How to set space-varying boundary conditions?

Question

Stephan 2017-3-1

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https://ww2.mathworks.cn/matlabcentral/answers/327506-how-to-set-space-varying-boundary-conditions

评论： Stephan 2017-3-2

Hello,

the following code gives 6 faces. I want to add a space-varying boundary condition for one face (F6). I think it is not possible to use applyBoundaryCondition(). How can I divide face F6 into small slices to specify constant boundary conditions for each of them?

Many thanks

Stephan

% 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')

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Answer 1

Alan Weiss 2017-3-1

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在 MATLAB Online 中打开

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))