BicubicSplineFunction

construction:Undocumented Class

The BicubicSplineFunction has not been documented. The content listed below should be used as a starting point for documenting the class, which includes the typical automatic documentation associated with a MooseObject; however, what is contained is ultimately determined by what is necessary to make the documentation clear for users.


# BicubicSplineFunction

!syntax description /Functions/BicubicSplineFunction

## Overview

!! Replace these lines with information regarding the BicubicSplineFunction object.

## Example Input File Syntax

!! Describe and include an example of how to use the BicubicSplineFunction object.

!syntax parameters /Functions/BicubicSplineFunction

!syntax inputs /Functions/BicubicSplineFunction

!syntax children /Functions/BicubicSplineFunction

Define a bicubic spline function from interpolated data defined by input parameters.

Input Parameters

x1The first independent coordinate.
C++ Type:std::vector<double>
Options:
Description:The first independent coordinate.
x2The second independent coordinate.
C++ Type:std::vector<double>
Options:
Description:The second independent coordinate.
yThe dependent values
C++ Type:std::vector<double>
Options:
Description:The dependent values

Required Parameters

normal_componentzThe component of the geometry that is normal to the spline x1/x2 values
Default:z
C++ Type:MooseEnum
Options:x, y, z
Description:The component of the geometry that is normal to the spline x1/x2 values
yx11e30The functional form of the derivative with respect to x1.
Default:1e30
C++ Type:FunctionName
Options:
Description:The functional form of the derivative with respect to x1.
yx11The values of the derivative wrt x1 on the lower interpolation grid points.
C++ Type:std::vector<double>
Options:
Description:The values of the derivative wrt x1 on the lower interpolation grid points.
yx1nThe values of the derivative wrt x1 on the upper interpolation grid points.
C++ Type:std::vector<double>
Options:
Description:The values of the derivative wrt x1 on the upper interpolation grid points.
yx21e30The functional form of the derivative with respect to x2.
Default:1e30
C++ Type:FunctionName
Options:
Description:The functional form of the derivative with respect to x2.
yx21The values of the derivative wrt x2 on the lower interpolation grid points.
C++ Type:std::vector<double>
Options:
Description:The values of the derivative wrt x2 on the lower interpolation grid points.
yx2nThe values of the derivative wrt x2 on the upper interpolation grid points.
C++ Type:std::vector<double>
Options:
Description:The values of the derivative wrt x2 on the upper interpolation grid points.

Optional Parameters

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.

Advanced Parameters

Input Files

(test/tests/utils/spline_interpolation/bicubic_spline_interpolation_x_normal.i)
(test/tests/utils/spline_interpolation/bicubic_spline_interpolation.i)
(test/tests/utils/spline_interpolation/bicubic_spline_interpolation_y_normal.i)

(test/tests/utils/spline_interpolation/bicubic_spline_interpolation_x_normal.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1 # needed to ensure Z is the problem dimension
  ny = 4
  nz = 4
  ymax = 4
  zmax = 4
[]

[Functions]
  [./yx1]
    type = ParsedFunction
    value = '3*y^2'
  [../]
  [./yx2]
    type = ParsedFunction
    value = '6*z^2'
  [../]
  [./spline_fn]
    type = BicubicSplineFunction
    normal_component = 'x'
    x1 = '0 2 4'
    x2 = '0 2 4 6'
    y = '0 16 128 432 8 24 136 440 64 80 192 496'
    yx11 = '0 0 0 0'
    yx1n = '48 48 48 48'
    yx21 = '0 0 0'
    yx2n = '216 216 216'
    yx1 = 'yx1'
    yx2 = 'yx2'
  [../]
  [./u_func]
    type = ParsedFunction
    value = 'y^3 + 2*z^3'
  [../]
  [./u2_forcing_func]
    type = ParsedFunction
    value = '-6*y - 12*z'
  [../]
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./bi_func_value]
    order = FIRST
    family = LAGRANGE
  [../]
  [./y_deriv]
    order = FIRST
    family = LAGRANGE
  [../]
  [./z_deriv]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxKernels]
  [./bi_func_value]
    type = FunctionAux
    variable = bi_func_value
    function = spline_fn
  [../]
  [./deriv_1]
    type = FunctionDerivativeAux
    function = spline_fn
    variable = y_deriv
    component = y
  [../]
  [./deriv_2]
    type = FunctionDerivativeAux
    function = spline_fn
    variable = z_deriv
    component = z
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./body_force]
    type = BodyForce
    variable = u
    function = u2_forcing_func
  [../]
[]

[BCs]
  [./sides]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right front back'
    function = u_func
  [../]
[]

[Postprocessors]
  [./nodal_l2_err_spline]
    type = NodalL2Error
    variable = u
    function = spline_fn
    execute_on = 'initial timestep_end'
  [../]
  [./nodal_l2_err_analytic]
    type = NodalL2Error
    variable = u
    function = u_func
    execute_on = 'initial timestep_end'
  [../]
  [./y_deriv_err_analytic]
    type = NodalL2Error
    variable = y_deriv
    function = yx1
    execute_on = 'initial timestep_end'
  [../]
  [./z_deriv_err_analytic]
    type = NodalL2Error
    variable = z_deriv
    function = yx2
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(test/tests/utils/spline_interpolation/bicubic_spline_interpolation.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nz = 1
  nx = 4
  ny = 4
  xmax = 4
  ymax = 4
[]

