Is there a way to import 2D meshes (nodes and triangles) into PDE model objects?

I am using the PDE toolbox to calculate coupled structural and acoustical problems. For 3D geometries it is possible to import a tetraeder mesh into the model by using the Matlab function

geometryFromMesh

I could not find a similar function for 2D geometry and the properties

model.Mesh.Nodes

and

model.Mesh.Elements

are read-only. I need such a function because I want to do the meshing outside the PDE toolbox. Is there a way to import my own 2D-mesh into the PDE model objects?

Regards Benjamin

Answer 1

[Alan Weiss]

There is currently no functionality for creating geometry from a 2-D mesh. Sorry.

You might be able to use legacy functions to solve a PDE using a [p,e,t] mesh. You'll have to figure out how to specify coefficients and boundary conditions. For example, use a boundary matrix (very difficult) as sketched in the legacy assemb function reference page. Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Benjamin Becker]

Thank's for the quick answer. I found an unsupported way of importing the 2D mesh by using

assoc = pde.FEMeshAssociation(t, e);
model.Mesh = pde.FEMesh(p, t, Hmax, Hmin, geomorder,assoc)
pde.FEMesh(nodes,tet,Hmax,Hmin, geomOrder,assoc);

where p, e, t are the mesh in the format used in the legacy workflow. Hmax and Hmin are the maximum and minimum lengths of the triangles' edges. This is more a hack than a solution but it seems to work.

[Alan Weiss]

Wow, I had no idea that functionality existed.

Alan Weiss

MATLAB mathematical toolbox documentation

[Benjamin Becker]

I found it by looking at the original code in the toolbox function generateMesh. I was lucky to find that the source code can be viewed. Here is an example of what I wanted to do:

[Kaveh Gharibi]

Thank you so much, it was really helpful! I wish I found this earlier.

[Manula]

Hi Benjamin, I need fine mesh on one of the boundary of a rectangular domain and not in the whole rectangle.How can I do that ? How did you able to change the source code of generateMesh. Any help would be appreciated.

[Kaveh Gharibi]

Hi, So this is what I do, First create a structured triangular mesh in another software (Patran-Nastran), Then I convert it to matlab’s mesh format (p,e,t).

The code is as follows.

if true
  % code
bdffile=‘mesh8.txt'  % cantaleaver
[nodeData,elemData] = elemnodeDatatria6(bdffile);
p=(nodeData(:,2:3))' ;
t=[(elemData(:,2:7)) ,ones(size(elemData,1),1)]'; 
figure(201)
plot(p(1,:),p(2,:),'.')
hold on 
[k,v] = boundary(p',0);
plot(p(1,k(:)),p(2,k(:)),'o')
hold on
xb=p(1,k(:)) ;
yb=p(2,k(:));
dl=xb(3)-xb(1)
Hmax=dl
Hmin=dl
R  = [3,6,0,0,2,2,2,2,0.5,-0.5,-0.5,-.05,.05, 0.5]';      % Cantaleaver 
gm = [R];
for i=1:size(R,2)
  str{i}  =  ( sprintf('R%d',i) );
end
sf=[];
for i=1:size(R,2)
  sf=char([str{i},'+',sf]);
end
sf=sf(1:end-1);
delete(model.Geometry)
model.Geometry = [];
ns = char(str);
ns = ns';
g=  decsg(gm,sf,ns);
geometryFromEdges(model,g);
figure
pdegplot(model,'EdgeLabels','on');
order='quadratic';
xmax=max(xb);
xmin=min(xb) ;
ymax=max(yb);
ymin=min(yb) ;
nx=(xmax-xmin)/abs(p(1,2)-p(1,1));
ny=(ymax-ymin)/abs(p(1,2)-p(1,1));
edge2=k(1:nx+1);
edge4=k(nx+1:nx+ny/2-1);
edge5=k(nx+ny/2-1:nx+ny/2+3);
edge6=k(nx+ny/2+3:nx+ny+1 );
edge3=k(nx+ny+1:2*nx+ny+1 );
edge1=k(2*nx+ny+1:2*nx+2*ny+1 );
E2s=(p(1,edge2(1:end-1))-p(1,edge2(1)))/(p(1,edge2(end))-p(1,edge2(1)));
E2e=(p(1,edge2(2:end))-p(1,edge2(1)))/(p(1,edge2(end))-p(1,edge2(1)));
E4s=(p(2,edge4(1:end-1))-p(2,edge4(1)))/(p(2,edge4(end))-p(2,edge4(1)));
E4e=(p(2,edge4(2:end))-p(2,edge4(1)))/ (p(2,edge4(end))-p(2,edge4(1)));
E5s=(p(2,edge5(1:end-1))-p(2,edge5(1)))/(p(2,edge5(end))-p(2,edge5(1)));
E5e=(p(2,edge5(2:end))-p(2,edge5(1)))/ (p(2,edge5(end))-p(2,edge5(1)));
E6s=(p(2,edge6(1:end-1))-p(2,edge6(1)))/(p(2,edge6(end))-p(2,edge6(1)));
E6e=(p(2,edge6(2:end))-p(2,edge6(1)))/ (p(2,edge6(end))-p(2,edge6(1)));  
E3s=(p(1,edge3(1:end-1))-p(1,edge3(1)))/(p(1,edge3(end))-p(1,edge3(1)));
E3e=(p(1,edge3(2:end))-p(1,edge3(1)))/(p(1,edge3(end))-p(1,edge3(1)));
E1s=(p(2,edge1(1:end-1))-p(2,edge1(1)))/(p(2,edge1(end))-p(2,edge1(1)));
E1e=(p(2,edge1(2:end))-p(2,edge1(1)))/ (p(2,edge1(end))-p(2,edge1(1))) ;
e(1,:)=[edge1(1:end-1)',edge2(1:end-1)',edge3(1:end-1)',edge4(1:end-1)',edge5(1:end-1)',edge6(1:end-1)'];
e(2,:)=[edge1(2:end)'  ,edge2(2:end)'  ,edge3(2:end)'  ,edge4(2:end)'  ,edge5(2:end)'  ,edge6(2:end)'];
e(3,:)=[E1s,E2s,E3s,E4s,E5s,E6s];
e(4,:)=[E1e,E2e,E3e,E4e,E5e,E6e];
e(5,:)=[1*ones( size(E1s)),2*ones(size(E2s)),3*ones(size(E3s)),4*ones(size(E4s)),5*ones(size(E5s)),6*ones(size(E6s))];
e(6,:)=ones(size(e(5,:)));
e(7,:)=zeros(size(e(5,:)));
whos t;
t=double(t);
assoc = pde.FEMeshAssociation(t, e);
model.Mesh = pde.FEMesh(p, t(1:6,:), Hmax, Hmin, order,assoc);
pde.FEMesh(p,t(1:6,:) ,Hmax,Hmin, order,assoc);
figure(200)
pdemesh(  model,'NodeLabels','on')
axis equal
end

This is an example, for your type of geometry or another meshing it might differ.

Thank you

[Manula]

Thank you very much.

[Kaveh Gharibi]

You are welcome!

[Manula]

Hi Kaveh I was trying to run your code in matlab but got error saying 'Undefined function or variable 'elemnodeDatatria6'.How can I avoid it. Appreciate your help.