h-Adaptivity

  • $$$h$$$-adaptivity is a method of automatically refining/coarsening the mesh in regions of high/low estimated solution error.
  • The idea is to concentrate degrees of freedom (DOFs) where the error is highest, while reducing DOFs where the solution is already well-captured.
  • This is achieved through splitting and joining elements from the original mesh based on an error Indicator.
  • Once an error Indicator has been computed, a Marker is used to decide which cells to refine and coarsen.
  • Mesh adaptivity can be employed in both Steady and Transient Executioners.

Refinement Patterns

  • MOOSE employs "self-similar", isotropic refinement patterns.
  • When an element is marked for refinement, it is split into elements of the same type.
  • For example, when using Quad4 elements, four "child" elements are created when the element is refined.
  • Coarsening happens in reverse, children are deleted and the "parent" element is reactivated.
  • The original mesh starts at refinement level 0.
  • Each time an element is split, the children are assigned a refinement level one higher than their parents.

element_adaptivity.png

Indicators

  • Indicators attempt to report a relative amount of "error" for each element.
  • Built-in Indicators include:
Indicator Description
GradientJumpIndicator Jump in the gradient of a variable across element edges (pictured to the right). A good "curvature" indicator that works well over a wide range of problems.
FluxJumpIndicator Similar to GradientJump, except that a scalar coefficient (e.g. thermal conductivity) can be provided to produce a physical "flux" quantity.
LaplacianJumpIndicator Jump in the second derivative of a variable. Only useful for $$$C^1$$$ shape functions.
AnalyticIndicator Computes the difference between the finite element solution and a user-supplied Function representing the analytic solution to the problem.

  • In higher dimensions, the gradient jump is integrated around element edges to find contributions to each connected element.

kelly.png

Markers

  • After an Indicator has computed the error for each element, a decision to refine or coarsen elements must be made.
  • The Marker class is used for this purpose. Built-in Markers include:
Marker Description
ErrorFractionMarker Selects elements based on their contribution to the total error (see Figure).
ErrorToleranceMaker Refine if error is greater than a specified value. Coarsen if less than.
ValueThresholdMarker Refine if variable value is greater than a specific value. Coarsen if less than.
UniformMarker Refine or coarsen all elements.
BoxMarker Refine or coarsen inside or outside a given box.
ComboMarker Combine several of the above Markers.

  • Markers produce an element field that can be viewed in your visualization utility.
  • Custom Markers are easy to create by inheriting from the Marker base class.

percent_of_error.png

Input File Syntax

  • To enable adaptivity, add an Adaptivity block to the input file.
  • The Adaptivity block has several parameters:
    • marker: (Optional) Name of the Marker to use. If not set, no mesh adaptivity will be done.
    • steps: Number of refinement steps to do in a steady state calculation. Ignored by Transient executioners.
  • Adaptivity has two sub-blocks: Indicators and Markers. Within these blocks, you can specify multiple Indicator and Marker objects that will be active in the simulation.

[Adaptivity]
  marker = errorfrac
  steps = 2

  [./Indicators]
    [./error]
      type = GradientJumpIndicator
      variable = convected
    [../]
  [../]

  [./Markers]
    [./errorfrac]
      type = ErrorFractionMarker
      refine = 0.5
      coarsen = 0
      indicator = error
    [../]
  [../]
[]

Example 5

Look at Example 5