Partial Differential Equation Toolbox

How Do I Define a PDE Problem?

The simplest way to define a PDE problem is using the GUI, implemented in pdetool. There are three modes that correspond to different stages of defining a PDE problem:

• In Draw mode, you create , the geometry, using the constructive solid geometry (CSG) model paradigm. A set of solid objects (rectangle, circle, ellipse, and polygon) is provided. You can combine these objects using set formulas.
• In Boundary mode, you specify the boundary conditions. You can have different types of boundary conditions on different boundary segments.
• In PDE mode, you interactively specify the type of PDE and the coefficients c, a, f, and d. You can specify the coefficients for each subdomain independently. This may ease the specification of, e.g., various material properties in a PDE model.

How Can I Solve a PDE Problem?

Most problems can be solved from the GUI. There are two major modes that help you solve a problem:

• In Mesh mode, you generate and plot meshes. You can control the parameters of the automated mesh generator.
• In Solve mode, you can invoke and control the nonlinear and adaptive solvers for elliptic problems. For parabolic and hyperbolic problems, you can specify the initial values, and the times for which the output should be generated. For the eigenvalue solver, you can specify the interval in which to search for eigenvalues.

After solving a problem, you can return to the Mesh mode to further refine your mesh and then solve again. You can also employ the adaptive mesh refiner and solver. This option tries to find a mesh that fits the solution.

Can I Use the Toolbox for Nonstandard Problems?

For advanced, nonstandard applications you can transfer the description of domains, boundary conditions etc. to your MATLAB workspace. From there you use the functions of the PDE Toolbox for managing data on unstructured meshes. You have full access to the mesh generators, FEM discretizations of the PDE and boundary conditions, interpolation functions, etc. You can design your own solvers or use FEM to solve subproblems of more complex algorithms. See also Using Command-Line Functions.

In Which Areas Can the Toolbox Be Used?

How Can I Visualize My Results?