Partial Differential Equation Toolbox |

Boundary Menu

Boundary Mode | Enter the boundary mode.
Specify Boundary Conditions . . . | Specify boundary conditions for the selected boundaries. If no boundaries are selected, the entered boundary condition applies to all boundaries.
Show Edge Labels | Toggle the labeling of the edges (outer boundaries and subdomain borders) on/off. The edges are labeled using the column number in the Decomposed Geometry matrix.
Show Subdomains Labels | Toggle the labeling of the subdomains on/off. The subdomains are labeled using the subdomain numbering in the Decomposed Geometry matrix.
Remove Subdomain Border | Remove selected subdomain borders.
Remove All Subdomain Borders | Remove all subdomain borders.
Export Decomposed Geometry, Boundary Cond's . . . | Export the Decomposed Geometry matrix `g` and the Boundary Condition matrix `b` to the main workspace.

Specify Boundary Conditions . . .

Specify boundary conditions . . . displays a dialog box in which you can specify the boundary condition for the selected boundary segments. There are three different condition types:

- Generalized Neumann conditions, where the boundary condition is determined by the coefficients `q` and `g` according to the following equation:

- In the system cases, `q` is a 2-by-2 matrix and `g` is a 2-by-1 vector.

- Dirichlet conditions: u is specified on the boundary. The boundary condition equation is hu = r, where h is a weight factor that can be applied (normally 1).

- In the system cases, `h` is a 2-by-2 matrix and `r` is a 2-by-1 vector.

- Mixed boundary conditions (system cases only), which is a mix of Dirichlet and Neumann conditions. `q` is a 2-by-2 matrix, `g` is a 2-by-1 vector, `h` is a 1-by-2 vector, and `r` is a scalar.

The following figure shows the boundary condition dialog box for the generic system PDE.

For boundary condition entries you can use the following variables in a valid MATLAB expression:

- The 2-D coordinates `x` and `y`.
- A boundary segment parameter `s`, proportional to arc length. `s` is 0 at the start of the boundary segment and increases to 1 along the boundary segment in the direction indicated by the arrow.
- The outward normal vector components `nx` and `ny`. If you need the tangential vector, it can be expressed using `nx` and `ny` since tx = -ny and ty = nx.
- The solution `u`.
- The time `t`.

Note If the boundary condition is a function of the solution u, you must use the nonlinear solver. If the boundary condition is a function of the time t, you must choose a parabolic or hyperbolic PDE.

Examples: `(100-80*s).*nx`, and `cos(x.^2)`

In the nongeneric application modes, the Description column contains descriptions of the physical interpretation of the boundary condition parameters.

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