LaplacianJumpIndicator

Compute the jump of the solution laplacian across element bondaries.

Description

The LaplacianJumpIndicator object computes the error as computed by the change in the Laplacian of a variable across element interfaces.

warning:LaplacianJumpIndicator requires second derivatives

The Laplacian ( $var element = document.getElementById("moose-equation-343be873-c040-45c4-abcf-12fc71ee980a");katex.render("\\nabla^2 u", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ or $var element = document.getElementById("moose-equation-90501063-1573-4044-b431-39a436e600ca");katex.render("\\nabla\\cdot\\nabla u", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ ) operator requires second derivaties with respect to the spacial dimensions. As such, the selected finite elements must be at least second order for the calculation to be valid.

Example Input File Syntax

The following code snippet demonstrates the use of the LaplacianJumpIndicator object within a typical input file.

[Adaptivity]
  [Indicators]
    [error]
      type = LaplacianJumpIndicator
      variable = u
      scale_by_flux_faces = true
    []
  []
[]

/opt/civet/build_0/moose/test/tests/indicators/laplacian_jump_indicator/biharmonic.i

[GlobalParams]
  # Parameters used by Functions.
  vars   = 'c'
  vals   = '50'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -.5
  xmax = .5
  ymin = -.5
  ymax = .5
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    order = THIRD
    family = HERMITE
  [../]
[]

[Kernels]
  [./biharmonic]
    type = Biharmonic
    variable = u
  [../]
  [./body_force]
    type = BodyForce
    variable = u
    function = forcing_func
  [../]
[]

[BCs]
  active = 'all_value all_flux'
  [./all_value]
    type = FunctionPenaltyDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = u_func
    penalty = 1e10
  [../]
  [./all_flux]
    type = FunctionPenaltyFluxBC
    variable = u
    boundary = 'left right top bottom'
    function = u_func
    penalty = 1e10
  [../]
  [./all_laplacian]
    type = BiharmonicLapBC
    variable = u
    boundary = 'left right top bottom'
    laplacian_function = lapu_func
  [../]
[]

[Adaptivity]
  [Indicators]
    [error]
      type = LaplacianJumpIndicator
      variable = u
      scale_by_flux_faces = true
    []
  []
[]

[Executioner]
  type = Steady

  # Note: the unusually tight tolerances here are due to the penalty
  # BCs (currently the only way of accurately Dirichlet boundary
  # conditions on Hermite elements in MOOSE).
  nl_rel_tol = 1.e-15
  l_tol = 1.e-15

  # We have exact Jacobians
  solve_type = 'NEWTON'

  # Use 6x6 quadrature to ensure the forcing function is integrated
  # accurately.
  [./Quadrature]
    type = GAUSS
    order = ELEVENTH
  [../]
[]

[Functions]
  [./u_func]
    type   = ParsedGradFunction
    value  = 'exp(-c*(x^2+y^2))'
    grad_x = '-2*c*exp(-c*(x^2+y^2))*x'
    grad_y = '-2*c*exp(-c*(x^2+y^2))*y'
  [../]
  [./lapu_func]
    type   = ParsedFunction
    value  = '4*c*(c*(x^2+y^2) - 1)*exp(-c*(x^2+y^2))'
  [../]
  [./forcing_func]
    type   = ParsedFunction
    value  = '16*c^2*(c^2*(x^2+y^2)^2 - 4*c*(x^2+y^2) + 2)*exp(-c*(x^2+y^2))'
  [../]
[]

[Postprocessors]
  [./l2_error]
    type = ElementL2Error
    variable = u
    function = u_func
  [../]
  [./h1_error]
    type = ElementH1Error
    variable = u
    function = u_func
  [../]
[]

[Outputs]
  exodus = true
[]

Input Parameters

variableThe name of the variable that this side indicator applies to
C++ Type:VariableName
Options:
Description:The name of the variable that this side indicator applies to

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
scale_by_flux_facesFalseWhether or not to scale the error values by the number of flux faces. This attempts to not penalize elements on boundaries for having less neighbors.
Default:False
C++ Type:bool
Options:
Description:Whether or not to scale the error values by the number of flux faces. This attempts to not penalize elements on boundaries for having less neighbors.

