Solve Problems Using PDEModel Objects
Put your problem in the correct form for Partial Differential Equation Toolbox™ solvers. For details, see Equations You Can Solve Using PDE Toolbox. If you need to convert your problem to divergence form, see Put Equations in Divergence Form.
PDEModelmodel container. For scalar PDEs, use
createpdewith no arguments.
model = createpde();
If N is the number of equations in your system, use
createpdewith input argument
model = createpde(N);
Import or create the geometry. For details, see Geometry and Mesh.
importGeometry(model,"geometry.stl"); % importGeometry for 3-D geometryFromEdges(model,g); % geometryFromEdges for 2-D
View the geometry so that you know the labels of the boundaries.
pdegplot(model,"FaceLabels","on") % "FaceLabels" for 3-D pdegplot(model,"EdgeLabels","on") % "EdgeLabels" for 2-D
To see labels of a 3-D model, you might need to rotate the model, or make it transparent, or zoom in on it. See STL File Import.
Create the boundary conditions. For details, see Specify Boundary Conditions.
% "face" for 3-D applyBoundaryCondition(model,"dirichlet","face",[2,3,5],"u",[0,0]); % "edge" for 2-D applyBoundaryCondition(model,"neumann","edge",[1,4],"g",1,"q",eye(2));
Create the PDE coefficients.
f = [1;2]; a = 0; c = [1;3;5]; specifyCoefficients(model,"m",0,"d",0,"c",c,"a",a,"f",f);
You can specify coefficients as numeric or as functions.
f, has a specific format. See f Coefficient for specifyCoefficients, c Coefficient for specifyCoefficients, and m, d, or a Coefficient for specifyCoefficients.
For time-dependent equations, or optionally for nonlinear stationary equations, create an initial condition. See Set Initial Conditions.
Create the mesh.
Call the appropriate solver. For all problems except for eigenvalue problems, call
result = solvepde(model); % for stationary problems result = solvepde(model,tlist); % for time-dependent problems
For eigenvalue problems, use
result = solvepdeeig(model);
Examine the solution. See Solution and Gradient Plots with pdeplot and pdeplot3D, 2-D Solution and Gradient Plots with MATLAB Functions, and 3-D Solution and Gradient Plots with MATLAB Functions.