrowthRemodel_ElastHyper
      • MAT_MultiplicativeSplitDefgradElastHyper
      • MAT_InelasticDefgradNoGrowth
      • MAT_InelasticDefgradLinScalarIso
      • MAT_InelasticDefgradLinScalarAniso
      • MAT_InelasticDefgradPolyIntercalFracIso
      • MAT_InelasticDefgradPolyIntercalFracAniso
      • MAT_InelasticDefgradLinTempIso
      • MAT_InelasticDefgradTimeFunct
      • MAT_InelasticDefgradTransvIsotropElastViscoplast
      • MAT_ViscoplasticLawReformulatedJohnsonCook
      • MAT_ScDepInterp
      • MAT_StructPoro
      • MAT_PoroLawLinear
      • MAT_PoroLawConstant
      • MAT_PoroLawNeoHooke
      • MAT_PoroLawIncompSkel
      • MAT_PoroLawLinBiot
      • MAT_PoroLawDensityDependent
    • Cloning material reference
    • Prescribed Condition Reference
      • DESIGN POINT NEUMANN CONDITIONS
      • DESIGN POINT MOMENT EB CONDITIONS
      • DESIGN LINE NEUMANN CONDITIONS
      • DESIGN SURF NEUMANN CONDITIONS
      • DESIGN VOL NEUMANN CONDITIONS
      • DESIGN POINT TRANSPORT NEUMANN CONDITIONS
      • DESIGN LINE TRANSPORT NEUMANN CONDITIONS
      • DESIGN SURF TRANSPORT NEUMANN CONDITIONS
      • DESIGN VOL TRANSPORT NEUMANN CONDITIONS
      • DESIGN POINT THERMO NEUMANN CONDITIONS
      • DESIGN LINE THERMO NEUMANN CONDITIONS
      • DESIGN SURF THERMO NEUMANN CONDITIONS
      • DESIGN VOL THERMO NEUMANN CONDITIONS
      • DESIGN POINT PORO NEUMANN CONDITIONS
      • DESIGN LINE PORO NEUMANN CONDITIONS
      • DESIGN SURF PORO NEUMANN CONDITIONS
      • DESIGN VOL PORO NEUMANN CONDITIONS
      • DESIGN POINT DIRICH CONDITIONS
      • DESIGN LINE DIRICH CONDITIONS
      • DESIGN SURF DIRICH CONDITIONS
      • DESIGN VOL DIRICH CONDITIONS
      • DESIGN POINT ALE DIRICH CONDITIONS
      • DESIGN LINE ALE DIRICH CONDITIONS
      • DESIGN SURF ALE DIRICH CONDITIONS
      • DESIGN VOL ALE DIRICH CONDITIONS
      • DESIGN POINT TRANSPORT DIRICH CONDITIONS
      • DESIGN LINE TRANSPORT DIRICH CONDITIONS
      • DESIGN SURF TRANSPORT DIRICH CONDITIONS
      • DESIGN VOL TRANSPORT DIRICH CONDITIONS
      • DESIGN POINT THERMO DIRICH CONDITIONS
      • DESIGN LINE THERMO DIRICH CONDITIONS
      • DESIGN SURF THERMO DIRICH CONDITIONS
      • DESIGN VOL THERMO DIRICH CONDITIONS
      • DESIGN POINT PORO DIRICH CONDITIONS
      • DESIGN LINE PORO DIRICH CONDITIONS
      • DESIGN SURF PORO DIRICH CONDITIONS
      • DESIGN VOL PORO DIRICH CONDITIONS
      • DESIGN POINT NURBS LS DIRICH CONDITIONS
      • DESIGN LINE NURBS LS DIRICH CONDITIONS
      • DESIGN SURF NURBS LS DIRICH CONDITIONS
      • DESIGN VOL NURBS LS DIRICH CONDITIONS
      • DESIGN POINT COUPLING CONDITIONS
      • DESIGN POINT THERMO COUPLING CONDITIONS
