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NDSolve`FEM`

NDSolve`FEM`

PDESolve

PDESolve[cdata,bcdata,vd,sd,mdata]

solves a PDE based on coefficient data cdata, boundary condition data bcdata, variable data vd, solution data sd and method data mdata to return new solution data.

Details and Options

PDESolve solves linear and nonlinear stationary partial differential equations.
PDESolve returns a list that is the solution data.
The coefficient data cdata is a PDECoefficientData object generated by InitializePDECoefficients.
The boundary condition data bcdata is a BoundaryConditionData object generated by InitializeBoundaryConditions.
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 method data mdata is a PDE method data object, such as FEMMethodData, generated through InitializePDEMethodData.
PDESolve takes the following options:
"FindRootOptions" Automatic specify options for FindRoot

"LinearSolver" Automatic specify a linear solver and options for it
Options given to PDESolve can be given to NDSolve by specifying "PDESolveOptions". »
Setting the option from NDSolve and related functions is explained in NDSolve Finite Element Options.

Examples

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Basic Examples (3)

Load the finite element package:

Set up a NumericalRegion:

Set up variable and solution data:

Initialize the partial differential equation data:

Set up the solution of the linear PDE . Initialize the linear coefficients:

Initialize the linear boundary condition data:

Solve the PDE:

Post-process the PDE:

Set up the solution of the nonlinear PDE . Initialize the nonlinear coefficients:

Initialize nonlinear boundary condition data:

Specify an initial guess:

Solve the nonlinear PDE:

Post-process the PDE:

Options (8)

"FindRootOptions" (5)

Inspect the number of function calls, steps and Jacobian evaluations needed:

Specify that PDESolve is to use the default FindRoot root-finding algorithm:

Specify that PDESolve is to use the default affine covariant Newton method:

Set up PDESolve to not use Broyden updates:

Set a PrecisionGoal for the default PDESolve FindRoot method:

"LinearSolver" (3)

Specify PDESolve to use a direct method for LinearSolve:

Specify PDESolve to use a Krylov method for LinearSolve:

Specify PDESolve to use a customer function for LinearSolve:

Properties & Relations (1)

Options given to PDESolve can be given to NDSolve by specifying "PDESolveOptions":

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