SolutionChangeNormFixedPoint

Computes the L2 norm of the change in a variable between consecutive fixed-point (Picard) iterations:

$var element = document.getElementById("moose-equation-4f7297d8-517b-4c9f-aecb-d3b1e3f23c8e");katex.render(" \\| d^{(k)} - d^{(k-1)} \\|_2 = \\sqrt{\\int_\\Omega \\left( d^{(k)} - d^{(k-1)} \\right)^2 \\, \\mathrm{d}V}", element, {displayMode:true,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left< I \\right>}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$

Intended for use as a staggered-scheme convergence criterion in conjunction with PostprocessorConvergence and the multiapp_fixed_point_convergence Executioner parameter.

Usage

The postprocessor defaults to execute_on = MULTIAPP_FIXED_POINT_CONVERGENCE, which causes it to evaluate after each sub-app solve and transfer but before the convergence decision is made.

note

When using this postprocessor with PostprocessorConvergence, the parameters max_iterations and converge_at_max_iterations belong to the [Convergence] block, not the [Executioner] block.

Example Input File Syntax


[AuxVariables]
  [d]
  []
[]

[Postprocessors]
  [d_fp_change]
    type = SolutionChangeNormFixedPoint
    variable = d
  []
[]

[Convergence]
  [fp_conv]
    type = PostprocessorConvergence
    postprocessor = d_fp_change
    tolerance = 1e-4
    max_iterations = 20
    converge_at_max_iterations = false
  []
[]

[Executioner]
  type = Transient
  multiapp_fixed_point_convergence = fp_conv
[]

Input Files

(test/tests/postprocessors/solution_change_norm_fp/main.i)

(test/tests/postprocessors/solution_change_norm_fp/main.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  []
[]

[Variables]
  [u]
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
[]

[BCs]
  [fix]
    type = DirichletBC
    variable = u
    boundary = 'left right top bottom'
    value = 0
  []
[]

[AuxVariables]
  [d]
  []
[]

[MultiApps]
  [fracture]
    type = TransientMultiApp
    input_files = sub.i
    execute_on = 'TIMESTEP_END'
  []
[]

[Transfers]
  [from_d]
    type = MultiAppCopyTransfer
    from_multi_app = fracture
    variable = d
    source_variable = d
  []
[]

[Postprocessors]
  [d_fp_change]
    type = SolutionChangeNormFixedPoint
    variable = d
  []
[]

[Convergence]
  [fp_conv]
    type = PostprocessorConvergence
    postprocessor = d_fp_change
    tolerance = 1e-8
    max_iterations = 1
    converge_at_max_iterations = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  num_steps = 2
  dt = 1
  multiapp_fixed_point_convergence = fp_conv
[]

[Outputs]
  csv = true
[]