Evaluating gradient of eigenvectors.

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?

Answer 1

[Ravi Kumar]

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

[Matt]

Hi Ravi

Thanks for the answer. Yes I am aware of this problem. However, suppose I normalise in some way, I would then like to compute the Neumann data on the boundary (for comparison to another numerical method). Any idea how this could be done easily?

Thanks, Matt

[Ravi Kumar]

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]

Thanks, I'll try it out. Looks ideal!

[Matt]

Works a treat, thank you very much!