How are eigenfunctions normalized with solvepdeeig?

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Marichi Gupta 2022-4-20

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回答： SAI SRUJAN 2023-10-20

When computing eigenfunctions with solvepdeeig, how are the returned eigenfunctions normalized? With respect to

-norm, etc? It seems that they are definitely not normalized with the

-norm.

In case it's relevant, my code looks a lot like the example in https://www.mathworks.com/help/pde/ug/pde.pdemodel.solvepdeeig.html.

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Answer 1

SAI SRUJAN 2023-10-20

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Hi Marichi gupta,

I understand that you are trying to get a grasp of the output arguments of "solvepdeeig" function.

Solvepdeeig function return a "Eigenresults" object as output, which contains eigenvectors and eigenvalues. We can use the "normalize" MATLAB function to normalize the eigenvectors.

Refer to the following coding snippet for better understanding of the same,

model = createpde(3);
importGeometry(model,"BracketTwoHoles.stl");
applyBoundaryCondition(model,"dirichlet","Face",1,"u",[0;0;0]);
E = 200e9; % elastic modulus of steel in Pascals
nu = 0.3; % Poisson's ratio
specifyCoefficients(model,"m",0,...
                          "d",1,...
                          "c",elasticityC3D(E,nu),...
                          "a",0,...
                          "f",[0;0;0]);
evr = [-Inf,1e7];
generateMesh(model);
results = solvepdeeig(model,evr);
EigenVectors=results.Eigenvectors;
% MATLAB function to normalize a vector.
normalizedEigenfunctions = normalize(EigenVectors);
% Follow this example for normalizing a vector
v= [1 2 3];
normalized_v=v./sqrt(sum(v.^2));