How to import geometry with holes to use with PDE toolbox?

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Brian Chen 2017-1-18

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https://ww2.mathworks.cn/matlabcentral/answers/320841-how-to-import-geometry-with-holes-to-use-with-pde-toolbox

评论： Alan Weiss 2017-2-2

So there are two main options for creating geometry for a PDE model: geometryFromMesh and importGeometry.

The geometry I have is essentially a hollow sphere (i.e. a solid sphere with a smaller spherical cutout inside). I have created an STL file and attempted to use importGeometry. However, I get the error "Assemblies of more than one geometric model are not currently supported"

Now I am looking into using geometryFromMesh. I have two questions: 1. Is this even possible? 2. If so, then how might I create a mesh that has holes in it?

This is the geometry I'm trying to use.

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Answer 1

Alan Weiss 2017-1-18

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编辑：Alan Weiss 2017-1-18

在 MATLAB Online 中打开

You could try something like the following series of commands:

[az,el,r] = meshgrid(linspace(0,2*pi-0.01),linspace(-pi,pi-0.01),linspace(0.25,1));
[x,y,z] = sph2cart(az,el,r);
shp = alphaShape(x(:),y(:),z(:),0.05);
[elements,nodes] = boundaryFacets(shp);
nodes = nodes';
elements = elements';
model = createpde();
geometryFromMesh(model,nodes,elements);
pdegplot(model,'FaceLabels','on','FaceAlpha',0.5)

Don't forget to mesh your resulting geometry by using generateMesh.

Alan Weiss

MATLAB mathematical toolbox documentation

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Brian Chen 2017-2-2

在 MATLAB Online 中打开

I can consistently get MATLAB to crash now when using generateMesh.

When I plot using pdegplot, everything looks fine. Checking the FEMesh also seems ok. However for some reason using your version of the code works.

Here is the code I use:

% Make a big sphere
[x,y,z]=sphere(24);
shp = alphaShape(x(:),y(:),z(:), 10);
[faces,vertices] = boundaryFacets(shp);
vertices = vertices.*10e-4;
% Make a small sphere
[x,y,z]=sphere(24);
shp = alphaShape(x(:),y(:),z(:), 10);
[f,v] = boundaryFacets(shp);
v = v.*10e-5;
% Combine the two spheres
fnew = [faces; f + length(vertices)];
vnew = [vertices; v];
faces = fnew;
vertices = vnew;
model = createpde();
gd = geometryFromMesh(model, vertices', faces');
pdegplot(model,'FaceLabels','on','FaceAlpha',0.5);
% the geometry seems plots alright and has 2 faces
% however the next step crashes
generateMesh(model);

I can also consistently get it to crash with STL files that I have sculpted in Meshmixer--and these are not even large STL files.

Alan Weiss 2017-2-2

I am very sorry that you are having such trouble with geometry creation. But really, you are trying to push the current 3-D geometry beyond what it can do. It is not designed for subdomains, nor for holes or multiple regions. My code is sort of fortuitously workable, but I don't really know why.

If you can afford to wait until the next release in March, then things might be somewhat better, but I cannot promise or even describe anything that is coming up. Sorry.

Alan Weiss

MATLAB mathematical toolbox documentation

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