Supporting documentation regarding PDE boundary files
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I am trying to solve a PDE on a square domain, and came across the boundary files squareb1,squareb2, etc. These are potentially useful to me, however I am not clear what boundary conditions each file gives. I want a file with Neumann conditions around each edge.
Thanks!
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Bill Greene
2013-8-16
Hi,
Your question is certainly a reasonable one. The boundary matrix format in those files is unquestionably difficult to decode.
I suggest an alternate approach instead of trying to decipher those example files. This example boundary file below will define a zero Neumann boundary condition on all edges of a model-- a square or something much more complicated.
function [ q, g, h, r ] = boundaryFileZeroNeumann( p, e, u, time )
% Define a zero Neumann condition on all edges
N = 1 % number of pde in the system
ne = size(e,2); % number of boundary edges
q = zeros(N^2, ne); % Neumann coefficient q is zero on all edges
g = zeros(N, ne); % Neumann coefficient g is zero on all edges
h = zeros(N^2, 2*ne); % Dirichlet h coefficient is zero at both ends of all edges
r = zeros(N,2*ne); % Dirichlet r coefficient is zero at both ends of all edges
end
The line N = 1 says that you have a single PDE (i.e. a scalar PDE) in your system. If you have more than one, you need to change this line. You can pass this function to assempde or the other high-level PDE Toolbox functions by defining
b = @boundaryFileZeroNeumann;
This function is a very simple boundary file example. You can easily generalize this to an arbitrary combination of Dirichlet and Neumann conditions. Take a look at this documentation page if you are interested in doing that.
Bill
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