FEMDocumentation`
FEMDocumentation`

DiscretizePDE

DiscretizePDE[cdata,mdata,sd,dep]

discretizes the part with dependence dep of the PDE coefficient data cdata based on method data mdata and solution data sd to generate a DiscretizedPDEData object.

Details

  • DiscretizePDE returns a DiscretizedPDEData object.
  • The coefficient data cdata is a PDECoefficientData object generated by InitializePDECoefficients.
  • The method data mdata is a PDE method data object, such as FEMMethodData, generated through InitializePDEMethodData.
  • The dependence dep can be one of the following:
  • "Discrete"linear coefficients depending on discrete variables
    "IndexedDiscrete"linear coefficients depending on indexed discrete variables
    "Parametric"linear coefficients depending on parameters but not on time
    "Stationary"linear coefficients depending on spatial independent variables but not on time or parameters
    "Transient"
  • linear coefficients depending on time
  • DiscretizePDE[cdata,mdata,sd] is equivalent to DiscretizePDE[cdata,mdata,sd,"Stationary"].
  • 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 current integration time, respectively.
  • For time-dependent problems with discrete or indexed discrete variables that only change at discrete times during the time integration, the "Discrete" and/or "IndexedDiscrete" component of vd and sd should be set to the discrete variables and the initial discrete values, respectively.
  • For problems with parameters that do not change during the solution process, the "Parameters" component of vd and sd should be set to the parametric variables and the initial parametric values, respectively.
  • The following options can be given:
  • "AssembleSystemMatrices"Automaticwhether to assemble system matrices
    "PartialSystemMatricesAssembly"Automaticwhich parts of the system matrices to assemble
    "SaveFiniteElements"Falsewhether to save computed elements

Examples

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Basic Examples  (1)

Load the finite element package:

In[1]:=
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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 coefficients:

In[4]:=
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Discretize the initialized PDE coefficients based on method data and solution data:

In[5]:=
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Out[5]=

Scope  (2)

Options  (3)

Possible Issues  (1)

See Also

InitializePDEMethodData  FEMMethodData  InitializePDECoefficients  PDECoefficientData  DiscretizedPDEData  DeployBoundaryConditions  DiscretizeBoundaryConditions

Tutorials