svFSI_master.inp

#---------------------------------------------------------------------
#  This is the master input file for svFSI with all possible options
#  that the code can read. One may use this file as a reference for
#  various commands and options, or as a template and modify it for
#  their application.
#
#  In general, the input file for svFSI is divided into three parts:
#     1.  General simulation parameters
#     2.  Mesh information
#     3.  Equations
#
#  As the name indicates, `General simulation parameters' describe
#  the basic parameters about the problem including spatial dimension,
#  time step control, file output, option to restart, etc. Mesh data
#  is provided in the second part that may also include additional
#  information such as domains, fiber orientation, initial values,
#  prestress, etc. Finally, information on equations being solved
#  is provided that includes the type of equation, coupling,
#  boundary conditions, settings for the linear and nonlinear solver,
#  and output control.
#
#  The input file for svFSI is a scripting code that sets values to
#  specific parameters. A colon ":" is used as a separator between
#  the keyword and its value. If the parameters being set are single-
#  valued constants, you may use a single line structure as,
#
#  This is a keyword with value: 1.3
#
#  First part, which is the part before ":", is the keyword to the
#  parameter, and the second part, which is the part after ":", is the
#  value. Keywords can occur in any order in the script.
#
#  There are five types of values that a keyword can read:
#     o   logical (true/false)
#     o   integer values
#     o   real/float values
#     o   strings or characters
#     o   file paths
#     o   vector of real or integer values
#
#  Some parameters have a range and should be selected from available
#  choices only. If a range is required, it is shown by brackets and a
#  dash, e.g. [0.0-inf) denotes a real number between 0.0 and
#  infinity. In the case that there are limited choices, those
#  choices are separated by slash /, e.g. (0/1) means either 0 or
#  1 must be selected. If there is no restriction on the selection,
#  then no brackets are used.
#
#  For logical false, any of `False', `0', `F', `f', `false' can be
#  used. Likewise, for logical true, any of `True', `1', `T', `t',
#  true can be used. Real numbers can be formatted as {10.0, 10.0D0,
#  1.e1, 1.D1}. Any line that begins with `#' is treated as a comment.
#  You may add comments, have space before keywords or after ":".
#
#  If the values to be set are a part of a bigger entity, you need
#  to use braces ("{", "}") to mark the scope of that entity. E.g.:
#
#   Domain: 1 {
#      Density:             0.1      # [epsilon - inf)
#      Poisson ratio:       0.35     # [0.0 - (0.5-epsilon)]
#   }
#
#  In this example, "Domain" is a keyword (i.e., the entity to be
#  specified) and "1" refers to the first "Domain". Within this
#  entity, "Density" is set to "0.1" and "Poisson ratio" is set to
#  "0.35".
#
#  Note that the order of lines doesn't matter within each block
#  enclosed by "{" and "}". If a keyword doesn't have a default value,
#  it has to be specified by the user. For the optional arguments,
#  default value is shown.

#  For more details, please refer to the examples provided in
#  "svFSI-Tests" repository at GitHub. You may also refer to
#  READFILES.f for a more complete set of available options.
#---------------------------------------------------------------------

######################################################################
# 1.  General parameters

#---------------------------------------------------------------------
#  Below are some of the basic and essential parameters for svFSI
Number of spatial dimensions:          2           # [2/3]
Number of time steps:                  1000        # [1 - inf)
Time step size:                        0.001       # (0 - inf)

#---------------------------------------------------------------------
Spectral radius of infinite time step: 0.5         # [0.0 - 1.0]       [DEFAULT: 0.2]
#  The code uses the generalized alpha method for time integration
#  implemented using Newmark's predictor and multi-step corrector
#  strategy. Spectral radius is used to compute parameters for the
#  generalized alpha method. A value of 0.0 leads to an over-damped
#  system while 1.0 leads to an undamped system. 0.5 is optimal.

#---------------------------------------------------------------------
Starting time step:                    0           # [0 - inf)         [DEFAULT: 0]
#  This is the starting time step value that is usually 0 if the
#  simulation is started from 0 or initialized from the restart file
#  for a restarted simulation. The users can override by providing
#  a specific number as the starting time step. This may be used in
#  FSI simulations where an equilibrium flow has already been
#  established using rigid walls and the users may want to start FSI
#  thereafter.

#---------------------------------------------------------------------
Number of initialization time steps:   10          # (0 - inf)         [DEFAULT: 0]
#  "Number of initialization time steps" (nITS) could be used to
#  initialize the simulation with a reduced time step (= dt/10). This
#  is useful to avoid any numerical instability due to zero
#  initialization.

#---------------------------------------------------------------------
Continue previous simulation:          f           # [f/t]
#  The above parameter, if set to true, will restart the simulation
#  by loading a svFSI compatible restart file. If the file is not
#  available, the code will issue a warning and start the simulation
#  from 0.

Restart file name:            stFile.bin           # [DEFAULT: stFile.bin]
#  Name of the file to be read for restarting simulations. This must
#  be the name of the file and not its path. The code will look for
#  this file within the results folder set by the keyword
#  "Save results in folder"

Overwrite restart file:                t           # [f/t]             [DEFAULT: f]
#  If set to true, restart files will be overwritten. Otherwise, a
#  restart file is written to a separate file at a frequency set by
#  the keyword "Increment in saving restart files".

Increment in saving restart files:     10          # [1 - inf)         [DEFAULT: saveIncr/[10]]

#---------------------------------------------------------------------
Convert BIN to VTK format:             f           # [t/f]             [DEFAULT: f]
#  If set to true, the code will read all the available restart files
#  and output desired quantities to vtk format for visualization in
#  Paraview. This feature will allow modifying output variables at a
#  later time if not already written during the original simulation.
#  The code will scan for all the restart files in the results folder
#  set by the keyword "Save results in folder" at a frequency set by
#  "Increment in saving restart files". However, if any restart file
#  is not found, the code will skip that time step to the next one.

#---------------------------------------------------------------------
Simulation initialization file path:   result001.vtu
#  Could be used to initialize variables from vtu format. However,
#  caution must be exercised when using this feature as the code will
#  only look for state variables such as velocity, pressure, displace-
#  ment, temperature, etc. for initialization. It is the user's
#  responsibility to make sure that this data is available in the vtu
#  file.

#---------------------------------------------------------------------
#  Below are some VTK output control parameters
Save results to VTK format:            t           # [f/t]
Name prefix of saved VTK files:        result
Start saving after time step:          20          # [1 - inf)         [DEFAULT: 1]
Increment in saving VTK files:         5           # [1 - inf)         [DEFAULT: 10]

#---------------------------------------------------------------------
Save averaged results:                 t           # [f/t]             [DEFAULT: f]
#  Computes time-averaged results from the entire simulation. Note
#  that the averaging operation is performed after the last time step
#  of the simulation using vtu files written at a frequency specified
#  by "Increment in saving VTK files". An error is thrown if a vtu
#  file is not found. For cardiovascular simulations, the user should
#  ensure that the total number of time steps corresponds to the
#  period of the cardiac cycle.

Start averaging from zero:             t           # [f/t]             [DEFAULT: f]
#  If set to true, averaging is performed from the first time step to
#  the last time step using vtu files written at a frequency specified
#  by "Increment in saving VTK files". If set to false, for e.g., when
#  a simulation is restarted, averaging starts from the time step when
#  the simulation is restarted from. This feature may be useful for
#  cases where averaging is desired only for the last cardiac cycle.

#---------------------------------------------------------------------
Save results in folder:                foldername  # [DEFAULT: *-procs]

#---------------------------------------------------------------------
Searched file name to trigger stop:    STOP_SIM                      [DEFAULT: STOP_SIM]
#  If the user wants to terminate a simulation but plans to restart it
#  later, instead of abruptly terminating the simulation using
#  Ctrl[Cmd]+C or analogous command, the user may create an empty file
#  named as, for e.g., STOP_SIM, within the results folder specified
#  by "Save results in folder". The code would then come to a clean
#  halt by writing a restart file. If an integer value is provided at
#  the beginning of the file, the code would then terminate at that
#  particular time step. An empty file could be created using Linux
#  command `touch' (for e.g., < touch 24-procs/STOP_SIM >).

#---------------------------------------------------------------------
Check IEN order:                       t           # [f/t]             [DEFAULT: t]
#  Checks for a compatible ordering of the element connectivity.

#---------------------------------------------------------------------
Simulation requires remeshing:         f           # [f/t]             [DEFAULT: f]
#  This feature is used for FSI simulation where the fluid mesh is
#  deformed. The solver will monitor for the element Jacobian as the
#  measure of element distortion, and perform an on-the-fly remeshing
#  if Jacobian <= 0. All the data structures will be projected from
#  the old mesh to the new mesh and the solver writes information
#  related to the new mesh and its new partitioning to the folder,
#  ".remesh_tmp_dir" within the results folder set by the
#  "Save results in folder" command. The new mesh and its partitioning
#  will be used if and when the simulation is restarted. Note that the
#  remeshing step could be expensive and depends on the edge size and
#  number of processors used. This feature is currently available for
#  linear tetrahedral elements only.