      • DESIGN POINT INITIAL FIELD CONDITIONS
      • DESIGN LINE INITIAL FIELD CONDITIONS
      • DESIGN SURF INITIAL FIELD CONDITIONS
      • DESIGN VOL INITIAL FIELD CONDITIONS
      • DESIGN POINT THERMO INITIAL FIELD CONDITIONS
      • DESIGN LINE THERMO INITIAL FIELD CONDITIONS
      • DESIGN SURF THERMO INITIAL FIELD CONDITIONS
      • DESIGN VOL THERMO INITIAL FIELD CONDITIONS
      • DESIGN DOMAIN INTEGRAL SURF CONDITIONS
      • DESIGN DOMAIN INTEGRAL VOL CONDITIONS
      • DESIGN BOUNDARY INTEGRAL SURF CONDITIONS
      • DESIGN LINE ALE WEAR CONDITIONS 2D
      • DESIGN SURFACE WEAR CONDITIONS 3D
      • DESIGN POINT LOCSYS CONDITIONS
      • DESIGN LINE LOCSYS CONDITIONS
      • DESIGN SURF LOCSYS CONDITIONS
      • DESIGN VOL LOCSYS CONDITIONS
      • DESIGN LINE PERIODIC BOUNDARY CONDITIONS
      • DESIGN SURF PERIODIC BOUNDARY CONDITIONS
      • DESIGN LINE WEAK DIRICHLET CONDITIONS
      • DESIGN SURFACE WEAK DIRICHLET CONDITIONS
      • DESIGN PATCH RECOVERY BOUNDARY LINE CONDITIONS
      • DESIGN PATCH RECOVERY BOUNDARY SURF CONDITIONS
      • DESIGN SURFACE VOLUME CONSTRAINT 3D
      • DESIGN SURFACE VOLUME CONSTRAINT 3D PEN
      • DESIGN SURFACE AREA CONSTRAINT 3D
      • DESIGN SURFACE VOLUME MONITOR 3D
      • DESIGN SURFACE AREA MONITOR 3D
      • DESIGN LINE AREA CONSTRAINT 2D
      • DESIGN LINE AREA MONITOR 2D
      • DESIGN SURFACE MULTIPNT CONSTRAINT 3D
      • DESIGN SURFACE NORMALDIR MULTIPNT CONSTRAINT 3D
      • DESIGN SURFACE NORMALDIR MULTIPNT CONSTRAINT 3D PEN
      • DESIGN LINE MULTIPNT CONSTRAINT 2D
      • DESIGN SURF MODE FOR KRYLOV SPACE PROJECTION
      • DESIGN VOL MODE FOR KRYLOV SPACE PROJECTION
      • DESIGN LINE MORTAR CONTACT CONDITIONS 2D
      • DESIGN SURF MORTAR CONTACT CONDITIONS 3D
      • DESIGN LINE MORTAR COUPLING CONDITIONS 2D
      • DESIGN SURF MORTAR COUPLING CONDITIONS 3D
      • DESIGN LINE MORTAR SYMMETRY CONDITIONS 3D
      • DESIGN POINT MORTAR SYMMETRY CONDITIONS 2D/3D
      • DESIGN LINE MORTAR EDGE CONDITIONS 3D
      • DESIGN POINT MORTAR CORNER CONDITIONS 2D/3D
      • DESIGN LINE MORTAR MULTI-COUPLING CONDITIONS 2D
      • DESIGN SURF MORTAR MULTI-COUPLING CONDITIONS 3D
      • DESIGN S2I MESHTYING LINE CONDITIONS
      • DESIGN S2I MESHTYING SURF CONDITIONS
      • DESIGN S2I KINETICS POINT CONDITIONS
      • DESIGN S2I KINETICS LINE CONDITIONS
      • DESIGN S2I KINETICS SURF CONDITIONS
      • DESIGN SCATRA MULTI-SCALE COUPLING POINT CONDITIONS
      • DESIGN S2I KINETICS GROWTH LINE CONDITIONS
      • DESIGN S2I KINETICS GROWTH SURF CONDITIONS
      • DESIGN S2I SCL COUPLING SURF CONDITIONS
      • SCATRA FLUX CALC LINE CONDITIONS
