ParsedODEKernel

This scalar kernel adds a source term $var element = document.getElementById("moose-equation-b42b51cb-185d-470f-8ce8-050b878ea7f0");katex.render("s(u, \\mathbf{v}, \\mathbf{p})", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ : $var element = document.getElementById("moose-equation-31648260-815a-4dd2-aa66-9c72e48ba887");katex.render(" \\frac{d u}{d t} = s(u, \\mathbf{v}, \\mathbf{p}) \\,,", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-25e5d226-995c-4b3b-b3a7-348ecb17353d");katex.render("u", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the variable the source acts upon, $var element = document.getElementById("moose-equation-bb3617bf-7581-4cc6-b15a-80772348b81a");katex.render("\\mathbf{v}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are other scalar variables, and $var element = document.getElementById("moose-equation-4f762b77-c2f6-43f3-85be-58d4e8162bb5");katex.render("\\mathbf{p}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are post-processor values.

The parameter function is a string expression for the source term $var element = document.getElementById("moose-equation-68a2dc86-3ee9-4b3b-8a21-690af39b2c96");katex.render("s(u, \\mathbf{v}, \\mathbf{p})", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ as it appears on the left-hand-side of the equation; thus it represents $var element = document.getElementById("moose-equation-0df11fac-ad2b-48d7-bc25-20737fdd4157");katex.render("-s(u, \\mathbf{v}, \\mathbf{p})", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ . The expression may use the following quantities:

the name of the scalar variable upon which the kernel acts,
the names of any scalar variables specified in the args parameter,
the names of any post-processors specified in the postprocessors parameter, and
the names supplied in the constant_names parameter, defined to have the values provided by the constant_expressions parameters.

Currently, the function expression cannot be a function of time.

[ScalarKernels]
  [./td1]
    type = ODETimeDerivative
    variable = x
  [../]

  #
  # This parsed expression ODE Kernel behaves exactly as the ImplicitODEx kernel
  # in the main example. Checkout ImplicitODEx::computeQpResidual() in the
  # source code file ImplicitODEx.C to see the matching residual function.
  #
  # The ParsedODEKernel automaticaly generates the On- and Off-Diagonal Jacobian
  # entries.
  #
  [./ode1]
    type = ParsedODEKernel
    function = '-3*x - 2*y'
    variable = x
    args = y
  [../]

  [./td2]
    type = ODETimeDerivative
    variable = y
  [../]

  #
  # This parsed expression ODE Kernel behaves exactly as the ImplicitODEy Kernel
  # in the main example.
  #
  [./ode2]
    type = ParsedODEKernel
    function = '-4*x - y'
    variable = y
    args = x
  [../]
[]

/opt/civet/build_0/moose/examples/ex18_scalar_kernel/ex18_parsed.i

#
# Example 18 modified to use parsed ODE kernels.
#
# The ParsedODEKernel takes function expressions in the input file and computes
# Jacobian entries via automatic differentiation. It allows for rapid development
# of new models without the need for code recompilation.
#
# This input file should produce the exact same result as ex18.i
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]

[Functions]
  # ODEs
  [./exact_x_fn]
    type = ParsedFunction
    value = (-1/3)*exp(-t)+(4/3)*exp(5*t)
  [../]
  [./exact_y_fn]
    type = ParsedFunction
    value = (2/3)*exp(-t)+(4/3)*exp(5*t)
  [../]
[]

[Variables]
  [./diffused]
    order = FIRST
    family = LAGRANGE
  [../]

  # ODE variables
  [./x]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./y]
    family = SCALAR
    order = FIRST
    initial_condition = 2
  [../]

[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = diffused
  [../]
  [./diff]
    type = Diffusion
    variable = diffused
  [../]
[]

[ScalarKernels]
  [./td1]
    type = ODETimeDerivative
    variable = x
  [../]

  #
  # This parsed expression ODE Kernel behaves exactly as the ImplicitODEx kernel
  # in the main example. Checkout ImplicitODEx::computeQpResidual() in the
  # source code file ImplicitODEx.C to see the matching residual function.
  #
  # The ParsedODEKernel automaticaly generates the On- and Off-Diagonal Jacobian
  # entries.
  #
  [./ode1]
    type = ParsedODEKernel
    function = '-3*x - 2*y'
    variable = x
    args = y
  [../]

  [./td2]
    type = ODETimeDerivative
    variable = y
  [../]

  #
  # This parsed expression ODE Kernel behaves exactly as the ImplicitODEy Kernel
  # in the main example.
  #
  [./ode2]
    type = ParsedODEKernel
    function = '-4*x - y'
    variable = y
    args = x
  [../]
[]

[BCs]
  [./right]
    type = ScalarDirichletBC
    variable = diffused
    boundary = 1
    scalar_var = x
  [../]

  [./left]
    type = ScalarDirichletBC
    variable = diffused
    boundary = 3
    scalar_var = y
  [../]
[]