#---------------------------------------------------------------------
Colorful terminal output:              t           # [f/t]             [DEFAULT: t]

Use separator in the history file:     t           # [f/t]             [DEFAULT: f]
#  If set to true, a separator is added in the screen output and
#  history file between each equation when solving multiple equations.

#  Below parameters control the level of screen output.
#  [Verbose] prints detailed messages to screen and the history file.
#  [Warning] prints out warning messages if the code finds unexpected
#  behavior or inputs. [Debug] prints out additional information that
#  may be used for debugging purposes.
Verbose:                               t           # [f/t]             [DEFAULT: t]
Warning:                               t           # [f/t]             [DEFAULT: t]
Debug:                                 f           # [f/t]             [DEFAULT: f]

######################################################################
# 2.  Mesh Data:
#  Below are the different example formats for reading mesh in svFSI.
#  Multiples meshes can be loaded for the same or different equations
#  within svFSI. svFSI supports reading multiple mesh formats as noted
#  below. Some additional information specific to an equation may also
#  be loaded within the mesh attribute such as domains, fiber
#  directions, and initial values.

#  SimVascular-based vtu/vtp format for mesh/faces is the default
#  choice. svFSI supports below element types in vtu/vtp format:
#  -  line (linear, quadratic)
#  -  triangle (linear, quadratic)
#  -  quadrilateral (bilinear, serendipity, biquadratic)
#  -  tetrahedron (linear, quadratic)
#  -  hexagonal brick (trilinear, quadratic/serendipity, triquadratic)
#  -  wedge

#  svFSI also supports loading NURBS meshes. Limited support is
#  available to import a bilinear quadrilateral mesh from Gambit-based
#  ".msh". An option to convert this into a biquadratic mesh is also
#  available. svFSI also supports importing mesh in the form of a list
#  of nodal coordinates and element connectivity. It is, however, the
#  user's responsibility to provide information on faces. The face
#  connectivity should include a "GlobalElementID" mapping between the
#  face element and the corresponding mesh element to which the face
#  belongs.

#  Nested keywords "Add mesh" and "Add face" could be used to provide
#  paths to the mesh and face files. The users should also provide a
#  string-based name for each mesh and face immediately after the
#  colon.

#---------------------------------------------------------------------
#  Add mesh using vtu/vtp format
Add mesh: mesh_name {

   #  Path to the mesh file
   Mesh file path:    ./mesh/mesh-complete.mesh.vtu

   #  Add multiples faces using "Add face" keyword and provide
   #  path to the corresponding face mesh file (.vtp format)
   Add face: < face_name_1 > {
      Face file path: ./mesh/mesh-surfaces/face_1.vtp
   }

   Add face: face_name_ 2 {
      Face file path: ./mesh/mesh-surfaces/face_2.vtp
   }

   Add face: face_name_3 {
      Face file path: ./mesh/mesh-surfaces/face_3.vtp
   }

   #------------------------------------------------------------------
   #  DOMAINS: The users should also provide information on domains to
   #  specify properties for solving the equations. For e.g., density
   #  and viscosity should be provided for fluid eqn., material
   #  properties for the solid dynamics eqn., etc. Note that svFSI
   #  uses bits to identify domains. Therefore, a maximum of 32
   #  domains are allowed for a 4-byte integer (INT32) system.

   #  A constant Domain ID may be specified for uniform properties.
   Domain: 1

   #  Domain IDs can also be loaded from file for multiple domains.
   #  The file can be in vtu format with an element-based data array
   #  named as, "DOMAIN_ID".
   #  Domain file path: ./mesh/domains_from_file.vtu

   #  An ASCII-formatted text file may also be provided for domains.
   #  Each line of the file must contain an integer-valued domain ID.
   #  IDs must be provided for all the elements of the mesh. This
   #  implies that the code expects to match the number of lines with
   #  the number of elements of the mesh.
   #  Domain file path: ./mesh/domains_from_file_ASCII.dat

   #-----------------------------------------------------------------
   #  A mesh scaling factor could be optionally applied. For e.g., if
   #  the parameters are in CGS units while the mesh is in mm-scale, a
   #  scale factor "0.1" may be used as,
   Mesh scale factor:   0.1

   #------------------------------------------------------------------
   #  Additional data may be provided depending on the equation solved
   #  # For FSI simulations, fluid domain may initialized as:
   #    Initial pressures file path:  ./init/flow_from_rigid_walls.vtu
   #    Initial velocities file path: ./init/flow_from_rigid_walls.vtu

   #  # For prestress-based FSI, solid domain may be initialized as:
   #    Prestress file path: ./init/wall_prestress.vtu
   #    Initial displacements file path: ./init/wall_disps.vtu

   #------------------------------------------------------------------
   #  # Fiber directions may be loaded for some material models. Fiber
   #  # direction must be stored at the element level using the data
   #  # array name, "FIB_DIR", in the vtu format.
   #    Fiber direction file path: ./mesh/fibers_longitudinal.vtu
   #    Fiber direction file path: ./mesh/fibers_sheet.vtu

   #------------------------------------------------------------------
   #  Fiber mesh: If the loaded mesh is a one-dimensional network of
   #  fibers, then the keyword, "Set mesh as fibers" should be set.
   #  This setting is useful, for e.g., in loading the Purkinje network
   #  for cardiac electrophysiology simulations.
   #    Set mesh as fibers: t
   #
   #  Couple 1D fibers to 3D domain:
   #    For simulating cardiac electrophysiology in a combined model
   #    of Purkinje fibers and myocardium, additional information is
   #    needed to couple the gap junction between 1D Purkinje fibers
   #    and 3D myocardium.
   #    a. The Purkinje mesh should be set as fibers.
   #    b. The end nodes of the Purkinje mesh should be loaded as a face.
   #    c. A projection should be performed between the end-nodes loaded
   #       as a face, and the endocardial face.
   #
   #    An example is provided below:
   #    # (a) Load purkinje mesh
   #    # Add mesh: pfib {
   #    #    Set mesh as fibers: t
   #    #    Mesh file path: mesh/purkinje.vtu
   #    #    Add face: pfib_ends {
   #    #       End nodes face file path: mesh/purkinje_end_nodes.txt
   #    #    }
   #    # }
   #
   #    # (b) Load myocardium mesh
   #    # Add mesh: myo {
   #    #    Mesh file path: mesh/myocardium.vtu
   #    #    Add face: endo {
   #    #       Face file path: mesh/mesh-surfaces/myo-endocardium.vtp
   #    #    }
   #    #    Add face: epi {
   #    #       Face file path: mesh/mesh-surfaces/myo-epicardium.vtp
   #    #    }
   #    #    Add face: base {
   #    #       Face file path: mesh/mesh-surfaces/myo-base.vtp
   #    #    }
   #    # }
   #
   #    # (c) Project Purkinje ends from endocardium
   #    # Add projection: pfib_ends{
   #    #    Project from face: endo
   #    #    Projection tolerance: -1.0
   #    # }
   #

   #------------------------------------------------------------------
   #  Below command loads the mesh as a shell so that the "shell"
   #  equation could be solved. This is also required for initializing
   #  CMM equation using inflation or prestress. See svFSI-Tests for
   #  more details.
   #  #  Set mesh as shell: t
   #
}


#---------------------------------------------------------------------
#  Add mesh using position coordinates and connectivity. Face data
#  is provided using eBC format where in addition to the face
#  connectivity, a mapping "GlobalElementID" should be provided that
#  maps the face element to the corresponding mesh element to which
#  the face belongs.

Add mesh: msh_from_connectivity_coordinates {
   Coordinates file path:  ./mesh/mesh.coordinates
   Connectivity file path: ./mesh/mesh.connectivity
   Domain file path:       ./mesh/domains.txt

   Add face: face_from_eBC_1 {
      Connectivity file (eBC) path: ./mesh/mesh-surfaces/face_1.eBC
   }
   Add face: face_from_eBC_2  {
      Connectivity file (eBC) path: ./MESH/mesh-surfaces/face_2.eBC
   }
   Add face: face_from_eBC_3 {
      Connectivity file (eBC) path: ./MESH/mesh-surfaces/face_3.eBC
   }
}

#---------------------------------------------------------------------
#  Add a NURBS mesh
Add mesh: NRB_msh {
   Mesh scale factor:                  10.0        (0 - inf)         [DEFAULT: 1.0]
   NURBS data file path:               ./mesh/nrb.msh
   Domain:                             3           [0 - 32)

   Set direction: 1 {
      Number of knot insertion:        10
      Inserted knots repetition:       1                             [DEFAULT: 1]
      Number of Gauss points:          1                             [DEFAULT: p+1]
      Number of sample points:         3                             [DEFAULT: p+1]
      Start face name:                 left_face                     [DEFAULT: <X,Y,Z>N_<mesh_name>]
      End face name:                   right_face                    [DEFAULT: <X,Y,Z>P_<mesh_name>]
   }
}

#---------------------------------------------------------------------
#  Add mesh from a Gambit .msh file. Note that only quadrilateral
#  elements are supported using this choice. An option to convert to
#  biquadratic element is available.
Add mesh: msh_from_gambit_file {
   Gambit mesh file path:              ./mesh/gambit_2D_quad.msh
   Convert elements to biquadratic elements: t     [f/t]             [DEFAULT: f]
   Set domain: solid {
      Domain:                          1           [0 - 32)
   }
}

#---------------------------------------------------------------------
#  Projection for fluid-structure interaction (FSI) simulations:
#  svFSI uses a monolithic coupling at the interface between the fluid
#  and the solid domains to satisfy the kinematic and dynamic
#  conditions. This is achieved through combining the individual faces
#  of the fluid and the solid domains at the interface into a single
#  face structure. This is performed through a projection step at the
#  interface between the meeting faces. Therefore, it is required to
#  have a nodal match between the fluid and solid surfaces meshes
#  at the interface. Below, the fluid/lumen interface to the solid/
#  wall interface as,

Add projection:   wall_interface {
   Project from face:   lumen_interface
}

#  Note that face names set using "Add face" keyword have to be used
#  for the projection step and not the actual file names/paths.

