MATLAB: Changing Faces of DiscreteGeometry (PDE Toolbox)

facesgeometryMATLABPartial Differential Equation Toolboxpdepde toolbox

I am trying to add a geometry to my PDE model from my given mesh (Nodes and Tetrahedron elements).

   model = createpde(1);
Nodes = [-1 -1 -1; 1 -1 -1; -1 1 -1; 1 1 -1; -1 -1 1; 1 -1 1; -1 1 1; 1 1 1]';
Elements = [1 2 3 6; 2 3 4 6; 1 3 5 6; 3 4 6 8; 3 5 6 7; 3 6 7 8]';
[G, Mesh] = geometryFromMesh(model,Nodes,Elements);
h = pdegplot(model, 'FaceLabels', 'on');
set(h(1), 'FaceAlpha', 0.5);

I am expecting the geometry G to have 6 Faces (obviously, because I have a cube), but the Geometry does not work like expected on the top and bottom Face, which are divided into several Faces, depending on the Tetrahedrons. On the "side" Faces it looks good.4

My question now is: Is there a way to change the Faces of the geometry, so for example that I say Face 1 should be the area between the Nodes 1-4 or something like that. Or alternatively: Does someone know, why the faces on top and bottom are divided like that and what I can change in my code to stop that from happen.

Best regards Nick

Best Answer

Elements 2,4,6 have reversed orientations. The input tetrahedral elements should honor the following numbering convention https://www.mathworks.com/help/pde/ug/mesh-data.html#buqc57w-1

Related Solutions

MATLAB: How to set space-varying boundary conditions

You can use applyBoundaryCondition. You just have to create a mesh for the geometry.

% Create a 3-dimensional PDE Model
model = createpde(3);
% Construct the Geometry
[x,y,z] = meshgrid([-3:0.25:3],[-2:0.25:2],[-1:0.25:1]);
% Create the convex hull.
x = x(:);
y = y(:);
z = z(:);
K = convhull(x,y,z);
% Put the data in the correct shape for |geometryFromMesh|.
nodes = [x';y';z'];
elements = K';
% Create a PDE model and import the mesh.
geometryFromMesh(model,nodes,elements);
% Plot geometry
figure
pdegplot(model,'FaceLabels','on')
title('Bracket with Face Labels')
% Now the new stuff
generateMesh(model)
ufun = @(region,state)[region.x.^2;region.x.^2 + region.y.^2;region.x.^2 + region.y.^2 - region.z]
applyBoundaryCondition(model,'dirichlet','Face',6,'u',ufun,'Vectorized','on')
specifyCoefficients(model,'m',0,'d',0,'c',1,'a',0,'f',[1;2;3]);
results = solvepde(model);
pdeplot3D(model,'ColorMapData',results.NodalSolution(:,1))

Alan Weiss

MATLAB mathematical toolbox documentation

MATLAB: How to specify non constant PDE boundary conditions on a sphere

You cannot easily change the internal face creation procedure. However, you can create nonconstant boundary conditions on that single face as a function of x, y, and z coordinates according to this procedure, and you can see a 2-D example here (but I am afraid that I did not create a 3-D example, sorry).