      • SCATRA FLUX CALC SURF CONDITIONS
      • DESIGN TOTAL AND MEAN SCALAR LINE CONDITIONS
      • DESIGN TOTAL AND MEAN SCALAR SURF CONDITIONS
      • DESIGN TOTAL AND MEAN SCALAR VOL CONDITIONS
      • DESIGN SCATRA RELATIVE ERROR LINE CONDITIONS
      • DESIGN SCATRA RELATIVE ERROR SURF CONDITIONS
      • DESIGN SCATRA RELATIVE ERROR VOL CONDITIONS
      • DESIGN SCATRA COUPLING SURF CONDITIONS
      • DESIGN TRANSPORT ROBIN LINE CONDITIONS
      • DESIGN TRANSPORT ROBIN SURF CONDITIONS
      • TRANSPORT NEUMANN INFLOW LINE CONDITIONS
      • TRANSPORT NEUMANN INFLOW SURF CONDITIONS
      • TRANSPORT THERMO CONVECTION LINE CONDITIONS
      • TRANSPORT THERMO CONVECTION SURF CONDITIONS
      • DESIGN SCATRA HETEROGENEOUS REACTION LINE CONDITIONS / MASTER
      • DESIGN SCATRA HETEROGENEOUS REACTION SURF CONDITIONS / MASTER
      • DESIGN SCATRA HETEROGENEOUS REACTION LINE CONDITIONS / SLAVE
      • DESIGN SCATRA HETEROGENEOUS REACTION SURF CONDITIONS / SLAVE
      • DESIGN SCATRA SURF CONDITIONS / PARTITIONING
      • DESIGN SCATRA VOL CONDITIONS / PARTITIONING
      • DESIGN ELECTRODE STATE OF CHARGE LINE CONDITIONS
      • DESIGN ELECTRODE STATE OF CHARGE SURF CONDITIONS
      • DESIGN ELECTRODE STATE OF CHARGE VOL CONDITIONS
      • DESIGN CELL VOLTAGE POINT CONDITIONS
      • DESIGN CELL VOLTAGE LINE CONDITIONS
      • DESIGN CELL VOLTAGE SURF CONDITIONS
      • ELECTRODE BOUNDARY KINETICS POINT CONDITIONS
      • ELECTRODE BOUNDARY KINETICS LINE CONDITIONS
      • ELECTRODE BOUNDARY KINETICS SURF CONDITIONS
      • ELECTRODE DOMAIN KINETICS LINE CONDITIONS
      • ELECTRODE DOMAIN KINETICS SURF CONDITIONS
      • ELECTRODE DOMAIN KINETICS VOL CONDITIONS
      • DESIGN CCCV CELL CYCLING POINT CONDITIONS
      • DESIGN CCCV CELL CYCLING LINE CONDITIONS
      • DESIGN CCCV CELL CYCLING SURF CONDITIONS
      • DESIGN CCCV HALF-CYCLE POINT CONDITIONS
      • DESIGN CCCV HALF-CYCLE LINE CONDITIONS
      • DESIGN CCCV HALF-CYCLE SURF CONDITIONS
      • DESIGN SURF TURBULENT INFLOW TRANSFER
      • FLUID TURBULENT INFLOW VOLUME
      • DESIGN SURFACE FLOW-DEPENDENT PRESSURE CONDITIONS
      • DESIGN LINE SLIP SUPPLEMENTAL CURVED BOUNDARY CONDITIONS
      • DESIGN SURFACE SLIP SUPPLEMENTAL CURVED BOUNDARY CONDITIONS
      • DESIGN LINE NAVIER-SLIP BOUNDARY CONDITIONS
      • DESIGN SURF NAVIER-SLIP BOUNDARY CONDITIONS
      • DESIGN SURFACE CONSERVATIVE OUTFLOW CONSISTENCY
      • FLUID NEUMANN INFLOW LINE CONDITIONS
      • FLUID NEUMANN INFLOW SURF CONDITIONS
      • DESIGN LINE MIXED/HYBRID DIRICHLET CONDITIONS
      • DESIGN SURFACE MIXED/HYBRID DIRICHLET CONDITIONS
      • DESIGN FLUID STRESS CALC LINE CONDITIONS
