How can I refine a subdomain in the PDE Toolbox mesh generation tool?

Hello,

I would like to refine a part of my domain without refining the whole mesh. Say for example that I have a unit square domain R1, which contains a circular sub-domain E1. Can I refine only E1 up to a desired element size, without imposing the same mesh size in the rest of the domain?

Answer 1

[michio]

I assume your problem is in 2D, then refinemesh function accepts an extra input argument "it", that is interpreted as a list of subdomains to refine, if it is a row vector.

See. http://jp.mathworks.com/help/pde/ug/refinemesh.html

[michio]

An example:

% Create a rectangle and a circle
R1 = [3;4;-0.5;0.5;0.5;-0.5;-0.5;-0.5;0.5;0.5];
C1 = [1;0;0;0.25];

% Append extra zeros to the circles
% so they have the same number of rows as the rectangle
C1 = [C1;zeros(length(R1) - length(C1),1)];
% Combine the shapes into one matrix
gd = [R1,C1];

% Give names for the three shapes
ns = char('R1','C1');
ns = ns';

% Specify the union of the rectangle and C1, and subtract C2
sf = 'R1+C1';
[dl,bt] = decsg(gd,sf,ns); % combines the basic shapes using the set formula

figure(1)
pdegplot(dl,'EdgeLabels','on','SubdomainLabels','on')
axis equal

[p,e,t] = initmesh(dl); 
[p1,e1,t1] = refinemesh(dl,p,e,t,2); % Refine a mesh of domain 2
figure(2),pdemesh(p1,e1,t1);
axis equal

[Zoi T.]

This is exactly what I was looking for! Thanks a lot!

[michio]

You are welcome :)

[shixiang zhao]

Hello:)) How to refine mesh in PDEmodel? I know that we can easily refine mesh by '[p,e,t] = refinemesh()', but with this [p,e,t] I can only get the solutions by using 'u = assempde()'. Hope that you can give me some advice, and I will really appreciate it.

[MarionJ]

It is not possible. I had the same problem. You have to use assempde, parabolic etc. if you want to refine mesh in certain Domains.

[Ali Hammouche]

How to generate a triangular mesh by MATLAB with the line joining the cell centre is orthogonal to the edges of the triangle?

Answer 2

[Devosmita Chatterjee]

How to refine a mesh for the poisson equation problem in a unitsquare domain by placing many triangles around the point (0.5,0.5) using Adaptive Finite Element Method and a posteriori error estimation? We need to find adaptive meshes for the problem with solution u=a*exp(-a*(r^2)), a =400 using two refinements, four refinements, six refinements, ten refinements. Can anyone provide me the Matlab code for this problem?

Answer 3

[Ian Jentz]

There is now a port of refinemesh() available for PDEModel. Like refinemesh(), it works for 2D linear triangular geometries only.

The new PDEModel compatible function is refinePDEMmesh().

This is likely how would run your problem:

create your model as a pde model

 model=createpde;

proceed with your geometry definitions.

When you get to meshing, you instantiate your mesh as usuall, but then can refine the mesh on a particular face using refinePDEMmesh().

 generateMesh(model);
 FaceID = 1; % the face ID of your E1 face?
 model = refinePDEMmesh(model,FaceID);

[Sean Littleton]

Hello,

Thank you for sharing this function. It is almost exactly what I need, except for the fact that it does not work with quadratic triangular elements -- the very elements that I need to use for my problem. Are there any plans to add this functionality in the future? If not, is there an approach you would recommend?

Note: The triangular elements I am using are still geometrically linear. The extra nodes are only used for the quadratic shape functions, since I need the derivatives of the solution to be continuous.