Stochastic collocation method for computing eigenspaces of parameter-dependent operators
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We consider computing eigenspaces of an elliptic self-adjoint operator depending on a countable number of parameters in an affine fashion. The eigenspaces of interest are assumed to be isolated in the sense that the corresponding eigenvalues are separated from the rest of the spectrum for all values of the parameters. We propose a stochastic collocation method on an anisoptropic sparse grid in the parameter domain for computing a basis for the parameter dependent eigenspace of interest. The convergence of this method is verified in a series of numerical examples based on the eigenvalue problem of a stochastic diffusion operator.