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NEP: A Module for the Parallel Solution of Nonlinear Eigenvalue Problems in SLEPc

Authors:

Jose E. RomanAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 47, Issue 3

Article No.: 23, Pages 1 - 29

https://doi.org/10.1145/3447544

Published: 26 June 2021 Publication History

Abstract

SLEPc is a parallel library for the solution of various types of large-scale eigenvalue problems. Over the past few 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 article 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.

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Cited By

Gravenkamp HPlestenjak BKiefer DJarlebring E(2025)Computation of leaky waves in layered structures coupled to unbounded media by exploiting multiparameter eigenvalue problemsJournal of Sound and Vibration10.1016/j.jsv.2024.118716596(118716)Online publication date: Feb-2025
https://doi.org/10.1016/j.jsv.2024.118716
Roman JAlvarruiz FCampos CDalcin LJolivet PLamas Daviña A(2023)Improvements to SLEPc in Releases 3.14–3.18ACM Transactions on Mathematical Software10.1145/360337349:3(1-11)Online publication date: 19-Sep-2023
https://dl.acm.org/doi/10.1145/3603373
Nicolet ADemésy GZolla FCampos CRoman JGeuzaine C(2023)Physically agnostic quasi normal mode expansion in time dispersive structures: From mechanical vibrations to nanophotonic resonancesEuropean Journal of Mechanics - A/Solids10.1016/j.euromechsol.2022.104809100(104809)Online publication date: Jul-2023
https://doi.org/10.1016/j.euromechsol.2022.104809
Show More Cited By

Index Terms

NEP: A Module for the Parallel Solution of Nonlinear Eigenvalue Problems in SLEPc
1. Computing methodologies
  1. Parallel computing methodologies
    1. Parallel algorithms
      1. Massively parallel algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Nonlinear equations
  2. Mathematical software
    1. Solvers

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 47, Issue 3

September 2021

251 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/3472960

Editors:
Zhaojun Bai
University of California at Davis, USA
,
Wolfgang Bangerth
Colorado State University, USA

Issue’s Table of Contents

Copyright © 2021 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 26 June 2021

Accepted: 01 January 2021

Revised: 01 July 2020

Received: 01 October 2019

Published in TOMS Volume 47, Issue 3

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Cited By

Gravenkamp HPlestenjak BKiefer DJarlebring E(2025)Computation of leaky waves in layered structures coupled to unbounded media by exploiting multiparameter eigenvalue problemsJournal of Sound and Vibration10.1016/j.jsv.2024.118716596(118716)Online publication date: Feb-2025
https://doi.org/10.1016/j.jsv.2024.118716
Roman JAlvarruiz FCampos CDalcin LJolivet PLamas Daviña A(2023)Improvements to SLEPc in Releases 3.14–3.18ACM Transactions on Mathematical Software10.1145/360337349:3(1-11)Online publication date: 19-Sep-2023
https://dl.acm.org/doi/10.1145/3603373
Nicolet ADemésy GZolla FCampos CRoman JGeuzaine C(2023)Physically agnostic quasi normal mode expansion in time dispersive structures: From mechanical vibrations to nanophotonic resonancesEuropean Journal of Mechanics - A/Solids10.1016/j.euromechsol.2022.104809100(104809)Online publication date: Jul-2023
https://doi.org/10.1016/j.euromechsol.2022.104809
Hiremath VRoman J(2023)Acoustic modal analysis with heat release fluctuations using nonlinear eigensolversApplied Mathematics and Computation10.1016/j.amc.2023.128249458:COnline publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1016/j.amc.2023.128249
Güttel SNegri Porzio GTisseur F(2022)Robust Rational Approximations of Nonlinear Eigenvalue ProblemsSIAM Journal on Scientific Computing10.1137/20M138053344:4(A2439-A2463)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1137/20M1380533
Afzali MFarrokh MCarrera E(2022)Thermal buckling loads of rectangular FG plates with temperature-dependent properties using Carrera Unified FormulationComposite Structures10.1016/j.compstruct.2022.115787295(115787)Online publication date: Sep-2022
https://doi.org/10.1016/j.compstruct.2022.115787

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