[Postprocessors]
  # to print the values of x, y into a file so we can plot it
  [./x]
    type = ScalarVariable
    variable = x
    execute_on = timestep_end
  [../]
  [./y]
    type = ScalarVariable
    variable = y
    execute_on = timestep_end
  [../]

  [./exact_x]
    type = FunctionValuePostprocessor
    function = exact_x_fn
    execute_on = timestep_end
  [../]

  [./exact_y]
    type = FunctionValuePostprocessor
    function = exact_y_fn
    execute_on = timestep_end
    point = '0 0 0'
  [../]

  # Measure the error in ODE solution for 'x'.
  [./l2err_x]
    type = ScalarL2Error
    variable = x
    function = exact_x_fn
  [../]

  # Measure the error in ODE solution for 'y'.
  [./l2err_y]
    type = ScalarL2Error
    variable = y
    function = exact_y_fn
  [../]
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 0.01
  num_steps = 10
  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = 'ex18_out'
  exodus = true
[]

Input Parameters

functionfunction expression
C++ Type:std::string
Options:
Description:function expression
variableThe name of the variable that this kernel operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this kernel operates on

Required Parameters

argsadditional coupled variables
C++ Type:std::vector
Options:
Description:additional coupled variables
constant_expressionsVector of values for the constants in constant_names (can be an FParser expression)
C++ Type:std::vector
Options:
Description:Vector of values for the constants in constant_names (can be an FParser expression)
constant_namesVector of constants used in the parsed function (use this for kB etc.)
C++ Type:std::vector
Options:
Description:Vector of constants used in the parsed function (use this for kB etc.)
postprocessorsVector of postprocessor names used in the function expression
C++ Type:std::vector
Options:
Description:Vector of postprocessor names used in the function expression

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
disable_fpoptimizerFalseDisable the function parser algebraic optimizer
Default:False
C++ Type:bool
Options:
Description:Disable the function parser algebraic optimizer
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
enable_ad_cacheTrueEnable cacheing of function derivatives for faster startup time
Default:True
C++ Type:bool
Options:
Description:Enable cacheing of function derivatives for faster startup time
enable_auto_optimizeTrueEnable automatic immediate optimization of derivatives
Default:True
C++ Type:bool
Options:
Description:Enable automatic immediate optimization of derivatives
enable_jitTrueEnable just-in-time compilation of function expressions for faster evaluation
Default:True
C++ Type:bool
Options:
Description:Enable just-in-time compilation of function expressions for faster evaluation
fail_on_evalerrorFalseFail fatally if a function evaluation returns an error code (otherwise just pass on NaN)
Default:False
C++ Type:bool
Options:
Description:Fail fatally if a function evaluation returns an error code (otherwise just pass on NaN)
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime system
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

test/tests/kernels/ode/coupled_ode_td.i
test/tests/problems/eigen_problem/scalar.i
examples/ex18_scalar_kernel/ex18_parsed.i
test/tests/kernels/ode/parsedode_pp_test.i
test/tests/controls/conditional_functional_enable/conditional_function_enable.i
test/tests/controls/time_periods/scalarkernels/scalarkernels.i
test/tests/ics/function_scalar_ic/function_scalar_ic.i
test/tests/kernels/ode/coupled_ode_td_var_ic_from_mesh.i
test/tests/time_integrators/actually_explicit_euler_verification/ee-ode.i
test/tests/tag/scalar_tag_vector.i
test/tests/outputs/nemesis/nemesis_scalar.i
test/tests/time_integrators/explicit_ssp_runge_kutta/explicit_ssp_runge_kutta.i
test/tests/time_integrators/scalar/stiff.i
test/tests/kernels/ode/parsedode_sys_impl_test.i
test/tests/time_integrators/scalar/scalar.i
test/tests/kernels/ode/coupled_ode_td_auxvar_ic_from_mesh.i
test/tests/kernels/bad_scaling_scalar_kernels/ill_conditioned_field_scalar_system.i

test/tests/kernels/ode/coupled_ode_td.i

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 1
  nx = 1
[]


[Variables]
  [./f]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./f_times_mult]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
[]

[ScalarKernels]
  [./dT]
    type = CoupledODETimeDerivative
    variable = f
    v = f_times_mult
  [../]

  [./src]
    type = ParsedODEKernel
    variable = f
    function = '-1'
  [../]

  [./f_times_mult_1]
    type = ParsedODEKernel
    variable = f_times_mult
    function = 'f_times_mult'
  [../]

  [./f_times_mult_2]
    type = ParsedODEKernel
    variable = f_times_mult
    function = '-f * g'
    args = 'f g'
  [../]
[]

[AuxVariables]
  [./g]
    family = SCALAR
    order = FIRST
  [../]
[]

[Functions]
  [./function_g]
    type = ParsedFunction
    value = '(1 + t)'
  [../]
[]

[AuxScalarKernels]
  [./set_g]
    type = FunctionScalarAux
    function = function_g
    variable = g
    execute_on = 'linear initial'
  [../]
[]

