FEMDocumentation`
FEMDocumentation`

InitializePDEMethodData

InitializePDEMethodData[vd,sd,m]

returns a method data object for the method specified by m according to variable data vd and solution data sd.

Details

  • InitializePDEMethodData initializes the PDE discretization method m.
  • InitializePDEMethodData computes and stores data such as geometry data.
  • The Automatic method for InitializePDEMethodData is the finite element method and the initialized data is returned as a FEMMethodData object.
  • Variable data vd and solution data sd are corresponding lists of variables and values. Templates for vd and sd may be generated using NDSolve`VariableData and NDSolve`SolutionData, and components may be set using NDSolve`SetSolutionDataComponent.
  • The "Space" component of vd and sd should be set to the spatial variables and the spatial mesh represented as an NumericalRegion object, respectively.
  • The "DependentVariables" component of vd should be set to the list of unknown function names without arguments.
  • For time-dependent problems, the "Time" component of vd and sd should be set to the temporal variable and the initial time, respectively.
  • In InitializePDEMethodData[vd,sd,m], the method m may be specified by mname or {mname,mopts}, where mname is the method name and mopts are method specific options. Currently only the "FiniteElement" method is supported.
  • InitializePDEMethodData[vd,sd] uses the "FiniteElement" method by default.
  • The "FiniteElement" method accepts the following options:
  • "IntegrationOrder"Automaticsets the element integration order
    "InterpolationOrder"Automaticsets the order of interpolation for each dependent variable
    "MeshOptions"Automaticspecifies options for mesh generation
    "PrecomputeGeometryData"Automaticprecomputes geometry data
  • With an ElementMesh having "MeshOrder" p, the "InterpolationOrder" can be at most p and "InterpolationOrder"->Automatic defaults to the order p. Multiple dependent variables may have a different interpolation order; at least one interpolation order needs to be set to the maximum mesh order p.
  • The "IntegrationOrder" is the order of accuracy used to integrate the finite element operators. For "InterpolationOrder"->2, the "IntegrationOrder" defaults to fourth order and for "InterpolationOrder"->1, the "IntegrationOrder" defaults to second order.
  • For the "FiniteElement" method, if the NumericalRegion does not contain an ElementMesh, then one is created automatically using ToElementMesh, with the options given in the setting of "MeshOptions".

Examples

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Basic Examples  (1)

Load the finite element package:

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Set up a NumericalRegion:

In[2]:=
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Out[2]=

Set up variable and solution data:

In[3]:=
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Initialize the partial differential equation data:

In[4]:=
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Out[4]=

Options  (5)

See Also

InitializePDECoefficients  InitializeBoundaryConditions  FEMMethodData  ToNumericalRegion  ToElementMesh

Tutorials