######################################################################
# 3.  Equations

#  svFSI is a multiphysics finite element solver. The equation solved
#  is specified using the "Add equation" keyword. Below is a list of
#  all the equation names and their description:

#  |------------------------|---------------------------------------|
#  |         Name           |            Description                |
#  |------------------------|---------------------------------------|
#  | heatS/laplace/poisson  |  unsteady diffusion equation          |
#  |------------------------|---------------------------------------|
#  | heatF/dyeTransport/    |  unsteady advection-diffusion         |
#  | scalarTransport/AD     |  equation                             |
#  |------------------------|---------------------------------------|
#  |         lElas          |  linear elastodynamics equation       |
#  |------------------------|---------------------------------------|
#  |         struct         |  nonlinear elastodynamics equation    |
#  |------------------------|---------------------------------------|
#  |         ustruct        |  nonlinear elastodynamics using       |
#  |                        |  mixed VMS-stabilized formulation     |
#  |------------------------|---------------------------------------|
#  |         stokes         |  unsteady Stokes equations            |
#  |------------------------|---------------------------------------|
#  |         fluid          |  unsteady viscous incompressible      |
#  |                        |  fluid flow (Navier-Stokes equations) |
#  |------------------------|---------------------------------------|
#  |         CMM            |  the coupled momentum method for      |
#  |                        |  fluid-structure interaction (FSI)    |
#  |------------------------|---------------------------------------|
#  |         FSI            |  FSI using arbitrary Lagrangian-      |
#  |                        |  Eulerian (ALE) formulation           |
#  |------------------------|---------------------------------------|
#  |         mesh           |  solves a modified lElas for mesh     |
#  |                        |  motion; should be used with FSI;     |
#  |------------------------|---------------------------------------|
#  |         CEP            |  solves the mono-domain model of      |
#  |                        |  cardiac electrophysiology            |
#  |------------------------|---------------------------------------|
#  |         shell          |  solves nonlinear thin shell          |
#  |                        |  mechanics (Kirchhoff-Love theory)    |
#  |------------------------|---------------------------------------|

#---------------------------------------------------------------------
#  Below we will use FSI as an example equation. Note that the code
#  mandates a separate equation for "mesh" when one of the equations
#  is FSI. Also, if multiple equations are solved and fluid/FSI is
#  involved, the code expects fluid/FSI to be always the first
#  equation. When FSI is solved, the "mesh" equation should follow
#  immediately before using other equations such as "scalarTransport",
#  etc.

Add equation: FSI  # [heatS/heatF/lElas/struct/ustruct/stokes/fluid/CMM/FSI/mesh/CEP/shell]
{
   #------------------------------------------------------------------
   #  In a multi-equation system, if Coupled is set to true, svFSI
   #  couples the convergence of the equations. This implies that in a
   #  time step, the nonlinear iterations are performed on all the
   #  coupled system of equations till convergence is achieved.
   #  If set to false, that particular equation is uncoupled implying
   #  convergence of the uncoupled equation is achieved separately
   #  within the time step.
   Coupled:                      1        # [f/t]             [DEFAULT: t]

   #  svFSI uses a full Newton method to achieve convergence of the
   #  nonlinear system of equations. Parameters for the nonlinear
   #  Newton-Raphson solver are set below:

   Min iterations:               1        # [1 - inf)         [DEFAULT: 1]
   Max iterations:               5        # [1 - inf)         [DEFAULT: 5]
   Tolerance:                    1e-3     # [0.0 - inf)       [DEFAULT: 1e64]

   # Note that the tolerance set above is the relative tolerance.

   #------------------------------------------------------------------
   #  Domain parameters:
   #    Domain parameters are set using the Domain keyword identifying
   #  the domain ID followed by a nested block of parameters. If the
   #  mesh comprises a single domain with uniform properties, the
   #  domain parameters can be simply listed without nesting inside
   #  "Domain" keyword and the "Equation" setting as the domain
   #  parameter is not needed.

   #  For e.g., if the equation is fluid, the domain parameters can be
   #  listed as,
   #
   #  Density:  1.04
   #  Viscosity: Constant { Value: 0.04 }
   #  Backflow stabilization coefficient: 0.2
   #  Force_X: 0.0
   #  Force_Y: 0.0
   #  Force_Z: 981.0
   #
   #  However, if we have multiple domains (for e.g., FSI with fluid
   #  and solid domains), the parameters have to be nested within the
   #  Domain keyword. Each "Domain" should also include the type of
   #  equation being solved.

   #  The Domain parameters for different types of equations are
   #  described at the end of the file.

   #  Fluid domain with constant viscosity (Newtonian)
   Domain: 0 {
      Equation: fluid
      Density:  1.04                                # (0 - inf)
      Viscosity:  Constant { Value: 0.04 }
      Backflow stabilization coefficient:  0.1      # [0.0 - inf)      [DEFAULT: 0.2]
      Force_X: 0.0
      Force_Y: 0.0
      Force_Z: 981.0
   }

   #  Solid domain modeled as NeoHookean material with a quadratic
   #  dilational penalty
   Domain: 1 {
      Equation: struct
      Density:             1.0                      # (epsilon - inf)
      Elasticity modulus:  2.5e6                    # (epsilon - inf)
      Poisson ratio:       0.35                     # [0.0 - 0.5)
      Force_Z: 981.0

      Constitutive model:  nHK
      Dilational penalty model: quad
   }

   #------------------------------------------------------------------
   #  Linear solver:
   #    svFSI offers multiple choices for linear solvers and
   #  preconditioners. While the default package comes with its own
   #  linear solver (svFSILS), svFSI can also be coupled with Trilinos
   #  for access to advanced preconditioners. svFSI uses diagonal
   #  preconditioner by default.

   #  The following linear solvers are available within svFSI:
   #  |--------------|----------------------------------------------|
   #  |   *LS name*  |              Default Equations               |
   #  |--------------|----------------------------------------------|
   #  |  NS / BIPN   |   Navier-Stokes solver based on bipartition  |
   #  |              |   method for "fluid" equation                |
   #  |--------------|----------------------------------------------|
   #  |   GMRES      |   heatF, ustruct, CMM, stokes, and FSI       |
   #  |--------------|----------------------------------------------|
   #  |   CG         |   heatS, lElas, mesh, struct, shell, and CEP |
   #  |--------------|----------------------------------------------|
   #  |   BICG       |                                              |
   #  |--------------|----------------------------------------------|
   #
   #  Note that except for NS/BIPN, the remaining linear solvers are
   #  available with svFSI and Trilinos package.
   #
   #  The following preconditioners are available from Trilinos:
   #  |-------------------------|-----------------------------------|
   #  |   Trilinos-Diagonal     |  diagonal preconditioner          |
   #  |-------------------------|-----------------------------------|
   #  |   Trilinos-BlockJacobi  |  block Jacobi preconditioner      |
   #  |-------------------------|-----------------------------------|
   #  |   Trilinos-ILU          |  incomplete LU preconditioner     |
   #  |-------------------------|-----------------------------------|
   #  |   Trilinos-ILUT         |  thresholded ILU preconditioner   |
   #  |-------------------------|-----------------------------------|
   #  |   Trilinos-IC           |  incomplete Cholesky              |
   #  |-------------------------|-----------------------------------|
   #  |   Trilinos-ICT          |  thresholded IC preconditioner    |
   #  |-------------------------|-----------------------------------|
   #  |   Trilinos-ML           |  multilevel smoothed aggregation  |
   #  |-------------------------|-----------------------------------|
   #
   #  Note that Trilinos preconditioners cannot be used with NS/BIPN
   #  as the linear solver.
   #