[Postprocessors]
  [./f]
    type = ScalarVariable
    variable = f
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  dt = 1
  num_steps = 3
  nl_abs_tol = 1e-9
[]

[Outputs]
  csv = true
[]

test/tests/problems/eigen_problem/scalar.i

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 1
  nx = 1
[]

[Variables]
  [./f1]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./f2]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
[]

[ScalarKernels]
  [./row1]
    type = ParsedODEKernel
    variable = f1
    function = '5*f1 + 2*f2'
    args = 'f2'
  [../]

  [./row2]
    type = ParsedODEKernel
    variable = f2
    function = '2*f1 + 5*f2'
    args = 'f1'
  [../]
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Eigenvalue
  which_eigen_pairs = LARGEST_MAGNITUDE
  eigen_problem_type = HERMITIAN
  n_eigen_pairs = 2
  n_basis_vectors = 4
  eigen_max_its = 10
  solve_type = KRYLOVSCHUR
  petsc_options = '-eps_view'
[]

[Outputs]
  csv = true
[]

examples/ex18_scalar_kernel/ex18_parsed.i

#
# Example 18 modified to use parsed ODE kernels.
#
# The ParsedODEKernel takes function expressions in the input file and computes
# Jacobian entries via automatic differentiation. It allows for rapid development
# of new models without the need for code recompilation.
#
# This input file should produce the exact same result as ex18.i
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]

[Functions]
  # ODEs
  [./exact_x_fn]
    type = ParsedFunction
    value = (-1/3)*exp(-t)+(4/3)*exp(5*t)
  [../]
  [./exact_y_fn]
    type = ParsedFunction
    value = (2/3)*exp(-t)+(4/3)*exp(5*t)
  [../]
[]

[Variables]
  [./diffused]
    order = FIRST
    family = LAGRANGE
  [../]

  # ODE variables
  [./x]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./y]
    family = SCALAR
    order = FIRST
    initial_condition = 2
  [../]

[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = diffused
  [../]
  [./diff]
    type = Diffusion
    variable = diffused
  [../]
[]

[ScalarKernels]
  [./td1]
    type = ODETimeDerivative
    variable = x
  [../]

  #
  # This parsed expression ODE Kernel behaves exactly as the ImplicitODEx kernel
  # in the main example. Checkout ImplicitODEx::computeQpResidual() in the
  # source code file ImplicitODEx.C to see the matching residual function.
  #
  # The ParsedODEKernel automaticaly generates the On- and Off-Diagonal Jacobian
  # entries.
  #
  [./ode1]
    type = ParsedODEKernel
    function = '-3*x - 2*y'
    variable = x
    args = y
  [../]

  [./td2]
    type = ODETimeDerivative
    variable = y
  [../]

  #
  # This parsed expression ODE Kernel behaves exactly as the ImplicitODEy Kernel
  # in the main example.
  #
  [./ode2]
    type = ParsedODEKernel
    function = '-4*x - y'
    variable = y
    args = x
  [../]
[]


[BCs]
  [./right]
    type = ScalarDirichletBC
    variable = diffused
    boundary = 1
    scalar_var = x
  [../]

  [./left]
    type = ScalarDirichletBC
    variable = diffused
    boundary = 3
    scalar_var = y
  [../]
[]

[Postprocessors]
  # to print the values of x, y into a file so we can plot it
  [./x]
    type = ScalarVariable
    variable = x
    execute_on = timestep_end
  [../]
  [./y]
    type = ScalarVariable
    variable = y
    execute_on = timestep_end
  [../]

  [./exact_x]
    type = FunctionValuePostprocessor
    function = exact_x_fn
    execute_on = timestep_end
  [../]

  [./exact_y]
    type = FunctionValuePostprocessor
    function = exact_y_fn
    execute_on = timestep_end
    point = '0 0 0'
  [../]

  # Measure the error in ODE solution for 'x'.
  [./l2err_x]
    type = ScalarL2Error
    variable = x
    function = exact_x_fn
  [../]

  # Measure the error in ODE solution for 'y'.
  [./l2err_y]
    type = ScalarL2Error
    variable = y
    function = exact_y_fn
  [../]
[]


[Executioner]
  type = Transient
  start_time = 0
  dt = 0.01
  num_steps = 10
  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = 'ex18_out'
  exodus = true
[]

test/tests/kernels/ode/parsedode_pp_test.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD4
[]

[Variables]
  [./x]
    family = SCALAR
    order = FIRST
    initial_condition = 0
  [../]
[]

[ScalarKernels]
  [./dt]
    type = ODETimeDerivative
    variable = x
  [../]
  [./ode1]
    type = ParsedODEKernel
    function = '-mytime'
    postprocessors = mytime
    variable = x
  [../]
[]

[Postprocessors]
  [./computed_x]
    type = ScalarVariable
    variable = x
    execute_on = 'initial timestep_end'
  [../]

