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FEMDocumentation`

InitializePDECoefficients

InitializePDECoefficients[vd,sd,rules]

initializes the coefficients specified by rules in accordance with variable data vd and solution data sd to generate a PDECoefficientData object.

Details and OptionsDetails
  • The coefficients are assumed to come from a second-order system of PDEs in space dimensions of the form:
  • sum_(j=1)^idel .(-c_(1j)del u_j+alpha_(1j)u_j-gamma_(1))+beta_(1j)del u_j+a_(1j)u_j-f_1=0 ; ... ; sum_(j=1)^idel .(-c_(ij)del u_j+alpha_(ij)u_j-gamma_(i))+beta_(ij)del u_j+a_(ij)u_j-f_i=0
  • In InitializePDECoefficients[vd,sd,rules], the rules should be of the form name->coefficient. The possible coefficient names are:
  • "LoadCoefficients"{{f1},{f2},}f_(i) is a scalar
    "LoadDerivativeCoefficients"{{γ1},{γ2},}gamma_(i) is a vector of length n
    "DiffusionCoefficients"{{c11,c12,},{c21,c22,},}c_(ij) may be specified as scalars, diagonal vectors of length n, or nxn matrices
    "ConservativeConvectionCoefficients"{{α11,α12,},{α21,α22,},}alpha_(ij) is a vector of length n
    "ConvectionCoefficients"{{β11,β12,},{β21,β22,},}beta_(ij) is a vector of length n
    "ReactionCoefficients"{{a11,a12,},{a21,a22,},}a_(ij) is a scalar
    "DampingCoefficients"{{d11,d12,},{d21,d22,},}d_(ij) is a scalar
    "MassCoefficients"{{m11,m12,},{m21,m22,},}m_(ij) is a scalar
  • If a rule is not specified for any of these coefficient names, the coefficients of that type are all assumed to be 0.
  • Transient system of PDEs may be specified up through second order based on the form:
  • sum_(j=1)^ipartial_(tt)m_(1j)u_j+partial_td_(1j)u_j+del .(c_(1j)del u_j-alpha_(1j)u_j+gamma_(1))+beta_(1j)del u_j+a_(1j)u_j-f_1=0 ; ...
  • NDSolve reduces transient systems so that they are first order in time.
  • The coefficients can be functions of space, time, and parameters.
  • 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.
  • InitializePDECoefficients verifies and optimizes the coefficients in accordance with variable data vd and solution data sd.
  • The "Space" component of vd and sd should be set to the spatial variables and the spatial mesh represented as a NumericalRegion object, respectively.
  • The "DependentVariables" component of vd should be a list of dependent variable name symbols 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.
  • For parametric problems, the "Parameters" component of vd and sd should be set to the parametric variables and the initial parametric values, respectively.
  • InitializePDECoefficients has the following options:
  • "VerificationData"Automaticspecify PDE coefficient verification data
  • Examples

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    Basic Examples  (2)

    Load the finite element package:

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    Set up a NumericalRegion:

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    Set up variable and solution data:

    In[3]:=
    Click for copyable input

    Convert a Laplace equation into coefficients:

    In[4]:=
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    Convert a Poisson equation into coefficients:

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    Scope  (5)

    Options  (1)

    Applications  (1)

    Possible Issues  (1)

    See Also

    PDECoefficientData  InitializePDEMethodData  InitializeBoundaryConditions  DiscretizePDE  DeployBoundaryConditions  ToNumericalRegion  ToElementMesh  Laplacian  D

    Tutorials