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

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.

References in corpus (3)

• Photonics in highly dispersive media: The exact modal expansion
• Non-linear eigenvalue problems with GetDP and SLEPc: Eigenmode computations of frequency-dispersive photonic open structures
• Computation of scattering resonances in absorptive and dispersive media with applications to metal-dielectric nano-structures

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• Acoustic modal analysis with heat release fluctuations using nonlinear eigensolvers
• Improving performance of contour integral-based nonlinear eigensolvers with infinite GMRES