      • DESIGN FLUID STRESS CALC SURF CONDITIONS
      • DESIGN FLUID SURF LIFT&DRAG
      • DESIGN FLOW RATE LINE CONDITIONS
      • DESIGN FLOW RATE SURF CONDITIONS
      • DESIGN SURF VOLUMETRIC FLOW CONDITIONS
      • DESIGN LINE VOLUMETRIC FLOW BORDER NODES
      • DESIGN SURF TOTAL TRACTION CORRECTION CONDITIONS
      • DESIGN LINE TOTAL TRACTION CORRECTION BORDER NODES
      • DESIGN SURFACE NORMAL NO PENETRATION CONDITION
      • DESIGN LINE NORMAL NO PENETRATION CONDITION
      • DESIGN VOLUME POROCOUPLING CONDITION
      • DESIGN SURFACE POROCOUPLING CONDITION
      • DESIGN SURFACE PORO PARTIAL INTEGRATION
      • DESIGN LINE PORO PARTIAL INTEGRATION
      • DESIGN SURFACE PORO PRESSURE INTEGRATION
      • DESIGN LINE PORO PRESSURE INTEGRATION
      • DESIGN ALE UPDATE LINE CONDITIONS
      • DESIGN ALE UPDATE SURF CONDITIONS
      • DESIGN FSI COUPLING LINE CONDITIONS
      • DESIGN FSI COUPLING SURF CONDITIONS
      • DESIGN FSI COUPLING CENTER DISP LINE CONDITIONS
      • DESIGN FSI COUPLING CENTER DISP SURF CONDITIONS
      • DESIGN STRUCTURE ALE COUPLING SURF CONDITIONS
      • DESIGN STRUCTURE FLUID VOLUME COUPLING VOL CONDITIONS
      • DESIGN FPSI COUPLING LINE CONDITIONS
      • DESIGN FPSI COUPLING SURF CONDITIONS
      • DESIGN SURFACE NEUMANN INTEGRATION
      • DESIGN LINE NEUMANN INTEGRATION
      • DESIGN FLUID MESH VOL CONDITIONS
      • DESIGN FLUID FLUID COUPLING SURF CONDITIONS
      • DESIGN ALE FLUID COUPLING SURF CONDITIONS
      • DESIGN XFEM DISPLACEMENT SURF CONDITIONS
      • DESIGN XFEM LEVELSET WEAK DIRICHLET VOL CONDITIONS
      • DESIGN XFEM LEVELSET NEUMANN VOL CONDITIONS
      • DESIGN XFEM LEVELSET NAVIER SLIP VOL CONDITIONS
      • DESIGN XFEM ROBIN DIRICHLET VOL CONDITIONS
      • DESIGN XFEM ROBIN NEUMANN VOL CONDITIONS
      • DESIGN XFEM LEVELSET TWOPHASE VOL CONDITIONS
      • DESIGN XFEM FLUIDFLUID SURF CONDITIONS
      • DESIGN XFEM FSI PARTITIONED SURF CONDITIONS
      • DESIGN XFEM FSI MONOLITHIC SURF CONDITIONS
      • DESIGN XFEM FPI MONOLITHIC SURF CONDITIONS
      • DESIGN XFEM WEAK DIRICHLET SURF CONDITIONS
      • DESIGN XFEM NEUMANN SURF CONDITIONS
      • DESIGN XFEM NAVIER SLIP SURF CONDITIONS
      • DESIGN XFEM ROBIN DIRICHLET SURF CONDITIONS
      • DESIGN XFEM ROBIN NEUMANN SURF CONDITIONS
      • DESIGN EMBEDDED MESH SOLID SURF COUPLING CONDITIONS
      • DESIGN EMBEDDED SOLID VOL BACKGROUND CONDITIONS
      • DESIGN BIOFILM GROWTH COUPLING SURF CONDITIONS
      • DESIGN NODE 1D ARTERY JUNCTION CONDITIONS
      • DESIGN NODE 1D ARTERY PRESCRIBED CONDITIONS
      • DESIGN NODE 1D ARTERY REFLECTIVE CONDITIONS