   #  Below is an example of NS/BIPN linear solver parameter setting:
   LS type: BIPN
   {
      Tolerance:            1e-3    # (0 - 1.0)         [DEFAULT: 0.4 for NS, 0.1 for the GMRES and 0.01 for CG and BICG]
      Max iterations:       10      # [1 - inf)         [DEFAULT: 10 for NS, 4 for GMRES, 1000 for CG, 500 for BICG]
      Krylov space dimension: 50    # [1 - inf)         [DEFAULT: 200]
      Absolute tolerance:   1e-12   # (0 - 1.0)         [DEFAULT: 1e-10]

      # Below are additional settings used for NS/BIPN only. These
      # are not required for GMRES/CG/BICG
      NS-GM tolerance:      1e-3    # (0 - 1.0)         [DEFAULT: 0.01]
      NS-GM max iterations: 3       # [1 - inf)         [DEFAULT: 1]
      NS-CG tolerance:      1e-3    # (0 - 1.0)         [DEFAULT: 0.2]
      NS-CG max iterations: 500     # [1 - inf)         [DEFAULT: 500]
   }

   #  Below is a case of using a Trilinos preconditioner with GMRES:
   #  LS type: GMRES
   #  {
   #     Preconditioner: Trilinos-ILUT   #                   [DEFAULT: Trilinos-Diagonal]
   #     Max iterations:       100       # [1 - inf)         [DEFAULT: 4]
   #     Tolerance:            1e-4      # (0 - 1.0)         [DEFAULT: 0.1 for GMRES]
   #     Krylov space dimension: 50      # [1 - inf)         [DEFAULT: 250]
   #  }

   #------------------------------------------------------------------
   #  Output types and settings:
   #    svFSI allows three different types of output:
   #
   #  1. Spatial : these quantities are written to a vtu file
   #  visualized in Paraview.
   #
   #  2. B_INT / Boundary_integral : these quantities represent flux
   #  through all the faces such as velocity flux, energy flux, etc.
   #
   #  3. V_INT / Volume_integral : these quantities represent volume-
   #  averaged quantities integrated over domains.
   #
   #  The output variables depends on the equation being solved and
   #  below is a list of all possible outputs for the corresponding
   #  equation:
   #
   #  |-----------------------|-------------------------------------|
   #  |         Name          |          Output Name                |
   #  |-----------------------|-------------------------------------|
   #  | heatS/laplace/poisson | Temperature, Heat_flux              |
   #  |-----------------------|-------------------------------------|
   #  | heatF/dyeTransport/   | Temperature, Heat_flux              |
   #  | scalarTransport/AD    |                                     |
   #  |-----------------------|-------------------------------------|
   #  |         lElas (p)     | Displacement, Stress, Strain        |
   #  |                       |                                     |
   #  |         lElas         | Displacement, VonMises_stress,      |
   #  |                       | Stress, Strain, Jacobian, Area/     |
   #  |                       | Volume, Velocity, Acceleration      |
   #  |-----------------------|-------------------------------------|
   #  |         struct (p)    | Displacement, Stress, Cauchy_stress,|
   #  |                       | Strain                              |
   #  |         struct        | Displacement, VonMises_stress,      |
   #  |                       | Stress, Cauchy_stress, Strain,      |
   #  |                       | Jacobian, Def_grad, Area/Volume,    |
   #  |                       | Fiber_direction, Fiber_alignment,   |
   #  |                       | Velocity, Acceleration              |
   #  |-----------------------|-------------------------------------|
   #  |         ustruct       | Displacement, VonMises_stress,      |
   #  |                       | Stress, Cauchy_stress, Strain,      |
   #  |                       | Jacobian, Def_grad, Area/Volume,    |
   #  |                       | Fiber_direction, Fiber_alignment,   |
   #  |                       | Velocity, Pressure, Acceleration,   |
   #  |                       | Divergence                          |
   #  |-----------------------|-------------------------------------|
   #  |         stokes        | Velocity, Pressure, WSS, Vorticity, |
   #  |                       | Traction, Strain_invariants,        |
   #  |                       | Viscosity, Divergence               |
   #  |-----------------------|-------------------------------------|
   #  |         fluid         | Velocity, Pressure, WSS, Traction,  |
   #  |                       | Vorticity, Vortex, Energy_flux,     |
   #  |                       | Strain_invariants, Acceleration,    |
   #  |                       | Viscosity, Divergence               |
   #  |-----------------------|-------------------------------------|
   #  |         CMM (i)       | Displacement                        |
   #  |         CMM (p)       | Displacement, Stress                |
   #  |         CMM           | Velocity, Pressure, Displacement,   |
   #  |                       | WSS, Vorticity, Vortex, Energy_flux,|
   #  |                       | Strain_invariants, Acceleration,    |
   #  |                       | Traction, Viscosity, Divergence     |
   #  |-----------------------|-------------------------------------|
   #  |         FSI           | Velocity, Pressure, Displacement,   |
   #  |                       | VonMises_stress, WSS, Traction,     |
   #  |                       | Vorticity, Vortex, Energy_flux,     |
   #  |                       | Strain_invariants, Viscosity,       |
   #  |                       | Absolute_velocity, Stress, Strain,  |
   #  |                       | Cauchy_stress, Jacobian, Deg_grad,  |
   #  |                       | Area/Volume, Fiber_direction,       |
   #  |                       | Fiber_alignment, Divergence,        |
   #  |                       | Acceleration                        |
   #  |-----------------------|-------------------------------------|
   #  |         mesh          | Displacement, Velocity, Acceleration|
   #  |-----------------------|-------------------------------------|
   #  |         CEP           | Action_potential                    |
   #  |-----------------------|-------------------------------------|
   #  |         shell         | Displacement, Velocity, Area        |
   #  |-----------------------|-------------------------------------|
   #
   #  In the above equations, "lElas (p)/struct (p)" indicates that
   #  prestress is solved. "CMM (i)" indicates that CMM is initialized
   #  using inflation whereas "CMM (p)" indicates that CMM is
   #  initialized using prestress approach.
   #

   Output: Spatial {
      Pressure:     t
      Velocity:     t
      Displacement: f
      WSS: t
   }

   Output: Boundary_integral {
      Velocity:     t
      Pressure:     t
      Energy_flux:  t
   }

   Output: Volume_integral {
      Velocity:     t
      Pressure:     t
   }

   #  If multiple equations are solved (e.g., FSI, 3 Laplace eqns.
   #  with different boundary conditions or source terms, etc.),
   #  the naming of output variables could be changed so that the
   #  vtu file has an appropriate name when visualized in Paraview.
   #  If the vtu file has data arrays with identical names, Paraview
   #  will display only the first occurrence. The "Alias" keyword
   #  will allow users to provide custom names to output data.
   #
   #  #  Output: Alias {
   #  #     Displacement: Displacement_fs
   #  #  }
   #
   #  #  Output: Alias { Temperature: Temperature_Eq_1 }
   #

