Nodal Functions L2 Norm Postprocessor

Description

The NodalFunctionsL2NormPD Postprocessor calculates the L2 norm of a set of functions using the discrete summation formulation.

$var element = document.getElementById("moose-equation-349ca38d-29c1-4e6a-a4cb-d79deb2f245a");katex.render(" \\text{L2} = \\int_{\\Omega} {\\left| \\mathbf{f} \\right|} d{\\Omega} = \\sum V_{\\mathbf{X}} \\cdot {\\left| \\bar{\\mathbf{f}}_{\\mathbf{X}} \\right|}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-fc9539bb-2e78-42ad-9f88-e8a3e62693d9");katex.render("V_{\\mathbf{X}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the area or volume of material point $var element = document.getElementById("moose-equation-c0a8dcc5-5458-4237-9ac7-f2773fffd79e");katex.render("\\mathbf{X}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , and $var element = document.getElementById("moose-equation-9e0ba3c5-fb05-439b-bf9c-f344f3b78b58");katex.render("\\bar{\\mathbf{f}}_{\\mathbf{X}}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the evaluation of functions $var element = document.getElementById("moose-equation-8e1bf64e-95db-488a-947e-4c9df44ba03b");katex.render("\\mathbf{f}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ at material point $var element = document.getElementById("moose-equation-345df775-8242-498e-aefd-05a3d4ac6368");katex.render("\\mathbf{X}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ .

Input Parameters

functionsThe known functions
C++ Type:std::vector<FunctionName>
Options:
Description:The known functions

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector<SubdomainName>
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector<BoundaryName>
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, TRANSFER
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
unique_node_executeFalseWhen false (default), block restricted objects will have the execute method called multiple times on a single node if the node lies on a interface between two subdomains.
Default:False
C++ Type:bool
Options:
Description:When false (default), block restricted objects will have the execute method called multiple times on a single node if the node lies on a interface between two subdomains.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Options:
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
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<OutputName>
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
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

(modules/peridynamics/test/tests/simple_tests/2D_regularD_constH_BPD.i)

(modules/peridynamics/test/tests/simple_tests/2D_regularD_constH_BPD.i)

# Test for bond-based peridynamic formulation
# for regular grid from generated mesh with const bond constants

# Square plate with Dirichlet boundary conditions applied
# at the left, top and bottom edges

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  type = PeridynamicsMesh
  horizon_number = 3

  [./gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 4
  [../]
  [./gpd]
    type = MeshGeneratorPD
    input = gmg
    retain_fe_mesh = false
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[BCs]
  [./left_x]
    type = DirichletBC
    variable = disp_x
    boundary = 1003
    value = 0.0
  [../]
  [./top_y]
    type = DirichletBC
    variable = disp_y
    boundary = 1002
    value = 0.0
  [../]
  [./bottom_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 1000
    function = '-0.001*t'
  [../]
[]

[Modules/Peridynamics/Mechanics/Master]
  [./all]
    formulation = BOND
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 2e5
    poissons_ratio = 0.33
  [../]

  [./force_density]
    type = ComputeSmallStrainConstantHorizonMaterialBPD
  [../]
[]

[Functions]
  [./disp_x_anal]
    type = PiecewiseLinear
    axis = x
    x = '0 1'
    y = '0 -0.00033'
  [../]
  [./disp_y_anal]
    type = PiecewiseLinear
    axis = y
    x = '0 1'
    y = '-0.001 0'
  [../]
[]

[Postprocessors]
  [./anal_disp_L2]
    type = NodalFunctionsL2NormPD
    functions = 'disp_x_anal disp_y_anal'
  [../]
  [./disp_diff_L2]
    type = NodalDisplacementDifferenceL2NormPD
    analytic_functions = 'disp_x_anal disp_y_anal'
  [../]
[]

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

[Executioner]
  type = Transient
  solve_type = PJFNK
  line_search = none
  start_time = 0
  end_time = 1
[]

[Outputs]
  file_base = 2D_regularD_constH_BPD
  exodus = true
[]

Description
Input Parameters
Input Files

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