      • DESIGN NODE 1D ARTERY IN_OUTLET CONDITIONS
      • DESIGN NODE 1D ARTERY TO POROFLUID COUPLING CONDITIONS
      • DESIGN NODE 1D ARTERY TO SCATRA COUPLING CONDITIONS
      • DESIGN 1D ARTERY/AIRWAY TO POROFLUID NONCONF COUPLING CONDITIONS
      • DESIGN 1D ARTERY/AIRWAY TO SCATRA NONCONF COUPLING CONDITIONS
      • DESIGN NODE REDUCED D To 3D FLOW COUPLING CONDITIONS
      • DESIGN SURF 3D To REDUCED D FLOW COUPLING CONDITIONS
      • DESIGN NODE Reduced D AIRWAYS PRESCRIBED CONDITIONS
      • DESIGN NODE Reduced D AIRWAYS SWITCH FLOW PRESSURE CONDITIONS
      • DESIGN LINE REDUCED D AIRWAYS VOL DEPENDENT PLEURAL PRESSURE CONDITIONS
      • DESIGN LINE REDUCED D AIRWAYS EVALUATE LUNG VOLUME CONDITIONS
      • DESIGN SURF IMPEDANCE CONDITIONS
      • DESIGN SURF CARDIOVASCULAR 0D 4-ELEMENT WINDKESSEL CONDITIONS
      • DESIGN SURF CARDIOVASCULAR 0D ARTERIAL PROX DIST CONDITIONS
      • DESIGN SURF CARDIOVASCULAR 0D SYS-PUL CIRCULATION CONDITIONS
      • DESIGN SURF CARDIOVASCULAR RESPIRATORY 0D SYS-PUL PERIPH CIRCULATION CONDITIONS
      • DESIGN SURF CARDIOVASCULAR 0D-STRUCTURE COUPLING CONDITIONS
      • DESIGN SURF ROBIN SPRING DASHPOT CONDITIONS
      • DESIGN POINT ROBIN SPRING DASHPOT CONDITIONS
      • DESIGN SURF ROBIN SPRING DASHPOT COUPLING CONDITIONS
      • DESIGN THERMO CONVECTION LINE CONDITIONS
      • DESIGN THERMO CONVECTION SURF CONDITIONS
      • DESIGN THERMO ROBIN LINE CONDITIONS
      • DESIGN THERMO ROBIN SURF CONDITIONS
      • DESIGN SSI COUPLING LINE CONDITIONS
      • DESIGN SSI COUPLING SURF CONDITIONS
      • DESIGN SSI COUPLING SOLIDTOSCATRA LINE CONDITIONS
      • DESIGN SSI COUPLING SOLIDTOSCATRA SURF CONDITIONS
      • DESIGN SSI COUPLING SOLIDTOSCATRA VOL CONDITIONS
      • DESIGN SSI COUPLING SCATRATOSOLID LINE CONDITIONS
      • DESIGN SSI COUPLING SCATRATOSOLID SURF CONDITIONS
      • DESIGN SSI COUPLING SCATRATOSOLID VOL CONDITIONS
      • DESIGN SSI INTERFACE MESHTYING POINT CONDITIONS
      • DESIGN SSI INTERFACE MESHTYING LINE CONDITIONS
      • DESIGN SSI INTERFACE MESHTYING SURF CONDITIONS
      • DESIGN SSI MANIFOLD SURF CONDITIONS
      • DESIGN SURF SCATRA MANIFOLD INITIAL FIELD CONDITIONS
      • DESIGN SSI MANIFOLD KINETICS SURF CONDITIONS
      • DESIGN POINT MANIFOLD DIRICH CONDITIONS
      • DESIGN LINE MANIFOLD DIRICH CONDITIONS
      • DESIGN SURF MANIFOLD DIRICH CONDITIONS
      • DESIGN SSI INTERFACE CONTACT LINE CONDITIONS
      • DESIGN SSI INTERFACE CONTACT SURF CONDITIONS
      • DESIGN SSTI INTERFACE MESHTYING LINE CONDITIONS
      • DESIGN SSTI INTERFACE MESHTYING SURF CONDITIONS
      • DESIGN SURFACE PARTICLE WALL
      • TAYLOR GALERKIN OUTFLOW SURF CONDITIONS
