Matlab: PDE toolbox, get length of each element on the boundary - matlab

Question

I setup and meshed a domain using Matlab's PDE toolbox. Along the boundary, is there someway to get the length of each element of the mesh? And the flux in the normal direction? (the bc are Dirichlet)
Edit:
See example code
RMax = 20;
RL = 1;
RU = 0.5;
HN = 5;
HL = 2;
HTT = 3;
HU = 1.5;
VL = -150;
p = [RL,0;RL,HN;0,HN+HL;0,HN+HL+HTT;RU,HN+HL+HTT+HU;RMax,HN+HL+HTT+HU;RMax,0];
t = [1;1;0;1;1;0;0];
v = [VL;VL;0;0;0;0;0];
dx = 0.5;
dy = 0.5;
bc = cell(size(t));
for i = 1:length(t)
if t(i) == 0
bc{i} = {'u', v(i)};
elseif t(i) == 1
bc{i} = {'g', v(i), 'q', 1};
else
error('Unrecognized boundary condition type.')
end
end
model = createpde;
gd = [2; size(p,1); p(:,1) ; p(:,2)];
ns = char('domain')';
sf = 'domain';
g = decsg(gd,sf,ns);
geometryFromEdges(model,g);
generateMesh(model, 'Hmax', min([dx,dy])/3, 'MesherVersion','R2013a');
for i = 1:size(bc,1)
applyBoundaryCondition(model, 'Edge', i, bc{i}{:});
end
u = assempde( model , 'x' , 0 , 0 );
pdemesh(model)
Edit: 2015-12-17 18:54 GMT
There are 2 points in the e shown at 1 and 2 in the figure below. I want to know the coordinate of 3 so I know which direction is into the domain.

Answer 1

You can answer your first question by using meshToPet to convert to [P,E,T] form:
[p,e,t] = meshToPet(model.Mesh);
x1 = p(1,e(1,:)); % x-coordinates of first point in each mesh edge
x2 = p(1,e(2,:)); % x-coordinates of second point in each mesh edge
y1 = p(2,e(1,:)); % y-coordinates of first point in each mesh edge
y2 = p(2,e(2,:)); % y-coordinates of second point in each mesh edge
% Plot first points of mesh edge
plot(x1,y1,'b.-',x1(1),y1(1),'go',x1(end),y1(end),'ro');
% Euclidean distance between first and second point in each edge
d = sqrt((x1-x2).^2+(y1-y2).^2);
I'm assuming you just want the lengths of the mesh edge/boundary. You can use similar methods to get the lengths of every single triangle using the t matrix.
As far as flux goes, there's pdecgrad. I think the following may work:
...
c = 'x';
u = assempde(model, c, 0, 0);
[p,e,t] = meshToPet(model.Mesh);
[cgxu,cgyu] = pdecgrad(p,t,c,u);