  [./mytime]
    type = FunctionValuePostprocessor
    function = t
    execute_on = 'initial timestep_begin'
  [../]

  [./exact_x]
    type = FunctionValuePostprocessor
    function = '0.5*t^2'
    execute_on = 'initial timestep_end'
  [../]

  [./l2err_x]
    type = ScalarL2Error
    variable = x
    function = '0.5*t^2'
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  dt = 0.1
  num_steps = 10

  solve_type = 'NEWTON'
[]

[Outputs]
  file_base = ode_pp_test_out
  hide = 'x mytime'
  csv = true
[]

test/tests/controls/conditional_functional_enable/conditional_function_enable.i

# This tests controllability of the enable parameter of a MOOSE object via a
# conditional function.
#
# There are 2 scalar variables, {u, v}, with the ODEs:
#   du/dt = 1    u(0) = 0
#   v = u        v(0) = -10
# A control switches the ODE 'v = u' to the following ODE when u >= 1.99:
#   dv/dt = 2
#
# 5 time steps (of size dt = 1) will be taken, and the predicted values are as follows:
#      t     u     v
# ------------------
#      0     0   -10
#      1     1     1
#      2     2     2
#      3     3     4
#      4     4     6
#      5     5     8

u_initial = 0
u_growth = 1
u_threshold = 1.99

v_initial = -10
v_growth = 2

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[Variables]
  [./u]
    family = SCALAR
    order = FIRST
  [../]
  [./v]
    family = SCALAR
    order = FIRST
  [../]
[]

[ICs]
  [./u_ic]
    type = ScalarConstantIC
    variable = u
    value = ${u_initial}
  [../]
  [./v_ic]
    type = ScalarConstantIC
    variable = v
    value = ${v_initial}
  [../]
[]

[ScalarKernels]
  [./u_time]
    type = ODETimeDerivative
    variable = u
  [../]
  [./u_src]
    type = ParsedODEKernel
    variable = u
    function = '-${u_growth}'
  [../]

  [./v_time]
    type = ODETimeDerivative
    variable = v
    enable = false
  [../]
  [./v_src]
    type = ParsedODEKernel
    variable = v
    function = '-${v_growth}'
    enable = false
  [../]
  [./v_constraint]
    type = ParsedODEKernel
    variable = v
    args = 'u'
    function = 'v - u'
  [../]
[]

[Functions]
  [./conditional_function]
    type = ParsedFunction
    vars = 'u_sol'
    vals = 'u'
    value = 'u_sol >= ${u_threshold}'
  [../]
[]

[Controls]
  [./u_threshold]
    type = ConditionalFunctionEnableControl
    conditional_function = conditional_function
    enable_objects = 'ScalarKernel::v_time ScalarKernel::v_src'
    disable_objects = 'ScalarKernel::v_constraint'
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[Executioner]
  type = Transient
  scheme = implicit-euler
  dt = 1
  num_steps = 5
  abort_on_solve_fail = true

  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
[]

[Outputs]
  csv = true
[]

test/tests/controls/time_periods/scalarkernels/scalarkernels.i

# This tests controllability of the enable parameter of scalar kernels.
#
# There are 2 scalar variables, {u, v}, with the ODEs:
#   du/dt = 1    u(0) = 0
#   v = u        v(0) = -10
# A control switches the ODE 'v = u' to the following ODE when t >= 2:
#   dv/dt = 2
#
# 5 time steps (of size dt = 1) will be taken, and the predicted values are as follows:
#      t     u     v
# ------------------
#      0     0   -10
#      1     1     1
#      2     2     2
#      3     3     4
#      4     4     6
#      5     5     8

u_initial = 0
u_growth = 1

v_initial = -10
v_growth = 2

t_transition = 2

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
[]

[Variables]
  [./u]
    family = SCALAR
    order = FIRST
  [../]
  [./v]
    family = SCALAR
    order = FIRST
  [../]
[]

[ICs]
  [./u_ic]
    type = ScalarConstantIC
    variable = u
    value = ${u_initial}
  [../]
  [./v_ic]
    type = ScalarConstantIC
    variable = v
    value = ${v_initial}
  [../]
[]

[ScalarKernels]
  [./u_time]
    type = ODETimeDerivative
    variable = u
  [../]
  [./u_src]
    type = ParsedODEKernel
    variable = u
    function = '-${u_growth}'
  [../]

  [./v_time]
    type = ODETimeDerivative
    variable = v
    enable = false
  [../]
  [./v_src]
    type = ParsedODEKernel
    variable = v
    function = '-${v_growth}'
    enable = false
  [../]
  [./v_constraint]
    type = ParsedODEKernel
    variable = v
    args = 'u'
    function = 'v - u'
  [../]
[]

[Controls]
  [./time_period_control]
    type = TimePeriod
    end_time = ${t_transition}
    enable_objects = 'ScalarKernel::v_constraint'
    disable_objects = 'ScalarKernel::v_time ScalarKernel::v_src'
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[Executioner]
  type = Transient
  scheme = implicit-euler
  dt = 1
  num_steps = 5
  abort_on_solve_fail = true