   #------------------------------------------------------------------
   #  Boundary conditions (BCs):
   #     BCs are an integral part of the problem and svFSI has
   #  multiple options to set BCS. BCs are set on a face using the
   #  "Add BC" keyword tagged to the face-name and followed by a nested
   #  set of commands. The basic types include:
   #
   #  |-------------------|-----------------------------------------|
   #  |               Boundary Condition "Type"                     |
   #  |-------------------|-----------------------------------------|
   #  |  Dirichlet / Dir  | sets values on the state variable       |
   #  |-------------------|-----------------------------------------|
   #  |  Neumann / Neu    | imposes a normal force on the face      |
   #  |-------------------|-----------------------------------------|
   #  |  Traction / Trac  | applied force can be along any direction|
   #  |-------------------|-----------------------------------------|
   #  |  Robin / Rbn      | force from a spring-mass-damper         |
   #  |-------------------|-----------------------------------------|
   #  |  Coupled Momentum | identifies the face to be treated       |
   #  |  / CMM            | using coupled momentum method (CMM)     |
   #  |-------------------|-----------------------------------------|
   #
   #  Further, users can provide both temporal and spatial distribution
   #  using "Time dependence" and "Profile" keywords. For e.g.,
   #
   #  Add BC: face_1 {
   #     Type: Dirichlet
   #     Time dependence: Steady
   #     Value: 10.0
   #     Profile: Parabolic
   #  }
   #
   #  where we are setting a Parabolic profile and a constant value
   #  of the state variable on the face "face_1". The state variable
   #  refers to the unknown of the equation. For e.g., velocity is the
   #  state variable for fluid.
   #
   #  Below is a list of state variables on which a Dirichlet BC is
   #  applied depending on the equation:
   #
   #  |-------------------|-----------------------------------------|
   #  | "State Variable"  |           "Equations"                   |
   #  |-------------------|-----------------------------------------|
   #  |  velocity         |   stokes, fluid, ustruct, CMM, FSI      |
   #  |-------------------|-----------------------------------------|
   #  |  displacement     |   lElas, struct, shell, mesh            |
   #  |-------------------|-----------------------------------------|
   #  |  temperature      |   heatS, heatF                          |
   #  |-------------------|-----------------------------------------|
   #  |  action_potential |   CEP                                   |
   #  |-------------------|-----------------------------------------|
   #
   #-------------- Time Dependence Settings Description ------------|
   #
   #  Below are the options available for setting "Time dependence":
   #  - Steady : [DEFAULT] A constant value is imposed on the state
   #      variable. The code expects to read a "Value" command that is
   #      usually a scalar value or a vector such as,
   #
   #        Value: 10.0   # for scalar value (Dirichlet/Neumann)
   #        Value: {1.0, -1.0, 0.0}  # for vector valued (Traction)
   #
   #  - Unsteady : A file input is expected to set an unsteady boundary
   #      condition. The file can contain time-dependent values of the
   #      state variable itself, or the Fourier coefficients from an
   #      interpolation fit could be directly provided as input.
   #
   #         Temporal values file path: unsteady_BC_values.dat
   #         Fourier coefficients file path: unsteady_BC_fcs.dat
   #
   #      If temporal values are provided as input, the code computes
   #      Fourier modes internally to interpolate data at intermediate
   #      time points. The code assumes that the input data is
   #      periodic with a time period equal to the time point of the
   #      last data entry.
   #
   #      If the users, however, want to ramp the boundary value
   #      instead of impulsively starting a simulation with a steady
   #      value, "Ramp function: t" can be set. The code then reads
   #      only the first two entries from the input file, linearly
   #      increments from the first value to the second value, and
   #      maintains a steady value thereafter. This feature is useful
   #      for performing quasi-static simulations in solid mechanics.
   #
   #  - Coupled : This indicates that the face is coupled to either
   #      GenBC or cplBC 0D reduced-order modeling codes.
   #
   #  - Resistance : A resistance value is applied only when a Neu/
   #      Neumann boundary condition type is used. Resistance value is
   #      input using the "Value" command. For e.g., "Value : 8850.0".
   #      Note that a resistance BC can be applied for fluid/CMM/FSI
   #      equations only.
   #
   #  - RCR/Windkessel : An RCR BC can be applied as a vector input.
   #      Similar to Resistance BC, an RCR BC can be applied for Neu/
   #      Neumann BC type, and for fluid/CMM/FSI equations only.
   #
   #        Type: Neu
   #        Time dependence: RCR
   #        RCR values: {100.0, 0.1, 1.0e3}
   #        Distal pressure: 0.0
   #        Initial pressure: 0.0
   #
   #      The order of "RCR values" is {proximal resistance,
   #      compliance/capacitance, distal resistance}. Distal and
   #      initial pressures used to initialize RCR can also be
   #      specified.
   #
   #  - Spatial : This is allowed for Neumann or Traction BC types
   #      only where a spatially varying load (pressure/traction) is
   #      applied by reading a vtp file.
   #
   #        Type: Neu  #  or Trac
   #        Time dependence: Spatial
   #        Spatial values file path: face_pressure_file.vtp
   #
   #  - General : This is the most general type of BC where both the
   #      spatial and temporal variations are provided in a file. The
   #      solver can load a SimVascular-compatible "BCt" file such as
   #      "BCt.vtp" or can be loaded in the form of an ASCII formatted
   #      text file.
   #
   #        Time dependence: General
   #        # BCT file path: BCt.vtp
   #        Temporal and spatial values file path: general_BC.dat
   #
   #      Note that BCT file loading is available for fluid/CMM/FSI
   #      simulation where only velocity information is loaded. The
   #      code expects vtp file to have data arrays named as,
   #      "velocity_<time point>" starting with 0 and should be
   #      monotonically increasing.
   #
   #
   #-------------------  Profile Settings Description  -------------|
   #
   #  svFSI allows prescribing a spatial profile for the applied
   #  boundary condition. Three options are currently available:
   #
   #  - Flat [DEFAULT]
   #  - Parabolic
   #  - User_defined
   #
   #  For the "User_defined" setting, the code to load a spatial
   #  in a file set by the command, "Spatial profile file path".
   #
   #
   #-----------------  Additional Settings Description  ------------|
   #
   #  Other settings on the boundary conditions include:
   #
   #  1. Impose flux: [DEFAULT : f] If set to true, the code will
   #        normalize the spatial profile with the area of the face so
   #        that an imposed flux value is appropriately converted into
   #        the state variable. For e.g., "Impose flux: f".
   #
   #  2. Impose on state variable integral: This setting is typically
   #        used for applying a Dirichlet BC on the displacement
   #        degrees of freedom when velocity is the state variable
   #        (e.g., fluid, CMM, FSI, and ustruct). Note that this flag
   #        is set to true for lElas/mesh/struct/shell equations.
   #
   #  #------------  Additional Dirichlet BC controls
   #  3. Effective direction: This applies to Dirichlet BC only. Users
   #        can enforce a Dirichlet BC along a particular Cartesian
   #        coordinate vector. The argument for the keyword
   #        "Effective direction" is an integer-valued vector denoting
   #        the Cartesian directions. For e.g.,
   #        "Effective direction: (1,0,0)" sets a Dir BC along X-axis.
   #
   #  4. Zero out perimeter: This applies to to Dirichlet BC only.
   #        Default setting is true for Dirichlet BC. When the flag is
   #        set to true, the solver will zero out the `ring' formed at
   #        the conjoining of two faces. The nodal values at the ring
   #        will then be 0. It is not required that the "zero out
   #        perimeter" needs to be true on both the meeting faces.
   #        Setting the flag on either one despite having distinct
   #        BC types can lead to zeroing out the perimeter. Note that
   #        for CMM type BC, zero out is required to be true and is
   #        enforced.
   #
   #  5. Weakly applied: This applies to to Dirichlet BC only and
   #        defaults to false. If "Weakly applied" is set to true, the
   #        Dirichlet BC is applied weakly using augmented Lagrange-
   #        multiplier formulation. This setting is applied to fluid/
   #        FSI equations only. Invoking this requires specifying
   #        penalty parameters using the "Penalty parameter" keyword.
   #        Directional control can be achieved using "Penalty
   #        parameter (tangential)" or "Penalty parameter (normal)"
   #        keywords.
   #
   #  #------------  Additional Neumann BC controls
   #  6. Follower pressure load: This applies to Neumann BC only.
   #        If set to true, the applied load `follows' deformation,
   #        implying that the magnitude of the load is proportional
   #        to the surface area during the deformation. The expression
   #        for applied force becomes, h = -p nA, where p is the
   #        applied pressure, n is the surface normal in the current
   #        configuration and A is the magnitude of area in the
   #        current configuration that changes with deformation.
   #
   #  7. Undeforming Neu face: This applies to for Neu BC and
   #        ustruct equation only. If set to true, this setting will
   #        mimic clamped condition on a specimen routinely done in
   #        experiments. Clamping will not allow the surface, on which
   #        the load is applied, to deform.
   #
   #  #------------  Additional Traction BC controls
   #  8. Traction values file path: Applicable for Traction BC only.
   #        Traction can be loaded directly by providing a vtp file
   #        containing nodally varying traction on the fluid wall.
   #
   #  9. Traction multiplier: [DEFAULT: 1.0] Applicable for Traction
   #        BC only. A real/float value can be given as input that
   #        acts as a scalar multiplier on the traction loaded from a
   #        vtp file. This setting may be useful when the direction of
   #        traction needs to be flipped ("Traction multiplier: -1.0").
   #
   #  #------------  Additional Robin BC controls
   #  10. Robin BC types involves a spring-mass-damper-type force
   #        application on the surface upon which Robin BC is applied.
   #        The mathematical expression evaluates to,
   #                    \sigma.n = -(k*u + c*v + p*n),
   #        where k is the stiffness parameter and c is the damping
   #        constant, while u and v are the surface displacement and
   #        velocity, respectively. p is the external pressure acting
   #        along normal direction.
   #          In svFSI, Robin BC is only an extension to the Neumann
   #        boundary condition and therefore, all the commands for the
   #        Neumann BC are accepted for Robin BC as well. However,
   #        additional parameters must be provided for Robin BC that
   #        include "Stiffness" and "Damping" constants, and whether
   #        the Robin BC is applied along the normal or not. For e.g.,
   #
   #          Add BC: face_name {
   #             Type: Robin
   #             Time dependence: Steady
   #             Value: 0.0
   #             Stiffness : 1.0e5
   #             Damping: 0.0
   #             Apply along normal direction: f
   #          }
   #
   #           When the Robin BC is applied along the normal direction,
   #        the applied surface traction takes the form,
   #               \sigma.n = -(k u.n + c v.n - p)n
   #
   #
   #  #------------  Additional CMM type BC controls
   #  11. If a face (typically a fluid wall/interface) is set to be
   #      "CMM" or "Coupled Momentum" BC type, then that face will be
   #      treated as a linear elastic membrane interacting with the
   #      flow. A couple of additional settings may also have to
   #      provided as,
   #
   #         Initial displacement file path: init/cmm_wall_disps.vtp
   #      or,
   #
   #         Prestress file path: init/cmm_wall_prestress.vtp
   #
   #      The first option is required if the CMM is initialized using
   #      inflation method due to diastolic or time-averaged fluid
   #      traction. The second option is required if the CMM method is
   #      initialized by prestressing the wall under equilibrium with
   #      fluid traction.
   #
   #  #--------------------------------------------
   #  An example "Add BC" is provided below:
   #

