NEP: a module for the parallel solution of nonlinear eigenvalue problems in SLEPc

TL;DR

This paper introduces the NEP module in SLEPc for efficiently solving large-scale nonlinear eigenvalue problems, including rational and other nonlinear functions, with parallel computing capabilities.

Contribution

The paper presents a new NEP module in SLEPc that extends capabilities to general nonlinear eigenproblems beyond polynomial cases, with parallel implementation and real application tests.

Findings

Effective parallel solvers for nonlinear eigenproblems

Demonstrated performance on real application problems

Reliable solutions for diverse nonlinear functions

Abstract

SLEPc is a parallel library for the solution of various types of large-scale eigenvalue problems. In the last years we have been developing a module within SLEPc, called NEP, that is intended for solving nonlinear eigenvalue problems. These problems can be defined by means of a matrix-valued function that depends nonlinearly on a single scalar parameter. We do not consider the particular case of polynomial eigenvalue problems (which are implemented in a different module in SLEPc) and focus here on rational eigenvalue problems and other general nonlinear eigenproblems involving square roots or any other nonlinear function. The paper discusses how the NEP module has been designed to fit the needs of applications and provides a description of the available solvers, including some implementation details such as parallelization. Several test problems coming from real applications are used to evaluate the performance and reliability of the solvers.