      • TAYLOR GALERKIN NEUMANN INFLOW SURF CONDITIONS
      • REINITIALIZATION TAYLOR GALERKIN SURF CONDITIONS
      • DESIGN LINE LEVEL SET CONTACT CONDITION
      • DESIGN POINT LEVEL SET CONTACT CONDITION
      • DESIGN LINE BEAM POTENTIAL CHARGE CONDITIONS
      • DESIGN POINT RIGIDSPHERE POTENTIAL CHARGE CONDITIONS
      • DESIGN LINE PERIODIC RVE 2D BOUNDARY CONDITIONS
      • DESIGN SURF PERIODIC RVE 3D BOUNDARY CONDITIONS
      • DESIGN POINT PERIODIC RVE 2D BOUNDARY REFERENCE CONDITIONS
      • DESIGN POINT COUPLED DOF EQUATION CONDITIONS
      • DESIGN LINE BEAM FILAMENT CONDITIONS
      • DESIGN POINT PENALTY COUPLING CONDITIONS
      • BEAM INTERACTION/BEAM TO BEAM CONTACT CONDITIONS
      • BEAM INTERACTION/BEAM TO SOLID VOLUME MESHTYING VOLUME
      • BEAM INTERACTION/BEAM TO SOLID VOLUME MESHTYING LINE
      • BEAM INTERACTION/BEAM TO SOLID SURFACE MESHTYING SURFACE
      • BEAM INTERACTION/BEAM TO SOLID SURFACE MESHTYING LINE
      • BEAM INTERACTION/BEAM TO SOLID SURFACE CONTACT SURFACE
      • BEAM INTERACTION/BEAM TO SOLID SURFACE CONTACT LINE
      • DESIGN LINE EHL MORTAR COUPLING CONDITIONS 2D
      • DESIGN SURF EHL MORTAR COUPLING CONDITIONS 3D
      • DESIGN OXYGEN PARTIAL PRESSURE CALCULATION LINE CONDITIONS
      • DESIGN OXYGEN PARTIAL PRESSURE CALCULATION SURF CONDITIONS
      • DESIGN OXYGEN PARTIAL PRESSURE CALCULATION VOL CONDITIONS
      • MICROSCALE CONDITIONS
      • DESIGN VOL STC LAYER
    • Contact Constitutive Law Reference
    • Result description reference
    • Functions reference
    • Header parameters
      • ALE DYNAMIC
      • ALE GEOMETRY
      • ARTERIAL DYNAMIC
      • ARTERY GEOMETRY
      • BEAM CONTACT
      • BEAM CONTACT/RUNTIME VTK OUTPUT
      • BEAM INTERACTION
      • BEAM INTERACTION/BEAM TO BEAM CONTACT
      • BEAM INTERACTION/BEAM TO SOLID SURFACE CONTACT
      • BEAM INTERACTION/BEAM TO SOLID SURFACE MESHTYING
      • BEAM INTERACTION/BEAM TO SOLID SURFACE/RUNTIME VTK OUTPUT
      • BEAM INTERACTION/BEAM TO SOLID VOLUME MESHTYING
      • BEAM INTERACTION/BEAM TO SOLID VOLUME MESHTYING/RUNTIME VTK OUTPUT
      • BEAM INTERACTION/BEAM TO SPHERE CONTACT
      • BEAM INTERACTION/CROSSLINKING
      • BEAM INTERACTION/SPHERE BEAM LINK
      • BEAM POTENTIAL
      • BEAM POTENTIAL/RUNTIME VTK OUTPUT
      • BINNING STRATEGY
      • BIOFILM CONTROL
      • BOUNDINGVOLUME STRATEGY
      • BROWNIAN DYNAMICS
      • CARDIAC MONODOMAIN CONTROL
      • CARDIOVASCULAR 0D-STRUCTURE COUPLING
      • CARDIOVASCULAR 0D-STRUCTURE COUPLING/RESPIRATORY PARAMETERS
      • CARDIOVASCULAR 0D-STRUCTURE COUPLING/SYS-PUL CIRCULATION PARAMETERS
      • CONTACT DYNAMIC
