MATLAB: Are the eigenmodes computed by the PDEEIG function in Partial Differential Equation Toolbox 1.0.10 (R2007a) normalized

Partial Differential Equation Toolbox

I would like to know if the eigenvector functions computed using the PDE Eigenvalue routines have unit norm over the finite element space over the bounded domain of my PDE problem, i.e. I would like to know if they form an orthonormal basis with respect to this norm.

Best Answer

Each column in the eigenvector matrix v returned by the PDEEIG function consists of solution values at the corresponding node points.
These eigenvectors are normalized such that sum(v(:,i).*conj(v(:,i)))==1, for all i (where v(:,i) corresponds to the ith eigenmode).
The eigenvectors are not normalized with respect to the norm over the finite element space, that is, int(v(:,i).*conj(v(,i)),Omega)==1, where Omega is the bounded domain of the PDE problem.
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