Evaluating gradient of eigenvectors.
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Suppose I use Matlab's pde toolbox to solve an eigenvalue problem using FEM. Specifically I am using:
result=solvepdeeig(model,[0,10]);
eigenvectors = result.Eigenvectors;
eigenvalues = result.Eigenvalues;
Is there a way of evaluating the gradient of the computed eigenvectors, say using something similar to the
evaluateGradient
function?
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Ravi Kumar
2018-2-14
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Hi Matt,
The values in eigenvectors are scaled values, with no option to re-scale them or normalize as per choice. Hence, they do not have a physical meaning. So evaluating gradients using them is not suggested.
Can you explain why do you need to take gradients of eigenvectors? I could suggest a workaround depending on your use case.
Regards, Ravi
4 个评论
Matt
2018-2-14
Ravi Kumar
2018-2-14
Create a new PDEModel with the same systems size as you used for eigenvalue analysis:
newModel = createpde(model.PDESystemSize)
Assign geometry and mesh from your analysis model to this new model:
newModel.Geometry = model.Geometry
newModel.Mesh = model.Mesh
Now create at a new StationaryResults object using the first mode, or any mode that you want, as:
newResult = createPDEResults(newModel,result.Eigenvectors(:,1))
newResult would have gradients in it, also has the method evaluateGradients. In case you are dealing with a system of PDEs, be sure to stack all the components of the specific eigenvector into a single column to pass it createPDEResults.
Hope this helps.
Matt
2018-2-14
Matt
2018-2-15
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