      • COUPLED REDUCED-D AIRWAYS AND TISSUE DYNAMIC
      • CUT GENERAL
      • DISCRETISATION
      • ELASTO HYDRO DYNAMIC
      • ELASTO HYDRO DYNAMIC/MONOLITHIC
      • ELASTO HYDRO DYNAMIC/PARTITIONED
      • ELCH CONTROL
      • ELCH CONTROL/DIFFCOND
      • ELCH CONTROL/SCL
      • EMBEDDED MESH COUPLING
      • FLUID BEAM INTERACTION
      • FLUID BEAM INTERACTION/BEAM TO FLUID MESHTYING
      • FLUID BEAM INTERACTION/BEAM TO FLUID MESHTYING/RUNTIME VTK OUTPUT
      • FLUID DYNAMIC
      • FLUID DYNAMIC/EDGE-BASED STABILIZATION
      • FLUID DYNAMIC/MULTIFRACTAL SUBGRID SCALES
      • FLUID DYNAMIC/NONLINEAR SOLVER TOLERANCES
      • FLUID DYNAMIC/POROUS-FLOW STABILIZATION
      • FLUID DYNAMIC/RESIDUAL-BASED STABILIZATION
      • FLUID DYNAMIC/SUBGRID VISCOSITY
      • FLUID DYNAMIC/TIMEADAPTIVITY
      • FLUID DYNAMIC/TURBULENCE MODEL
      • FLUID DYNAMIC/TURBULENT INFLOW
      • FLUID DYNAMIC/WALL MODEL
      • FLUID GEOMETRY
      • FPSI DYNAMIC
      • FS3I DYNAMIC
      • FS3I DYNAMIC/PARTITIONED
      • FS3I DYNAMIC/STRUCTURE SCALAR STABILIZATION
      • FSI DYNAMIC
      • FSI DYNAMIC/CONSTRAINT
      • FSI DYNAMIC/MONOLITHIC SOLVER
      • FSI DYNAMIC/PARTITIONED SOLVER
      • FSI DYNAMIC/TIMEADAPTIVITY
      • IO
        • IO
      • IO/EVERY ITERATION
      • IO/MONITOR STRUCTURE DBC
      • IO/RUNTIME VTK OUTPUT
      • IO/RUNTIME VTK OUTPUT/BEAMS
      • IO/RUNTIME VTK OUTPUT/FLUID
      • IO/RUNTIME VTK OUTPUT/STRUCTURE
      • IO/RUNTIME VTP OUTPUT STRUCTURE
      • LEVEL-SET CONTROL
      • LEVEL-SET CONTROL/REINITIALIZATION
      • LOMA CONTROL
      • LUBRICATION DYNAMIC
      • LUBRICATION GEOMETRY
      • MESH PARTITIONING
      • MOR
      • MORTAR COUPLING
      • MORTAR COUPLING/PARALLEL REDISTRIBUTION
      • MULTI POINT CONSTRAINTS
      • NURBS
      • PARTICLE DYNAMIC
      • PARTICLE DYNAMIC/DEM
      • PARTICLE DYNAMIC/INITIAL AND BOUNDARY CONDITIONS
      • PARTICLE DYNAMIC/SPH
      • PASI DYNAMIC
      • PERIODIC BOUNDINGBOX GEOMETRY
      • POROELASTICITY DYNAMIC
      • POROFLUIDMULTIPHASE DYNAMIC
      • POROFLUIDMULTIPHASE DYNAMIC/ARTERY COUPLING
      • POROMULTIPHASE DYNAMIC
      • POROMULTIPHASE DYNAMIC/MONOLITHIC
      • POROMULTIPHASE DYNAMIC/PARTITIONED
      • POROMULTIPHASESCATRA DYNAMIC
      • POROMULTIPHASESCATRA DYNAMIC/MONOLITHIC
      • POROMULTIPHASESCATRA DYNAMIC/PARTITIONED
      • POROSCATRA CONTROL
      • PROBLEM SIZE
      • PROBLEM TYPE
      • REDUCED D AIRWAYS GEOMETRY
      • REDUCED DIMENSIONAL AIRWAYS DYNAMIC
      • SCALAR TRANSPORT DYNAMIC
      • SCALAR TRANSPORT DYNAMIC/ARTERY COUPLING
      • SCALAR TRANSPORT DYNAMIC/EXTERNAL FORCE
