| Partial Differential Equation Toolbox |
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The GUI Modes
The PDE solving process can be divided into several steps:
- Define the geometry (2-D domain).
- Define the boundary conditions.
- Define the PDE.
- Create the triangular mesh.
- Solve the PDE.
- Plot the solution and other physical properties calculated from the solution (post processing).
The pdetool GUI is designed in a similar way. You work in six different modes, each corresponding to one of the steps in the PDE solving process:
- In Draw mode, you can create the 2-D geometry using the constructive solid geometry (CSG) model paradigm. A set of solid objects (rectangle, circle, ellipse, and polygon) is provided. These objects can be combined using set formulas in a flexible way.
- In Boundary mode, you can specify the boundary conditions. You can have different types of boundary conditions on different boundaries. In this mode, the original shapes of the solid objects constitute borders between subdomains of the model. Such borders can be eliminated in this mode.
- In PDE mode, you can interactively specify the type of PDE problem, and the PDE coefficients. You can specify the coefficients for each subdomain independently. This makes it easy to specify, e.g., various material properties in a PDE model.
- In Mesh mode, you can control the automated mesh generation and plot the mesh.
- In Solve mode, you can invoke and control the nonlinear and adaptive solver for elliptic problems. For parabolic and hyperbolic PDE 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.
- In Plot mode there is wide range of visualization possibilities. You can visualize both in the
pdetool GUI and in a separate figure window. You can visualize three different solution properties at the same time, using color, height, and vector field plots. There are surface, mesh, contour, and arrow (quiver) plots available. For parabolic and hyperbolic equations, you can animate the solution as it changes with time.
| | The Toolbar | | The CSG Model and the Set Formula | |