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Specify Boundary Conditions in the PDE Modeler App

Select Boundary Mode from the Boundary menu or click the rectangle with an arrow button. Then select a boundary or multiple boundaries for which you are specifying the conditions. Note that no if you do not select any boundaries, then the specified conditions apply to all boundaries.

  • To select a single boundary, click it using the left mouse button.

  • To select several boundaries and to deselect them, use Shift+click (or click using the middle mouse button).

  • To select all boundaries, use the Select All option from the Edit menu.

Select Specify Boundary Conditions from the Boundary menu.

Dialog box for specifying Neumann or Dirichlet boundary conditions

Specify Boundary Conditions opens a dialog box where 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 dialog box for the generic system PDE (Options > Application > Generic System).

Dialog box for specifying Neumann, Dirichlet, and mixed boundary conditions for a system of two equations. Listed coefficients are g1, g2, q11, q12, q21, q22, h11, h12, h21, h22, r1, and r2.

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.


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.