FEAST Eigensolver for Nonlinear Eigenvalue Problems

TL;DR

This paper introduces a generalized FEAST eigensolver capable of efficiently solving nonlinear eigenvalue problems within specified regions of the complex plane, enabling parallel computation of multiple eigenpairs.

Contribution

It extends the linear FEAST algorithm to nonlinear problems, allowing for parallelized eigenpair computation in complex regions, demonstrated through physically-motivated examples.

Findings

Effective for large-scale nonlinear eigenvalue problems

Enables parallel computation of eigenpairs

Demonstrated on physically-motivated examples

Abstract

The linear FEAST algorithm is a method for solving linear eigenvalue problems. It uses complex contour integration to calculate the eigenvectors whose eigenvalues that are located inside some user-defined region in the complex plane. This makes it possible to parallelize the process of solving eigenvalue problems by simply dividing the complex plane into a collection of disjoint regions and calculating the eigenpairs in each region independently of the eigenpairs in the other regions. In this paper we present a generalization of the linear FEAST algorithm that can be used to solve nonlinear eigenvalue problems. Like its linear progenitor, the nonlinear FEAST algorithm can be used to solve nonlinear eigenvalue problems for the eigenpairs whose eigenvalues lie in a user-defined region in the complex plane, thereby allowing for the calculation of large numbers of eigenpairs in parallel. We describe the nonlinear FEAST algorithm, and use several physically-motivated examples to demonstrate its properties.