      • SCALAR TRANSPORT DYNAMIC/NONLINEAR
      • SCALAR TRANSPORT DYNAMIC/S2I COUPLING
      • SCALAR TRANSPORT DYNAMIC/STABILIZATION
      • SEARCH TREE
      • SEMI-SMOOTH PLASTICITY
      • SOLVER 1
      • SOLVER 2
      • SOLVER 3
      • SOLVER 4
      • SOLVER 5
      • SOLVER 6
      • SOLVER 7
      • SOLVER 8
      • SOLVER 9
      • SSI CONTROL
      • SSI CONTROL/ELCH
      • SSI CONTROL/MANIFOLD
      • SSI CONTROL/MONOLITHIC
      • SSI CONTROL/PARTITIONED
      • SSTI CONTROL
      • SSTI CONTROL/MONOLITHIC
      • SSTI CONTROL/THERMO
      • STI DYNAMIC
      • STI DYNAMIC/MONOLITHIC
      • STI DYNAMIC/PARTITIONED
      • STRUCT NOX
      • STRUCT NOX/Direction
      • STRUCT NOX/Direction/Newton
      • STRUCT NOX/Direction/Newton/Linear Solver
      • STRUCT NOX/Direction/Steepest Descent
      • STRUCT NOX/Line Search
      • STRUCT NOX/Line Search/Backtrack
      • STRUCT NOX/Line Search/Full Step
      • STRUCT NOX/Line Search/More’-Thuente
      • STRUCT NOX/Line Search/Polynomial
      • STRUCT NOX/Printing
      • STRUCT NOX/Pseudo Transient
      • STRUCT NOX/Solver Options
      • STRUCT NOX/Status Test
      • STRUCT NOX/Trust Region
      • STRUCTURAL DYNAMIC
      • STRUCTURAL DYNAMIC/ERROR EVALUATION
      • STRUCTURAL DYNAMIC/GENALPHA
      • STRUCTURAL DYNAMIC/ONESTEPTHETA
      • STRUCTURAL DYNAMIC/TIMEADAPTIVITY
      • STRUCTURAL DYNAMIC/TIMEADAPTIVITY/JOINT EXPLICIT
      • STRUCTURE GEOMETRY
      • THERMAL DYNAMIC
      • THERMAL DYNAMIC/GENALPHA
      • THERMAL DYNAMIC/ONESTEPTHETA
      • THERMAL DYNAMIC/RUNTIME CSV OUTPUT
      • THERMAL DYNAMIC/RUNTIME VTK OUTPUT
      • THERMO GEOMETRY
      • TRANSPORT GEOMETRY
      • TRANSPORT2 GEOMETRY
      • TSI CONTACT
      • TSI DYNAMIC
      • TSI DYNAMIC/MONOLITHIC
      • TSI DYNAMIC/PARTITIONED
      • VOLMORTAR COUPLING
      • WEAR
      • XFEM GENERAL
      • XFLUID DYNAMIC/GENERAL
      • XFLUID DYNAMIC/STABILIZATION
      • XFLUID DYNAMIC/XFPSI MONOLITHIC
  • Tools and Scripts
    • abaqus to 4C input converter
    • 4C converter to other formats
  • Appendix
    • Writing documentation
      • Usage
    • Miscellaneous math guide
      • Surface areas and surface integrals
        • Motivation and definition.
        • Integration on submanifolds.
        • Example.
        • Remark.
    • Index
    • References
      • ~
      • ~
4C
  • Appendix
  • Miscellaneous math guide
  • View page source

Miscellaneous math guide

  • Surface areas and surface integrals
    • Motivation and definition.
    • Integration on submanifolds.
    • Example.
    • Remark.
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