  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
[]

[Outputs]
  csv = true
[]

test/tests/ics/function_scalar_ic/function_scalar_ic.i

[Mesh]
  # a dummy mesh
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 1
  ny = 1
  elem_type = QUAD4
[]

[Variables]
  [./n]
    family = SCALAR
    order = FIRST
  [../]
[]

[Functions]
  [./f]
    type = ParsedFunction
    value = cos(t)
  [../]
[]

[ICs]
  [./f]
    type = FunctionScalarIC
    variable = n
    function = f
  [../]
[]

[ScalarKernels]
  [./dn]
    type = ODETimeDerivative
    variable = n
  [../]
  [./ode1]
    type = ParsedODEKernel
    function = '-n'
    variable = n
  [../]
[]

[Executioner]
  type = Transient
  start_time = 0
  end_time = 1
  dt = 0.01
  scheme = bdf2
  solve_type = 'PJFNK'
  timestep_tolerance = 1e-12
[]

[Outputs]
  csv = true
[]

test/tests/kernels/ode/coupled_ode_td_var_ic_from_mesh.i

[Mesh]
  type = FileMesh
  file = 'coupled_ode_td_out.e'
[]

[Variables]
  [./f]
    family = SCALAR
    order = FIRST
    initial_from_file_var = f
    initial_from_file_timestep = 'LATEST'
  [../]
  [./f_times_mult]
    family = SCALAR
    order = FIRST
    initial_from_file_var = f_times_mult
    initial_from_file_timestep = 'LATEST'
  [../]
[]

[ScalarKernels]
  [./dT]
    type = CoupledODETimeDerivative
    variable = f
    v = f_times_mult
  [../]

  [./src]
    type = ParsedODEKernel
    variable = f
    function = '-1'
  [../]

  [./f_times_mult_1]
    type = ParsedODEKernel
    variable = f_times_mult
    function = 'f_times_mult'
  [../]

  [./f_times_mult_2]
    type = ParsedODEKernel
    variable = f_times_mult
    function = '-f * g'
    args = 'f g'
  [../]
[]

[AuxVariables]
  [./g]
    family = SCALAR
    order = FIRST
  [../]
[]

[Functions]
  [./function_g]
    type = ParsedFunction
    value = '(1 + t)'
  [../]
[]

[AuxScalarKernels]
  [./set_g]
    type = FunctionScalarAux
    function = function_g
    variable = g
    execute_on = 'linear initial'
  [../]
[]

[Postprocessors]
  [./f]
    type = ScalarVariable
    variable = f
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  dt = 1
  num_steps = 3
  nl_abs_tol = 1e-9
[]

[Outputs]
  csv = true
[]

test/tests/time_integrators/actually_explicit_euler_verification/ee-ode.i

# Tests that ActuallyExplicitEuler works with scalar variables.
#
# The ODE and IC used are the following:
#   du/dt = 2,       u(0) = 0
# Thus the solution is u(t) = 2*t.

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
[]

[Variables]
  [./u]
    family = SCALAR
    order = FIRST
    initial_condition = 0
  [../]
[]

[ScalarKernels]
  [./time]
    type = ODETimeDerivative
    variable = u
  [../]
  [./source]
    type = ParsedODEKernel
    variable = u
    function = -2
  [../]
[]

[Executioner]
  type = Transient

  [./TimeIntegrator]
    type = ActuallyExplicitEuler
  [../]
  dt = 1
  num_steps = 5
[]

[Outputs]
  csv = true
[]

test/tests/tag/scalar_tag_vector.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 1
  ny = 1
  elem_type = QUAD4
[]

[Variables]
  [./n]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
[]

[AuxVariables]
  [./tag_vector_var1]
    family = SCALAR
    order = FIRST
  [../]
  [./tag_vector_var2]
    family = SCALAR
    order = FIRST
  [../]
  [./tag_matrix_var2]
    family = SCALAR
    order = FIRST
  [../]
[]

[ScalarKernels]
  [./dn]
    type = ODETimeDerivative
    variable = n
    extra_matrix_tags = 'mat_tag1 mat_tag2'
    extra_vector_tags = 'vec_tag1'
  [../]

  [./ode1]
    type = ParsedODEKernel
    function = '-n'
    variable = n
    extra_matrix_tags = 'mat_tag1'
    extra_vector_tags = 'vec_tag1'
  [../]

  [./ode2]
    type = ParsedODEKernel
    function = '-n'
    variable = n
    vector_tags = 'vec_tag2'
    matrix_tags = 'mat_tag2'
  [../]
[]

[AuxScalarKernels]
  [./TagVectorAux]
    type = ScalarTagVectorAux
    variable = tag_vector_var1
    v = n
    vector_tag  = vec_tag1
    execute_on = timestep_end
  [../]

