Partial Differential Equation Toolbox

The Application Modes and the GUI

The PDE Toolbox can be applied to a great number of problems in engineering and science. To help you in using the pdetool GUI for some important and common applications, eight different application modes are available in addition to the generic scalar and system modes.

The available application modes are

• Generic scalar (the default mode)
• Generic system
• Structural Mechanics -- Plane Stress
• Structural Mechanics -- Plane Strain
• Electrostatics
• Magnetostatics
• AC Power Electromagnetics
• Conductive Media DC
• Heat Transfer
• Diffusion

Note    From the GUI, the system PDEs are restricted to problems with vector valued u of dimension two. Using command-line functions, there is no formal restriction on the dimension of u.

The application mode can be selected directly from the pop-up menu in the upper right part of the GUI or by selecting an application from the Application submenu in the Options menu. Note that changing the application resets all PDE coefficients and boundary conditions to the default values for that specific application mode.

When using an application mode, the generic PDE coefficients are replaced by application-specific parameters such as Young's modulus for problems in structural mechanics. The application-specific parameters are entered by selecting Parameters . . . from the PDE menu or by clicking the PDE button. You can also access the PDE parameters by double-clicking a subdomain, if you are in the PDE mode. That way it is possible to define PDE parameters for problems with regions of different material properties. The Boundary condition dialog box is also altered so that the Description column reflects the physical meaning of the different boundary condition coefficients. Finally, the Plot Selection dialog box allows you to visualize the relevant physical variables for the selected application.

Note    In the User entry options in the Plot Selection dialog box, the solution and its derivatives are always referred to as u, ux, and uy (v, vx, and vy for the system cases) even if the application mode is nongeneric and the solution of the application-specific PDE normally is named, e.g., V or T.

In the remaining part of this section, we explain each of the application modes in more detail and give examples of how to solve application specific problems using the PDE Toolbox.

Application Modes

Structural Mechanics -- Plane Stress