[Functions]
  [./yx1]
    type = ParsedFunction
    value = '3*x^2'
  [../]
  [./yx2]
    type = ParsedFunction
    value = '6*y^2'
  [../]
  [./spline_fn]
    type = BicubicSplineFunction
    x1 = '0 2 4'
    x2 = '0 2 4 6'
    y = '0 16 128 432 8 24 136 440 64 80 192 496'
    yx11 = '0 0 0 0'
    yx1n = '48 48 48 48'
    yx21 = '0 0 0'
    yx2n = '216 216 216'
    yx1 = 'yx1'
    yx2 = 'yx2'
  [../]
  [./u_func]
    type = ParsedFunction
    value = 'x^3 + 2*y^3'
  [../]
  [./u2_forcing_func]
    type = ParsedFunction
    value = '-6*x - 12*y'
  [../]
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./bi_func_value]
    order = FIRST
    family = LAGRANGE
  [../]
  [./x_deriv]
    order = FIRST
    family = LAGRANGE
  [../]
  [./y_deriv]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxKernels]
  [./bi_func_value]
    type = FunctionAux
    variable = bi_func_value
    function = spline_fn
  [../]
  [./deriv_1]
    type = FunctionDerivativeAux
    function = spline_fn
    variable = x_deriv
    component = x
  [../]
  [./deriv_2]
    type = FunctionDerivativeAux
    function = spline_fn
    variable = y_deriv
    component = y
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./body_force]
    type = BodyForce
    variable = u
    function = u2_forcing_func
  [../]
[]

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

[Postprocessors]
  [./nodal_l2_err_spline]
    type = NodalL2Error
    variable = u
    function = spline_fn
    execute_on = 'initial timestep_end'
  [../]
  [./nodal_l2_err_analytic]
    type = NodalL2Error
    variable = u
    function = u_func
    execute_on = 'initial timestep_end'
  [../]
  [./x_deriv_err_analytic]
    type = NodalL2Error
    variable = x_deriv
    function = yx1
    execute_on = 'initial timestep_end'
  [../]
  [./y_deriv_err_analytic]
    type = NodalL2Error
    variable = y_deriv
    function = yx2
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
[]

(test/tests/utils/spline_interpolation/bicubic_spline_interpolation_y_normal.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  ny = 1 # needed to ensure Z is the problem dimension
  nx = 4
  nz = 4
  xmax = 4
  zmax = 4
[]

[Functions]
  [./yx1]
    type = ParsedFunction
    value = '3*z^2'
  [../]
  [./yx2]
    type = ParsedFunction
    value = '6*x^2'
  [../]
  [./spline_fn]
    type = BicubicSplineFunction
    normal_component = y
    x1 = '0 2 4'
    x2 = '0 2 4 6'
    y = '0 16 128 432 8 24 136 440 64 80 192 496'
    yx11 = '0 0 0 0'
    yx1n = '48 48 48 48'
    yx21 = '0 0 0'
    yx2n = '216 216 216'
    yx1 = 'yx1'
    yx2 = 'yx2'
  [../]
  [./u_func]
    type = ParsedFunction
    value = 'z^3 + 2*x^3'
  [../]
  [./u2_forcing_func]
    type = ParsedFunction
    value = '-6*z - 12*x'
  [../]
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./bi_func_value]
    order = FIRST
    family = LAGRANGE
  [../]
  [./x_deriv]
    order = FIRST
    family = LAGRANGE
  [../]
  [./z_deriv]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxKernels]
  [./bi_func_value]
    type = FunctionAux
    variable = bi_func_value
    function = spline_fn
  [../]
  [./deriv_1]
    type = FunctionDerivativeAux
    function = spline_fn
    variable = z_deriv
    component = z
  [../]
  [./deriv_2]
    type = FunctionDerivativeAux
    function = spline_fn
    variable = x_deriv
    component = x
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./body_force]
    type = BodyForce
    variable = u
    function = u2_forcing_func
  [../]
[]

[BCs]
  [./sides]
    type = FunctionDirichletBC
    variable = u
    boundary = 'left right front back'
    function = u_func
  [../]
[]

[Postprocessors]
  [./nodal_l2_err_spline]
    type = NodalL2Error
    variable = u
    function = spline_fn
    execute_on = 'initial timestep_end'
  [../]
  [./nodal_l2_err_analytic]
    type = NodalL2Error
    variable = u
    function = u_func
    execute_on = 'initial timestep_end'
  [../]
  [./x_deriv_err_analytic]
    type = NodalL2Error
    variable = x_deriv
    function = yx2
    execute_on = 'initial timestep_end'
  [../]
  [./z_deriv_err_analytic]
    type = NodalL2Error
    variable = z_deriv
    function = yx1
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

Input Parameters
Input Files

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