PDEModel

PDE model object

Description

A PDEModel object contains information about a PDE problem: the number of equations, geometry, mesh, and boundary conditions.

Creation

Create a PDEModel object using createpde. Initially, the only nonempty property is PDESystemSize. It is 1 for scalar problems.

Properties

PDESystemSize — Number of equations

1 (default) | positive integer

Number of equations, N, specified as a positive integer. See Equations You Can Solve Using Partial Differential Equation Toolbox.

Example: 1

Data Types: double

BoundaryConditions — PDE boundary conditions

vector of BoundaryCondition objects

PDE boundary conditions, specified as a vector of BoundaryCondition Properties objects. You create boundary conditions using the applyBoundaryCondition function

Geometry — Geometry description

AnalyticGeometry | DiscreteGeometry

Geometry description, specified as AnalyticGeometry for a 2-D geometry or DiscreteGeometry for a 2-D or 3-D geometry.

Mesh — Mesh for solution

FEMesh object

Mesh for solution, specified as an FEMesh object. You create the mesh using the generateMesh function.

IsTimeDependent — Indicator if model is time-dependent

0 (false) (default) | 1 (true)

Indicator if model is time-dependent, specified as 1 (true) or 0 (false). The property is true when the m or d coefficient is nonzero, and is false otherwise.

EquationCoefficients — PDE coefficients

vector of CoefficientAssignment objects

PDE coefficients, specified as a vector of CoefficientAssignment Properties objects. See specifyCoefficients.

InitialConditions — Initial conditions or initial solution

GeometricInitialConditions object | NodalInitialConditions object

Initial conditions or initial solution, specified as a GeometricInitialConditions Properties or NodalInitialConditions Properties object.

In case of GeometricInitialConditions, for time-dependent problems, you must give one or two initial conditions: one if the m coefficient is zero, and two if the m coefficient is nonzero. For nonlinear stationary problems, you can optionally give an initial solution that solvepde uses to start its iterations. See setInitialConditions.

In case of NodalInitialConditions, you use the results of previous analysis to set the initial conditions or initial guess. The geometry and mesh of the previous analysis and current model must be the same.

SolverOptions — Algorithm options for PDE solvers

PDESolverOptions object

Algorithm options for the PDE solvers, specified as a PDESolverOptions Properties object. The properties of PDESolverOptions include absolute and relative tolerances for internal ODE solvers, maximum solver iterations, and so on.

Object Functions

applyBoundaryCondition	Add boundary condition to PDEModel container
generateMesh	Create triangular or tetrahedral mesh
geometryFromEdges	Create 2-D geometry from decomposed geometry matrix
geometryFromMesh	Create 2-D or 3-D geometry from mesh
importGeometry	Import geometry from STL or STEP file
setInitialConditions	Give initial conditions or initial solution
specifyCoefficients	Specify coefficients in PDE model
solvepde	Solve PDE specified in a PDEModel
solvepdeeig	Solve PDE eigenvalue problem specified in a PDEModel

Examples

Create and Populate a PDE Model

Create and populate a PDEModel object.

Create a container for a scalar PDE (N = 1).

model = createpde()

model = 
  PDEModel with properties:

           PDESystemSize: 1
         IsTimeDependent: 0
                Geometry: []
    EquationCoefficients: []
      BoundaryConditions: []
       InitialConditions: []
                    Mesh: []
           SolverOptions: [1×1 pde.PDESolverOptions]

Include a torus geometry, zero Dirichlet boundary conditions, coefficients for Poisson's equation, and the default mesh.

importGeometry(model,"Torus.stl");
applyBoundaryCondition(model,"dirichlet","Face",1,"u",0);
specifyCoefficients(model,"m",0,...
                          "d",0,...
                          "c",1,...
                          "a",0,...
                          "f",1);
generateMesh(model);

Solve the PDE.

results = solvepde(model)

results = 
  StationaryResults with properties:

    NodalSolution: [13475×1 double]
       XGradients: [13475×1 double]
       YGradients: [13475×1 double]
       ZGradients: [13475×1 double]
             Mesh: [1×1 FEMesh]

Version History

Introduced in R2015a