FEMDocumentation`
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

• The coefficients are assumed to come from a second-order system of PDEs in space dimensions of the form:
• • In InitializePDECoefficients[vd,sd,rules], the rules should be of the form name->coefficient. The possible coefficient names are:
•  "LoadCoefficients" {{f1},{f2},…} is a scalar "LoadDerivativeCoefficients" {{γ1},{γ2},…} is a vector of length "DiffusionCoefficients" {{-c11,-c12,…},{-c21,-c22,…},…} may be specified as scalars, diagonal vectors of length , or × matrices "ConservativeConvectionCoefficients" {{-α11,-α12,…},{-α21,-α22,…},…} is a vector of length "ConvectionCoefficients" {{β11,β12,…},{β21,β22,…},…} is a vector of length "ReactionCoefficients" {{a11,a12,…},{a21,a22,…},…} is a scalar "DampingCoefficients" {{d11,d12,…},{d21,d22,…},…} is a scalar "MassCoefficients" {{m11,m12,…},{m21,m22,…},…} 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:
• • NDSolve reduces transient systems so that they are first order in time.
• The coefficients can be functions of space, time, parameters, dependent variables and first order derivatives of dependent variables.
• 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 nonlinear problems, the "DependentVariables" component of sd should be set to the initial seedings for the dependent variables.
• 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" Automatic specify PDE coefficient verification data

# Examples

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## Basic Examples(2)

 In:= Set up a NumericalRegion:

 In:= Out= Set up variable and solution data:

 In:= Convert a Laplace equation into coefficients:

 In:= Out= Convert a Poisson equation into coefficients:

 In:= Out= 