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.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
outputsVector of output names were you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
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

Input Files

test/tests/indicators/laplacian_jump_indicator/biharmonic_transient.i
test/tests/indicators/laplacian_jump_indicator/biharmonic.i

test/tests/indicators/laplacian_jump_indicator/biharmonic_transient.i

[GlobalParams]
  # Parameters used by Functions.
  vars   = 'c'
  vals   = '50'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -.5
  xmax = .5
  ymin = -.5
  ymax = .5
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    order = THIRD
    family = HERMITE
  [../]
[]

[Kernels]
  [./biharmonic]
    type = Biharmonic
    variable = u
  [../]
  [./body_force]
    type = BodyForce
    variable = u
    function = forcing_func
  [../]
[]

[BCs]
  [./all_value]
    type = FunctionPenaltyDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = u_func
    penalty = 1e10
  [../]
  [./all_flux]
    type = FunctionPenaltyFluxBC
    variable = u
    boundary = 'left right top bottom'
    function = u_func
    penalty = 1e10
  [../]
[]

[Adaptivity]
  [./Indicators]
    [./error]
      type = LaplacianJumpIndicator
      variable = u
      scale_by_flux_faces = true
    [../]
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 4
  dt = 0.1

  # Note: the unusually tight tolerances here are due to the penalty
  # BCs (currently the only way of accurately Dirichlet boundary
  # conditions on Hermite elements in MOOSE).
  nl_rel_tol = 1.e-15
  l_tol = 1.e-15

  # We have exact Jacobians
  solve_type = 'NEWTON'

  # Use 6x6 quadrature to ensure the forcing function is integrated
  # accurately.
  [./Quadrature]
    type = GAUSS
    order = ELEVENTH
  [../]
[]

[Functions]
  [./u_func]
    type   = ParsedGradFunction
    value  = 'exp(-c*(x^2+y^2))*exp(-t)'
    grad_x = '-2*c*exp(-c*(x^2+y^2))*x*exp(-t)'
    grad_y = '-2*c*exp(-c*(x^2+y^2))*y*exp(-t)'
  [../]
  [./forcing_func]
    type   = ParsedFunction
    value  = '16*c^2*(c^2*(x^2+y^2)^2 - 4*c*(x^2+y^2) + 2)*exp(-c*(x^2+y^2))*exp(-t)'
  [../]
[]

[ICs]
  [./u_ic]
    type = FunctionIC
    function = u_func
    variable = u
  [../]
[]

[Postprocessors]
  [./l2_error]
    type = ElementL2Error
    variable = u
    function = u_func
  [../]
  [./h1_error]
    type = ElementH1Error
    variable = u
    function = u_func
  [../]
[]

[Outputs]
  exodus = true
[]

test/tests/indicators/laplacian_jump_indicator/biharmonic.i

[GlobalParams]
  # Parameters used by Functions.
  vars   = 'c'
  vals   = '50'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -.5
  xmax = .5
  ymin = -.5
  ymax = .5
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    order = THIRD
    family = HERMITE
  [../]
[]

[Kernels]
  [./biharmonic]
    type = Biharmonic
    variable = u
  [../]
  [./body_force]
    type = BodyForce
    variable = u
    function = forcing_func
  [../]
[]

[BCs]
  active = 'all_value all_flux'
  [./all_value]
    type = FunctionPenaltyDirichletBC
    variable = u
    boundary = 'left right top bottom'
    function = u_func
    penalty = 1e10
  [../]
  [./all_flux]
    type = FunctionPenaltyFluxBC
    variable = u
    boundary = 'left right top bottom'
    function = u_func
    penalty = 1e10
  [../]
  [./all_laplacian]
    type = BiharmonicLapBC
    variable = u
    boundary = 'left right top bottom'
    laplacian_function = lapu_func
  [../]
[]

[Adaptivity]
  [Indicators]
    [error]
      type = LaplacianJumpIndicator
      variable = u
      scale_by_flux_faces = true
    []
  []
[]

[Executioner]
  type = Steady

  # Note: the unusually tight tolerances here are due to the penalty
  # BCs (currently the only way of accurately Dirichlet boundary
  # conditions on Hermite elements in MOOSE).
  nl_rel_tol = 1.e-15
  l_tol = 1.e-15

  # We have exact Jacobians
  solve_type = 'NEWTON'

  # Use 6x6 quadrature to ensure the forcing function is integrated
  # accurately.
  [./Quadrature]
    type = GAUSS
    order = ELEVENTH
  [../]
[]

[Functions]
  [./u_func]
    type   = ParsedGradFunction
    value  = 'exp(-c*(x^2+y^2))'
    grad_x = '-2*c*exp(-c*(x^2+y^2))*x'
    grad_y = '-2*c*exp(-c*(x^2+y^2))*y'
  [../]
  [./lapu_func]
    type   = ParsedFunction
    value  = '4*c*(c*(x^2+y^2) - 1)*exp(-c*(x^2+y^2))'
  [../]
  [./forcing_func]
    type   = ParsedFunction
    value  = '16*c^2*(c^2*(x^2+y^2)^2 - 4*c*(x^2+y^2) + 2)*exp(-c*(x^2+y^2))'
  [../]
[]

[Postprocessors]
  [./l2_error]
    type = ElementL2Error
    variable = u
    function = u_func
  [../]
  [./h1_error]
    type = ElementH1Error
    variable = u
    function = u_func
  [../]
[]

[Outputs]
  exodus = true
[]

Description
Example Input File Syntax
Input Parameters
Input Files

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