  [./TagVectorAux2]
    type = ScalarTagVectorAux
    variable = tag_vector_var2
    v = n
    vector_tag  = vec_tag2
    execute_on = timestep_end
  [../]

  [./TagMatrixAux2]
    type = ScalarTagMatrixAux
    variable = tag_matrix_var2
    v = n
    matrix_tag  = mat_tag2
    execute_on = timestep_end
  [../]
[]

[Problem]
  type = TagTestProblem
  test_tag_vectors =  'time nontime residual vec_tag1 vec_tag2'
  test_tag_matrices = 'mat_tag1 mat_tag2'

  extra_tag_matrices = 'mat_tag1 mat_tag2'
  extra_tag_vectors  = 'vec_tag1 vec_tag2'
[]

[Executioner]
  type = Transient
  start_time = 0
  num_steps = 10
  dt = 0.001
  dtmin = 0.001 # Don't allow timestep cutting
  solve_type = NEWTON
  nl_max_its = 2
  nl_abs_tol = 1.e-12 # This is an ODE, so nl_abs_tol makes sense.
[]

[Functions]
  [./exact_solution]
    type = ParsedFunction
    value = exp(t)
  [../]
[]

[Postprocessors]
  [./error_n]
    # Post processor that computes the difference between the computed
    # and exact solutions.  For the exact solution used here, the
    # error at the final time should converge at O(dt^p), where p is
    # the order of the method.
    type = ScalarL2Error
    variable = n
    function = exact_solution
    # final is not currently supported for Postprocessor execute_on...
    # execute_on = 'final'
  [../]
[]

[Outputs]
  csv = true
[]

test/tests/outputs/nemesis/nemesis_scalar.i

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 1
  nx = 4
[]


[Variables]
  [./f]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./f_times_mult]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
[]

[ScalarKernels]
  [./dT]
    type = CoupledODETimeDerivative
    variable = f
    v = f_times_mult
  [../]

  [./src]
    type = ParsedODEKernel
    variable = f
    function = '-1'
  [../]

  [./f_times_mult_1]
    type = ParsedODEKernel
    variable = f_times_mult
    function = 'f_times_mult'
  [../]

  [./f_times_mult_2]
    type = ParsedODEKernel
    variable = f_times_mult
    function = '-f * g'
    args = 'f g'
  [../]
[]

[AuxVariables]
  [./g]
    family = SCALAR
    order = FIRST
  [../]
[]

[Functions]
  [./function_g]
    type = ParsedFunction
    value = '(1 + t)'
  [../]
[]

[AuxScalarKernels]
  [./set_g]
    type = FunctionScalarAux
    function = function_g
    variable = g
    execute_on = 'linear initial'
  [../]
[]

[Postprocessors]
  [./f]
    type = ScalarVariable
    variable = f
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  dt = 1
  num_steps = 3
  nl_abs_tol = 1e-9
[]

[Outputs]
  nemesis = true
[]

test/tests/time_integrators/explicit_ssp_runge_kutta/explicit_ssp_runge_kutta.i

# This test solves the following IVP:
#   du/dt = f(u(t), t),   u(0) = 1
#   f(u(t), t) = -u(t) + t^3 + 3t^2
# The exact solution is the following:
#   u(t) = exp(-t) + t^3

[Mesh]
  [./mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 1
  [../]
[]

[Variables]
  [./u]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
[]

[ScalarKernels]
  [./time_derivative]
    type = ODETimeDerivative
    variable = u
  [../]
  [./source_part1]
    type = ParsedODEKernel
    variable = u
    function = 'u'
  [../]
  [./source_part2]
    type = PostprocessorSinkScalarKernel
    variable = u
    postprocessor = sink_pp
  [../]
[]

[Functions]
  [./sink_fn]
    type = ParsedFunction
    value = '-t^3 - 3*t^2'
  [../]
[]

[Postprocessors]
  [./sink_pp]
    type = FunctionValuePostprocessor
    function = sink_fn
    execute_on = 'LINEAR NONLINEAR'
  [../]
  [./l2_err]
    type = ScalarL2Error
    variable = u
    function = ${fparse exp(-0.5) + 0.5^3}
  [../]
[]

[Executioner]
  type = Transient

  [./TimeIntegrator]
    type = ExplicitSSPRungeKutta
    order = 1
  [../]

  end_time = 0.5
  dt = 0.1
[]

[Outputs]
  file_base = 'first_order'
  exodus = true
  [./csv]
    type = CSV
    show = 'u'
    execute_on = 'FINAL'
  [../]
[]

test/tests/time_integrators/scalar/stiff.i

# This is a linear model problem described in Frank et al, "Order
# results for implicit Runge-Kutta methods applied to stiff systems",
# SIAM J. Numerical Analysis, vol. 22, no. 3, 1985, pp. 515-534.
#
# Problems "PL" and "PNL" from page 527 of the paper:
# { dy1/dt = lambda*y1 + y2**p, y1(0) = -1/(lambda+p)
# { dy2/dt = -y2,               y2(0) = 1
#
# The exact solution is:
# y1 = -exp(-p*t)/(lambda+p)
# y2 = exp(-t)
#
# According to the following paragraph from the reference above, the
# p=1 version of this problem should not exhibit order reductions
# regardless of stiffness, while the nonlinear version (p>=2) will
# exhibit order reductions down to the "stage order" of the method for
# lambda large, negative.