   Add BC: face_inlet
   {
      Type: Neumann
      Time dependence: Steady    [Steady/Unsteady/Resistance/General/Coupled] [DEFAULT: Steady]
      #  If "Time dependance" is "Steady" or "Resistance",
      Value: 0.0
      #  If "Time dependance is "Unsteady", one of the following two
      #  lines is required.
      Temporal values file path:  foo.dat
      Fourier coefficients file path: foo.dat
      #  If "Time dependance is "General",
      Temporal and spatial values file path: foo.dat

      Profile: Flat              [Flat/Parabolic/User_defined/D_dependent] [DEFAULT: Flat]
      #  If "Profile" is set to "User_defined",
      Spatial profile file path: foo.dat

      Zero out perimeter: f      [f/t]         [DEFAULT: t for Dirichlet and f for Neumann]
      Impose flux: f             [f/t]         [DEFAULT: f]
      Impose on state variable integral: t   [f/t]   [DEFAULT: t for struct/lElas/mesh and f for the rest]
      Effective direction: (0,0,1)
   }

   #------------------------------------------------------------------
   #  Couple to reduced-order models (0D):
   #    svFSI allows two ways of coupling for either open-loop or
   #  close-loop simulations to set boundary conditions for cardio-
   #  vascular flow simulations:
   #
   #  1.  Coupling to GenBC
   #  2.  Coupling to cplBC
   #
   #  Options to couple both 0D codes with svFSI are,
   #  N: none; I: implicit; SI: semi-implicit; E: explicit
   #
   #  A detailed documentation about GenBC and creating its executable
   #  is provided at http://simvascular.github.io/docsGenBC.html
   #
   #  Example for svFSI coupling with GenBC:
   #  #  Couple to genBC: SI {            [N/I/SI/E]
   #  #     0D code file path: genBC/genBC.exe
   #  #  }
   #
   #  Example for svFSI coupling with cplBC:
   #  #  Couple to cplBC: SI {            [N/I/SI/E]
   #  #     0D code file path:  cplBC/cplBC.exe
   #  #     Number of unknowns:  10
   #  #     Unknowns initialization file path: cplBC/foo.ini
   #  #     File name for 0D-3D communication: CPLBC_0D_3D.tmp
   #  #     File name for saving unknowns: cplBC_AllData
   #  #     Number of user-defined outputs: 15
   #  #  }

   #------------------------------------------------------------------
   #  Body force (BF):
   #     In addition to prescribing body force as a domain property,
   #  svFSI allows prescribing nodally-dependent body force that varies
   #  in space (and time). This setting is useful for the method of
   #  manufactured solutions where the body forces computed using the
   #  analytical solution is used to obtain numerical solution and
   #  compare against analytical solution.
   #     Body force over a mesh is provided using the "Add BF" command.
   #  svFSI allows three types of body force including,
   #  -  Volumetric/Vol/Internal/Int
   #  -  Traction/Neu
   #  -  Neumann/Neu/Pressure
   #
   #  The Traction or Neumann type of body force is applied only when
   #  the mesh is set as a shell surface.
   #     Similar to the boundary condition set up, a "Time dependence"
   #  can be set for body force but with limited options as,
   #
   #  - Steady : [DEFAULT] A constant value is imposed on the state
   #      variable. The code expects to read a "Value" command that is
   #      usually a scalar value or a vector such as,
   #
   #        Value: {1.0, -1.0, 0.0}  # for vector (Vol/Trac)
   #        Value: 10.0   # for scalar value (Neu)
   #
   #  - Unsteady : A file input is expected to set an unsteady boundary
   #      condition. The file can contain time-dependent values of the
   #      state variable itself, or the Fourier coefficients from an
   #      interpolation fit could be directly provided as input.
   #
   #         Temporal values file path: unsteady_BF_values.dat
   #         Fourier coefficients file path: unsteady_BF_fcs.dat
   #
   #      If temporal values are provided as input, the code computes
   #      Fourier modes internally to interpolate data at intermediate
   #      time points. The code assumes that the input data is
   #      periodic with a time period equal to the time point of the
   #      last data entry.
   #
   #      If the users, however, want to ramp the body force instead
   #      of impulsively starting a simulation with a steady value,
   #      "Ramp function: t" can be set. The code then reads only
   #      first two entries from the input file, linearly increments
   #      from the first value to the second, and maintains a steady
   #      value thereafter.
   #
   #  - Spatial : A spatially varying body force is applied by reading
   #      a vtu file.
   #
   #        Type: Volumetric
   #        Time dependence: Spatial
   #        Spatial values file path: body_force_file.vtu
   #
   #  - General : This is the most general type of BF application
   #      where both spatial and temporal variations are provided in a
   #      file. The file loaded should be in the form of an ASCII
   #      formatted text file.
   #
   #        Time dependence: General
   #        Temporal and spatial values file path: general_BF.dat
   #

   #------------  Additional Equation-Dependent Settings  ------------
   #-----------------------------------------------------------------
   #  Prestress for lElas/struct:
   #     Cardiovascular biomechanics simulations typically involve
   #  prestressing the blood vessel to mimic physiological conditions.
   #  This is achieved in svFSI by setting the "Prestress" command
   #  to true and is allowed for lElas and struct equations only.
   #  For e.g.,
   #     Add equation: lElas {   # or struct
   #        Prestress: t
   #     }
   #  Note that in the above example, other settings in "Add equation"
   #  were omitted.
   #
   #------------------------------------------------------------------
   #  Taylor-Hood bases for mixed-type systems:
   #     For equations employing mixed formulation (ustruct/fluid/
   #  stokes/FSI), svFSI allows using Taylor-Hood type discretization
   #  for the velocity and pressure function spaces.
   #    Use Taylor-Hood type basis:   f        # [f/t]           [DEFAULT: f]
   #
   #-----------------------------------------------------------------
   #  Remesher for FSI:
   #     For large deformation FSI simulations, the initial mesh
   #  can get distorted and may need remeshing. svFSI supports on-the-
   #  fly remeshing, where the solver examines local element Jacobian.
   #  If the element Jacobian equals 0 or becomes negative, then the
   #  solver triggers remesher. The mesh that is distorted is remeshed
   #  and the data variables are projected from the old mesh to the
   #  new mesh, and the solver continues marching forward. Below
   #  are the settings used by the remesher:
   #
   #    The General simulation parameter, "Simulation requires
   #  remeshing" need to be set to true in order for the code to
   #  search for remesh settings in the "Add equation" block. The code
   #  also expects the equation to be FSI to read any remesh settings.
   #  If these two requirements are satisfied, the code will look for
   #  keyword, "Remesher" followed by the name of the remeshing tool
   #  and other parameters. Currently, Tetgen is the only supported
   #  remeshing tool. Below is the description of other parameters:
   #
   #  1. Max edge size: [DEFAULT: 0.5] This nested block requires
   #     specifying edge size for the particular mesh. For e.g.,
   #       Max edge size: mesh_name { val: 0.2 }
   #
   #  2. Min dihedral angle: [DEFAULT 10.0] Tetgen parameter that
   #     prescribes minimum dihedral angle in the tetrahedron.
   #
   #  3. Max radius ratio: [DEFAULT: 1.15] Tetgen parameter that sets
   #     the maximum radius ratio of the tetrahedral elements.
   #
   #  4. Frequency for copying data: [DEFAULT: 10] Sets the frequency
   #     at which data is copied for remeshing. When the remeshing is
   #     triggered, the solver uses the latest copied data for
   #     remeshing and projection so that the new mesh has sufficient
   #     time to evolve and doesn't get distorted as the older mesh.
   #
   #  5. Remesh frequency: [DEFAULT: 100] In addition to the negative
   #     element Jacobian, the user can set a definite frequency for
   #     remeshing. The code will automatically remesh at this rate
   #     even if the mesh quality didn't deteriorate. Setting this to
   #     large value will cause the remesher to be triggered only
   #     if the mesh quality deteriorates.
   #
   #  Below is an example usage of remesher:
   #
   #  # Remsher setting, currently only supports Tetgen.
   #  Remesher: Tetgen {
   #     Max edge size:                mesh_from_vtu { val: 1.5 }
   #     Min dihedral angle:           10
   #     Max radius ratio:             1.1
   #     Remesh frequency:             1000
   #     Frequency for copying data:   5
   #  }
   #
   #-----------------------------------------------------------------
   #  CMM initialization:
   #     The fluid wall needs to be initialized using either inflation
   #  prestress methods to be used for subsequent CMM-based fluid-
   #  structure interaction simulation. This is achieved by,
   #  a. Load the fluid outer wall and set it as a shell.
   #  b. "Initialize" CMM equation using "inflate" or "prestress".
   #  c. Apply pressure or traction boundary conditions at the wall.
   #
   #  An example is provided below:
   #
   #  # (a) Load wall mesh as a shell surface
   #  # Add mesh: wall {
   #  #    Set mesh as shell: t
   #  #    Mesh file path: mesh/walls_combined.vtp
   #  # }
   #
   #  # (b) Initialize CMM equation
   #  # Add equation: CMM {
   #  #    Initialize: inflate  # or prestress
   #  # }
   #
   #  # (c) Set traction/pressure at the wall
   #  # Add equation: CMM {
   #  #    Initialize: prestress  # or inflate
   #  #    Add BF: wall {
   #  #       Type: Trac
   #  #       Time dependence: Spatial
   #  #       Spatial values file path: rigid_wall_traction.vtp
   #  #    }
   #  # }

