Regarding use of assempde in the following code.

I was trying to understand this code. So, I have noted down my understanding in brief and I'll be thankful if anyone could clarify my doubts.

[p,e,t] = initmesh('lshapeg'); This will return a 2D triangular mesh for 'L' shape. However, how can I change the boundary of L-shape? I mean the default L-shape is bounded between -1 to 1 on x and y axis. Also, are there other shapes like lshapeg...like say for a square?

[p,e,t] = refinemesh('lshapeg',p,e,t);

pdemesh(p,e,t)

The code says: Now solve Poisson's equation –Δu = 1 over the geometry defined by the L-shaped membrane. Use Dirichlet boundary conditions u = 0 on ∂Ω, and plot the result.

u = assempde('lshapeb',p,e,t,1,0,1);

Now here I could not understand the significance of 1, 0, 1. I know it is the c,a and f with regard to the given poisson equation. But I could not understand how are the Boundary conditions being applied, i.e. "Use Dirichlet boundary conditions u = 0 on ∂Ω, and plot the result"...How does this come into play? Also, what is the difference between lshapeb and lshapeg?

pdemesh(p,e,t,u)

Please help.

Answer 1

[Alan Weiss]

To create 2-D geometry, see the documentation.

The file lshapeb defines Dirichlet boundary conditions for the L-shaped region. To see how to specify boundary conditions, consult the documentation. lshapeb is a boundary function, which currently is not the simplest form of boundary conditions, but was the best choice prior to R2014a.

Alan Weiss

MATLAB mathematical toolbox documentation