Adaptive approximation of nonlinear eigenproblems by minimal rational interpolation

Abstract

We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is carried out via the minimal rational interpolation method. Notably, an adaptive sampling approach is employed: the expensive data needed for the approximation is gathered at locations that are optimally chosen by following a greedy error indicator. This allows the algorithm to employ computational resources only where "most of the information" on not-yet-approximated eigenvalues can be found. Then, through a post-processing of the surrogate, the sought-after eigenvalues and eigenvectors are recovered. Numerical examples are used to showcase the effectiveness of the method.

References in corpus (1)

• Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes

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