# Use Dollar Bracket Expressions (DBEs) to set the value of LAMBDA in
# a single place.  You can also set this on the command line with
# e.g. LAMBDA=-4, but note that this does not seem to override the
# value set in the input file.  This is a bit different from the way
# that command line values normally work...
# Note that LAMBDA == Y2_EXPONENT is not allowed!
# LAMBDA = -10
# Y2_EXPONENT = 2

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 1
  ny = 1
  elem_type = QUAD4
[]

[Variables]
  [./y1]
    family = SCALAR
    order = FIRST
  [../]
  [./y2]
    family = SCALAR
    order = FIRST
  [../]
[]

[ICs]
  [./y1_init]
    type = FunctionScalarIC
    variable = y1
    function = y1_exact
  [../]
  [./y2_init]
    type = FunctionScalarIC
    variable = y2
    function = y2_exact
  [../]
[]

[ScalarKernels]
  [./y1_time]
    type = ODETimeDerivative
    variable = y1
  [../]
  [./y1_space]
    type = ParsedODEKernel
    variable = y1
    function = '-(${LAMBDA})*y1 - y2^${Y2_EXPONENT}'
    args = 'y2'
  [../]
  [./y2_time]
    type = ODETimeDerivative
    variable = y2
  [../]
  [./y2_space]
    type = ParsedODEKernel
    variable = y2
    function = 'y2'
  [../]
[]

[Executioner]
  type = Transient
  [./TimeIntegrator]
    type = LStableDirk2
  [../]
  start_time = 0
  end_time = 1
  dt = 0.125
  solve_type = 'PJFNK'
  nl_max_its = 6
  nl_abs_tol = 1.e-13
  nl_rel_tol = 1.e-32 # Force nl_abs_tol to be used.
  line_search = 'none'
[]

[Functions]
  [./y1_exact]
    type = ParsedFunction
    value = '-exp(-${Y2_EXPONENT}*t)/(lambda+${Y2_EXPONENT})'
    vars = 'lambda'
    vals = ${LAMBDA}
  [../]
  [./y2_exact]
    type = ParsedFunction
    value = exp(-t)
  [../]
[]

[Postprocessors]
  [./error_y1]
    type = ScalarL2Error
    variable = y1
    function = y1_exact
    execute_on = 'initial timestep_end'
  [../]
  [./error_y2]
    type = ScalarL2Error
    variable = y2
    function = y2_exact
    execute_on = 'initial timestep_end'
  [../]
  [./max_error_y1]
    # Estimate ||e_1||_{\infty}
    type = TimeExtremeValue
    value_type = max
    postprocessor = error_y1
    execute_on = 'initial timestep_end'
  [../]
  [./max_error_y2]
    # Estimate ||e_2||_{\infty}
    type = TimeExtremeValue
    value_type = max
    postprocessor = error_y2
    execute_on = 'initial timestep_end'
  [../]
  [./value_y1]
    type = ScalarVariable
    variable = y1
    execute_on = 'initial timestep_end'
  [../]
  [./value_y2]
    type = ScalarVariable
    variable = y2
    execute_on = 'initial timestep_end'
  [../]
  [./value_y1_abs_max]
    type = TimeExtremeValue
    value_type = abs_max
    postprocessor = value_y1
    execute_on = 'initial timestep_end'
  [../]
  [./value_y2_abs_max]
    type = TimeExtremeValue
    value_type = abs_max
    postprocessor = value_y2
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  csv = true
[]

test/tests/kernels/ode/parsedode_sys_impl_test.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD4
[]

[Functions]
  [./f_fn]
    type = ParsedFunction
    value = -4
  [../]
  [./bc_all_fn]
    type = ParsedFunction
    value = x*x+y*y
  [../]

  # ODEs
  [./exact_x_fn]
    type = ParsedFunction
    value = (-1/3)*exp(-t)+(4/3)*exp(5*t)
  [../]
[]

# NL

[Variables]
  [./u]
    family = LAGRANGE
    order = FIRST
  [../]

  # ODE variables
  [./x]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./y]
    family = SCALAR
    order = FIRST
    initial_condition = 2
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./uff]
    type = BodyForce
    variable = u
    function = f_fn
  [../]
[]

[ScalarKernels]
  [./td1]
    type = ODETimeDerivative
    variable = x
  [../]
  [./ode1]
    type = ParsedODEKernel
    function = '-3*x - 2*y'
    variable = x
    args = y
  [../]

