Boundary Mode | Enter the boundary mode. |
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 Subdomain 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 |
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:
$$\overrightarrow{n}\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\left(c\nabla u\right)+qu=g.$$
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).
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 t_{x} = –n_{y} and t_{y} = n_{x}.
The solution u
.
The time t
.
Note
If the boundary condition is a function of the solution |
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.