   #-----------------------------------------------------------------
   #  CMM variable wall properties:
   #     svFSI allows setting variable wall properties for the CMM
   #  equation which sets elasticity modulus and thickness as varying
   #  spatially and node-dependent. A vtp file containing the data
   #  arrays "Thickness" and "Elasticity_modulus" should be provided
   #  as input. An example is provided below:
   #
   #  Add equation: CMM {
   #     Variable wall properties: wall {
   #        Wall properties file path: cmm_wall_props.vtp
   #     }
   #  }
   #
}

#---------------------------------------------------------------------
#  For the FSI equation, a mesh equation should immediately follow.
#  Default settings are used for parameters that are not explicitly
#  set below.
Add equation: mesh
{
   # Nonlinear solver tolerance
   Tolerance:           1e-3

   #  Domain parameters
   Poisson ratio:       0.35     # [0 - 0.5)

   # Output parameters
   Output: Spatial {
      Displacement:     t
   }

   # Boundary conditions
   Add BC: wall {
      Type:             Dirichlet
      Value:            0.0
   }
}

#---------------------------------------------------------------------
#  Here we provide an inclusive list of all the available domain
#  parameters including material properties for solids, viscosity
#  models for fluid flows, and cellular activation models for
#  cardiac electrophysiology.

#  1. A list of basic domain properties are provided below:
#
#  |-----------------------|-----------------------------------------|
#  |       Equation        |          Domain Properties              |
#  |-----------------------|-----------------------------------------|
#  | heatS/laplace/poisson | "Conductivity", "Source term",          |
#  |                       | "Density"                               |
#  |-----------------------|-----------------------------------------|
#  | heatF/dyeTransport/   | "Conductivity", "Source term"           |
#  | scalarTransport/AD    |                                         |
#  |-----------------------|-----------------------------------------|
#  |         lElas         | "Density", "Elasticity modulus",        |
#  |                       | "Poisson ratio", "Force_X", "Force_Y",  |
#  |                       | "Force_Z" (3D)                          |
#  |-----------------------|-----------------------------------------|
#  |         struct        | "Density", "Elasticity modulus",        |
#  |                       | "Poisson ratio", "Damping", "Viscosity",|
#  |                       | "Force_X", "Force_Y", "Force_Z" (3D)    |
#  |-----------------------|-----------------------------------------|
#  |         ustruct       | "Density", "Elasticity modulus",        |
#  |                       | "Poisson ratio", "Viscosity",           |
#  |                       | "Force_X", "Force_Y", "Force_Z" (3D),   |
#  |                       | "Momentum stabilization coefficient",   |
#  |                       | "Condinuity stabilization coefficient"  |
#  |-----------------------|-----------------------------------------|
#  |         stokes        | "Momentum stabilization coefficient",   |
#  |                       | "Force_X", "Force_Y", "Force_Z" (3D)    |
#  |-----------------------|-----------------------------------------|
#  |         fluid         | "Density", "Force_X", "Force_Y",        |
#  |                       | "Force_Z" (3D),                         |
#  |                       | "Backflow stabilization coefficient"    |
#  |-----------------------|-----------------------------------------|
#  |         CMM (i/p)     | "Poisson ratio", "Shell thickness",     |
#  |                       | "Elasticity modulus"                    |
#  |         CMM           | "Fluid density", "Solid density",       |
#  |                       | "Backflow stabilization coefficient",   |
#  |                       | "Poisson ratio", "Shell thickness",     |
#  |                       | "Elasticity modulus"                    |
#  |                                                                 |
#  | Note: "Shell thickness" and "Elasticity modulus" are read if and|
#  |       only if the command "Variable wall properties" is not set.|
#  |       Refer to section "Variable wall properties" for more info.|
#  |                                                                 |
#  |-----------------------|-----------------------------------------|
#  |         FSI           | Combination of fluid and either of      |
#  |                       | lElas/struct/ustruct properties         |
#  |-----------------------|-----------------------------------------|
#  |         mesh          | "Poisson ratio"                         |
#  |-----------------------|-----------------------------------------|
#  |         CEP           | Action_potential                        |
#  |-----------------------|-----------------------------------------|
#  |         shell         | "Density", "Elasticity modulus",        |
#  |                       | "Poisson ratio", "Damping", "Force_X",  |
#  |                       | "Force_Y", "Force_Z", "Shell thickness" |
#  |-----------------------|-----------------------------------------|
#
#
#------------------  Material Properties Settings  ------------------|
#
#  2. Specifying material properties for struct/ustruct:
#     If the equation or domain physics is struct/ustruct, svFSI
#  looks for the following commands to read material properties.
#
#  o Constitutive model: This command defines the constitutive model
#    for the isochoric component of the strain energy function.
#    Available choices are:
#
#    |----------------------|----------------------------------------|
#    |  "stVK" /            | St. Venant-Kirchhoff material          |
#    |  "stVenantKirchhoff" |                                        |
#    |----------------------|----------------------------------------|
#    |  "m-stVK" /          | Modified form of St. Venant-Kirchhoff  |
#    |  "modified-stVK"     | material                               |
#    |----------------------|----------------------------------------|
#    |  "nHK" / "nHK91"     | NeoHookean material model              |
#    |  "neoHookean"        |                                        |
#    |----------------------|----------------------------------------|
#    |                      | Mooney-Rivlin type material model.     |
#    |                      | This is a nested block that requires   |
#    |                      | additional parameter inputs, "c1" and  |
#    |  "MR" /              | "c2". For e.g.,                        |
#    |  "Mooney-Rivlin"     |    Constitutive model: MR {            |
#    |                      |       c1:                              |
#    |                      |       c2:                              |
#    |                      |    }                                   |
#    |----------------------|----------------------------------------|
#    |                      | Holzapfel-Gasser-Ogden type material   |
#    |                      | model for vascular tissue in the de-   |
#    |                      | coupled form where all the anisotropic |
#    |                      | terms use isochoric invariants. This is|
#    |                      | a nested block that requires additional|
#    |                      | parameter inputs, "a4", "b4", "a6",    |
#    |                      | "b6", and "kappa". For e.g.,           |
#    |  "HGO" /             |    Constitutive model: HGO-d {         |
#    |  "HGO-d" /           |       a4:                              |
#    |  "HGO-decoupled"     |       b4:                              |
#    |                      |       a6:                              |
#    |                      |       b7:                              |
#    |                      |       kappa:                           |
#    |                      |    }                                   |
#    |                      | For this model to be used, two families|
#    |                      | of fibers must be loaded in "Add mesh" |
#    |----------------------|----------------------------------------|
#    |                      | Holzapfel-Gasser-Ogden type material   |
#    |                      | model for vascular tissue with modified|
#    |                      | anisotropy where all the anisotropic   |
#    |                      | terms use full invariants. This is a   |
#    |                      | nested block that requires additional  |
#    |                      | parameter inputs, "a4", "b4", "a6",    |
#    |                      | "b6", and "kappa". For e.g.,           |
#    |  "HGO-ma" /          |    Constitutive model: HGO-ma {        |
#    |  "HGO-modified"      |       a4:                              |
#    |                      |       b4:                              |
#    |                      |       a6:                              |
#    |                      |       b7:                              |
#    |                      |       kappa:                           |
#    |                      |    }                                   |
#    |                      | For this model to be used, two families|
#    |                      | of fibers must be loaded in "Add mesh" |
#    |----------------------|----------------------------------------|
#    |                      | Guccione transverse isotropy model     |
#    |                      | for myocardium. This is a nested block |
#    |                      | that requires additional parameter     |
#    |                      | inputs, "C", "bf", "bs", and "bfs".    |
#    |                      | For e.g.,                              |
#    |  "Gucci" /           |    Constitutive model: Guccione {      |
#    |  "Guccione"          |       C:                               |
#    |                      |       bf:                              |
#    |                      |       bs:                              |
#    |                      |       bfs:                             |
#    |                      |    }                                   |
#    |                      | For this model to be used, two families|
#    |                      | of fibers must be loaded in "Add mesh" |
#    |----------------------|----------------------------------------|
#    |                      | Holzapfel's orthotropic material model |
#    |                      | for myocardium in the decoupled form   |
#    |                      | where the anisotropic terms in the     |
#    |                      | strain energy involve isochoric invar- |
#    |                      | iants. This is a nested block that re- |
#    |                      | quires additional parameter inputs,    |
#    |                      | "a", "b", "a4f", "b4f", "a4s", "b4s",  |
#    |                      | "afs", "bfs", and "k". For e.g.,       |
#    |  "HO" /              |    Constitutive model: HO-d {          |
#    |  "Holzapfel" /       |       a:                               |
#    |  "HO-d" /            |       b:                               |
#    |  "HO-decoupled"      |       a4f:                             |
#    |                      |       b4f:                             |
#    |                      |       a4s:                             |
#    |                      |       b4s:                             |
#    |                      |       afs:                             |
#    |                      |       bfs:                             |
#    |                      |       k:                               |
#    |                      |    }                                   |
#    |                      | For this model to be used, two families|
#    |                      | of fibers must be loaded in "Add mesh" |
#    |----------------------|----------------------------------------|
#    |                      | Holzapfel's orthotropic material model |
#    |                      | for myocardium in the modified form    |
#    |                      | where the anisotropic terms in the     |
#    |                      | strain energy involve full invariants. |
#    |                      | This is a nested block that requires   |
#    |                      | additional parameter inputs including, |
#    |                      | "a", "b", "a4f", "b4f", "a4s", "b4s",  |
#    |                      | "afs", "bfs", and "k". For e.g.,       |
#    |                      |    Constitutive model: HO-ma {         |
#    |  "HO-ma" /           |       a:                               |
#    |  "HO-modified"       |       b:                               |
#    |                      |       a4f:                             |
#    |                      |       b4f:                             |
#    |                      |       a4s:                             |
#    |                      |       b4s:                             |
#    |                      |       afs:                             |
#    |                      |       bfs:                             |
#    |                      |       k:                               |
#    |                      |    }                                   |
#    |                      | For this model to be used, two families|
#    |                      | of fibers must be loaded in "Add mesh" |
#    |----------------------|----------------------------------------|
#
#  o Fiber reinforcement stress: This setting applies additional fiber
#    reinforcement stress and can be prescribed as either a "Steady"
#    value or "Unsteady" time dependent input from a file. For e.g.,
#       Fiber reinforcement stress: Steady { Value: 1.0e4 }
#       Fiber reinforcement stress: Unsteady {
#          Temporal values file path: unsteady_fiber_stress_file.dat
#          Ramp function: f
#       }
#
#  o Dilational penalty model: This setting defines the dilational
#    or volume-preserving component of the hyperelastic strain energy
#    function. It cannot be defined for stVK and m-stVK constitutive
#    models. Available choices are,
#    -  "Quad" or "Quadratic"
#    -  "ST91" or "Simo-Taylor91"   [DEFAULT]
#    -  "M94"  or "Miehe94"
#
#  o Penalty parameter: If the Poisson ratio for a given case is close
#    to 0.5, then calculated bulk modulus used for dilational penalty
#    model can be extremely high leading to poor linear solver
#    convergence. The users may then override the physical bulk
#    modulus with a penalty constant sufficiently large enough for the
#    linear solver to converge. For e.g.,
#      Domain: 1 {
#         Equation: struct
#         Elastic modulus: 1.0e7
#         Poisson ratio: 0.4999
#         Constitutive model: nHK
#         Dilational penalty model: ST91
#         Penalty parameter: 1.0e8    # Bulk modulus = 1.67e+10
#      }
#
#
#---------------------  Fluid Viscosity Models  ---------------------|
#
#  3. Specifying viscosity model and parameters for fluid/stokes:
#        svFSI allows simulating both Newtonian and non-Newtonian
#     fluid flows. The available non-Newtonian viscosity models are
#     "Carreau-Yasuda" and "Cassons". Additional parameters need to be
#     specified for these models as shown below:
#
#  o  Example for Newtonian viscosity model:
#        Domain: 0 {
#           Equation: fluid
#           Density: 1.06
#           Backflow stabilization coefficient: 0.2
#           Viscosity: Constant {Value: 0.04}
#        }
#
#  o  Example for Carreau-Yasuda non-Newtonian viscosity model:
#        Domain: 0 {
#           Equation: fluid
#           Density: 1.06
#           Backflow stabilization coefficient: 0.2
#           Viscosity: CY {  # or Carreau-Yasuda
#              Limiting high shear-rate viscosity: 0.022
#              Limiting low shear-rate viscosity: 0.22
#              Shear-rate tensor multipler (lamda): 0.11
#              Shear-rate tensor exponent (a): 0.644
#              Power-law index (n): 0.392
#           }
#        }
#
#  o  Example for Cassons non-Newtonian viscosity model:
#        Domain: 0 {
#           Equation: fluid
#           Density: 1.06
#           Backflow stabilization coefficient: 0.2
#           Viscosity: Cassons {  # or Cass
#              Asymptotic viscosity parameter: 0.3953
#              Yield stress parameter: 0.22803
#              Low shear-rate threshold: 0.5
#           }
#        }
#
#
#----------------  Cardiac Electrophysiology Models  ----------------|
#
#  Electrical activity in the heart muscle is modeled in svFSI using
#  the mono-domain model of cellular activation. svFSI includes both
#  phenomenological (e.g., Aliev-Panfilov, Fitzhugh-Nagumo, Buono-
#  Orovio) and biophysically detailed (e.g., ten Tusscher-Panfilov)
#  myocyte activation models. Additional settings include stimulus
#  current details, choice of the time integration method, and
#  conductivity (isotropic/anisotropic). These are described below.
#
#  o  Electrophysiology model: The following choices for the cardiac
#       "Electrophysiology model" are available
#       - "Aliev-Panfilov" or "AP"
#       - "Fitzhugh-Nagumo" or "FN"
#       - "Bueno-Orovio" or "BO"
#       - "tenTusscher-Panfilov" or "TTP"
#
#  o  Conductivity (iso): Sets the isotropic conductivity constant.
#
#  o  Conductivity (ani): Sets the anisotropic conductivity constant.
#       The anisotropic conductivity "Conductivity (ani)" can occur
#       multiple times in the input file and the number of instances
#       of "Conductivity (ani)" should match the number of fiber
#       directions set in the "Add mesh" block. The total conductivity
#       tensor would then be computed as,
#             D = Diso*I + \sum_i [Dani_{i} f_{i} x f_{i}]
#       where Diso is the isotropic conductivity constant, I is the
#       identity tensor, Dani_{i} is the anisotropic conductivity
#       constant for each fiber direction (f_{i}), and a summation
#       is performed on all the fibers directions {i}.
#
#  o  Myocardial zone: Some parameters of the biophysically detailed
#       activation models (e.g., TTP model) depend on whether the
#       myocyte belongs to endocardium/Purkinje, mid-myocardium, or
#       epicardium. This is set using the "Myocardial zone" domain
#       property command.
#
#  o  Stimulus: This is a nested block that describes the stimulus
#       settings for pacemaker cells. This block is not required for
#       non-pacemaker cells. Other settings in this block include
#       "Amplitude", "Start time", "Duration", and "Cycle length".
#       If the "Cycle length" is not provided the code will compute
#       it as the product of the total number of time steps and the
#       the step size.
#
#  o  Time step for integration: To be set if choosing a different
#       time step size compared to the one set by "Time step size"
#       general simulation parameter.
#
#  o  ODE solver: Options available for time integration method are
#       - "Euler"/"FE"/"Explicit"  [DEFAULT]
#       - "Runge"/"RK"/"RK4"
#       - "Implicit"/"CN"/"CN2"
#     However, note that if the time step size is large, "Implicit"
#     option can lead to unexpected results. In general, we recommend
#     "Euler" or "RK4".
#
#  o  "Implicit" time integrator involves using Newton method as the
#       strongly coupled equations are highly nonlinear. Therefore,
#       additional settings need to be provided as,
#       -  Maximum iterations:  3      # [DEFAULT: 5]
#       -  Relative tolerance: 1e-6    # [DEFAULT: 1e-4]
#       -  Absolute tolerance: 1e-10   # [DEFAULT: 1e-6]
#
#  Below we provide examples for pacemaker and non-pacemaker cells:
#
#  # Here domain id == 1 are non-pacemaker cells
#    Domain: 1 {
#       Electrophysiology model: TTP
#       Conductivity (iso): 0.012571
#       Conductivity (ani): 0.082715
#       ODE solver: RK
#    }
#
#    # Here domain id == 2 are pacemaker cells
#    Domain: 2 {
#       Electrophysiology model: TTP
#       Conductivity (iso): 0.012571
#       Conductivity (ani): 0.082715
#       Stimulus: Istim {
#          Amplitude: -35.714
#          Start time: 0.0
#          Duration: 2.0
#          Cycle length: 10000.0
#       }
#       ODE solver: RK
#    }
#
#  Note that in the above example, "Istim" indicates that the applied
#  stimulus is a source current and not a voltage source. The current
#  source is the only possible option available in svFSI.
#
#