Determine subdomains for 3D models in the PDE toolbox

Question

Zoi T. 2016-12-14

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/316846-determine-subdomains-for-3d-models-in-the-pde-toolbox

回答： Alan Weiss 2016-12-14

Hello,

I am having some trouble with 3D examples in the PDE toolbox. I would like to have subdomains with different parameter values for a simple diffusion problem. However, I have not found a way to define my subdomains. I tried defining and .stl type format by

[x1,y1,z1] = meshgrid(-2:4:2);
[x2,y2,z2] = meshgrid(-1:2:1);
x1 = x1(:);     y1 = y1(:);     z1 = z1(:);
x2 = x2(:);     y2 = y2(:);     z2 = z2(:);
K1 = convhull(x1,y1,z1);  K2 = convhull(x2,y2,z2);
nodes = [[x1; x2]';[y1; y2]';[z1; z2]'];
elements = [K1', K2'+size(x1,1)]; 
model = createpde();
geometryFromMesh(model,nodes,elements);

This should create two surfaces of two cubes one within the other. When I try to call the mesh generation function though, by

generateMesh(model,'Hmax',0.5,'Hmin',0.2);

MATLAB shuts down (Error message: "MATLAB has encountered an internal error and needs to close").

I am assuming that there is some problem with the tetrahedral mesh generation. But what could it be? Calling the function works fine if I have only one cube.

It looks like subdomain tags are supported, because if I check at the [p,e,t] matrices from by the function

[p,e,t] = meshToPet(model.Mesh);

the t matrix has an extra entry for subdomain tags (i.e. if my elements are linear each element has 4 entries with the node indices and a 5th entry set to 1).

Am I right to assume that if I import a tetrahedral mesh file file with predefined subdomains I can work with the PDE creation and specification functions as in the 2D cases?

Can I replace the FEMesh in my model by one created externally?

The only workaround I have found so far is this Previous question "How can I specify different PDE coefficients for different regions in a 3D geometry using PDE toolbox?" by determining coefficients in function form. However my subdomains correspond to isosurfaces for different material densities and cannot be geometrically described.

Thank you in advance.