A Sylvester equation approach for the computation of zero-group-velocity points in waveguides

Plestenjak, Bor (avtor), Kiefer, Daniel A. (avtor), Gravenkamp, Hauke (avtor)

Eigenvalues of parameter-dependent quadratic eigenvalue problems form eigencurves. The critical points on these curves, where the derivative vanishes, are of practical interest. A particular example is found in the dispersion curves of elastic waveguides, where such points are called zero-group-velocity (ZGV) points. Recently, it was revealed that the problem of computing ZGV points can be modeled as a multiparameter eigenvalue problem (MEP), and several numerical methods were devised. Due to their complexity, these methods are feasible only for problems involving small matrices. In this paper, we improve the efficiency of these methods by exploiting the link to the Sylvester equation. This approach enables the computation of ZGV points for problems with much larger matrices, such as multi-layered plates and three-dimensional structures of complex cross-sections.

• Jezik: Angleški jezik
• Ključne besede: parameter-dependent quadratic eigenvalue problem, eigencurves, zero-group-velocity point, Sylvester equation, method of fixed relative distance, two-parameter eigenvalue problem
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.11.2025
• Leto izida: 2025
• Št. strani: Str. 1443–1456
• Številčenje: Vol. 76, iss. 5
• PID: 20.500.12556/RUL-175777
• UDK: 519.6
• ISSN pri članku: 0178-7675
• DOI: 10.1007/s00466-025-02656-8
• COBISS.SI-ID: 245905155
• Datum objave v RUL: 07.11.2025

Gradivo je del revije

• Naslov: Computational mechanics
• Skrajšan naslov: Comput. mech.
• Založnik: Springer
• ISSN: 0178-7675
• COBISS.SI-ID: 6668037

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: parametrični kvadratični problem lastnih vrednosti, lastne krivulje, točka ničelne skupinske hitrosti, Sylvestrova enačba, metoda fiksne relativne razdalje, dvoparametrični problem lastnih vrednosti