  [./td2]
    type = ODETimeDerivative
    variable = y
  [../]
  [./ode2]
    type = ParsedODEKernel
    function = '-4*x - y'
    variable = y
    args = x
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = bc_all_fn
  [../]
[]

[Postprocessors]
  active = 'exact_x l2err_x x y'

  [./x]
    type = ScalarVariable
    variable = x
    execute_on = 'initial timestep_end'
  [../]
  [./y]
    type = ScalarVariable
    variable = y
    execute_on = 'initial timestep_end'
  [../]

  [./exact_x]
    type = FunctionValuePostprocessor
    function = exact_x_fn
    execute_on = 'initial timestep_end'
    point = '0 0 0'
  [../]

  [./l2err_x]
    type = ScalarL2Error
    variable = x
    function = exact_x_fn
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 0.01
  num_steps = 100

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = ode_sys_impl_test_out
  exodus = true
[]

test/tests/time_integrators/scalar/scalar.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 1
  ny = 1
  elem_type = QUAD4
[]

[Variables]
  [./n]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
[]

[ScalarKernels]
  [./dn]
    type = ODETimeDerivative
    variable = n
  [../]
  [./ode1]
    type = ParsedODEKernel
    function = '-n'
    variable = n
    # implicit = false
  [../]
[]

[Executioner]
  type = Transient
  [./TimeIntegrator]
    # type = ImplicitEuler
    # type = BDF2
    type = CrankNicolson
    # type = ImplicitMidpoint
    # type = LStableDirk2
    # type = LStableDirk3
    # type = LStableDirk4
    # type = AStableDirk4
    #
    # Explicit methods
    # type = ExplicitEuler
    # type = ExplicitMidpoint
    # type = Heun
    # type = Ralston
  [../]
  start_time = 0
  end_time = 1
  dt = 0.001
  dtmin = 0.001 # Don't allow timestep cutting
  solve_type = 'PJFNK'
  nl_max_its = 2
  nl_abs_tol = 1.e-12 # This is an ODE, so nl_abs_tol makes sense.
[]

[Functions]
  [./exact_solution]
    type = ParsedFunction
    value = exp(t)
  [../]
[]

[Postprocessors]
  [./error_n]
    # Post processor that computes the difference between the computed
    # and exact solutions.  For the exact solution used here, the
    # error at the final time should converge at O(dt^p), where p is
    # the order of the method.
    type = ScalarL2Error
    variable = n
    function = exact_solution
    # final is not currently supported for Postprocessor execute_on...
    # execute_on = 'final'
  [../]
[]

[Outputs]
  csv = true
[]

test/tests/kernels/ode/coupled_ode_td_auxvar_ic_from_mesh.i

[Mesh]
  type = FileMesh
  file = 'coupled_ode_td_out.e'
[]

[Variables]
  [./f]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./f_times_mult]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
[]

[ScalarKernels]
  [./dT]
    type = CoupledODETimeDerivative
    variable = f
    v = f_times_mult
  [../]

  [./src]
    type = ParsedODEKernel
    variable = f
    function = '-1'
  [../]

  [./f_times_mult_1]
    type = ParsedODEKernel
    variable = f_times_mult
    function = 'f_times_mult'
  [../]

  [./f_times_mult_2]
    type = ParsedODEKernel
    variable = f_times_mult
    function = '-f * g'
    args = 'f g'
  [../]
[]

[AuxVariables]
  [./g]
    family = SCALAR
    order = FIRST
    initial_from_file_var = g
    initial_from_file_timestep = 'LATEST'
  [../]
[]

[Functions]
  [./function_g]
    type = ParsedFunction
    value = '(1 + t)'
  [../]
[]

[AuxScalarKernels]
  [./set_g]
    type = FunctionScalarAux
    function = function_g
    variable = g
    execute_on = 'timestep_end'
  [../]
[]

[Postprocessors]
  [./f]
    type = ScalarVariable
    variable = f
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  dt = 1
  num_steps = 3
  nl_abs_tol = 1e-9
[]

[Outputs]
  csv = true
[]

test/tests/kernels/bad_scaling_scalar_kernels/ill_conditioned_field_scalar_system.i

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 2
[]

[Variables]
  [./u]
  [../]
  [v]
    family = SCALAR
    initial_condition = 1
  []
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [scalar]
    type = ScalarLagrangeMultiplier
    variable = u
    lambda = v
  []
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[ScalarKernels]
  [reaction]
    type = ParsedODEKernel
    function = '10^20 * v'
    variable = v
  []
  [time]
    type = ODETimeDerivative
    variable = v
  []
[]

[Executioner]
  type = Transient
  num_steps = 1
  dtmin = 1
  solve_type = NEWTON
  petsc_options = '-pc_svd_monitor -ksp_view_pmat -snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -snes_stol'
  petsc_options_value = 'svd      0'
[]

[Outputs]
  exodus = true
[]

Input Parameters
Input Files

Application Usage

Physics and Syntax

Application Development

Framework Development

MOOSEDocs

Infrastructure

Questions

Information and Tools