A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as "FEAST", has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of the algorithm beyond the confines of the theoretical assumptions. The utility of the algorithm is illustrated by applying it to compute guided transverse core modes of a realistic optical fiber.

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An efficient technique to solve polynomial eigenproblems is shown to result in an accurate method for computing leaky modes of optical fibers. The nonlinear eigenproblem arises from a frequency-dependent perfectly matched layer and is solved using a contour integral eigensolver. Extensive computations on an antiresonant fiber with a complex transverse microstructure are reported. Even when employing up to one million degrees of freedom, the fiber model appears to remain in a preasymptotic regime where computed confinement loss values are likely to be off by orders of magnitude. This and other difficulties in computing mode losses, together with some techniques to overcome them, are detailed.

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