Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1-8 |
| Seitenumfang | 8 |
| Fachzeitschrift | PAMM |
| Jahrgang | 23 |
| Ausgabenummer | 3 |
| Publikationsstatus | Veröffentlicht - 1 Nov. 2023 |
Abstract
by means of Principal Geodesic Analysis (PGA) on the Riemannian manifolds S2
(the sphere) and SO(3) (the rotation group). MOR requires highly accurate and
efficient implementations of the logarithm maps and the resulting lifts across
multiple branches. However, in our cases these maps have singularities due to
periodicity. In this work we focus on the logarithm and lift maps for the sphere S 2 .
We conduct detailed numerical experiments on mechanical systems to achieve
maximal accuracy in spite of the singularities.
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in: PAMM, Jahrgang 23, Nr. 3, 01.11.2023, S. 1-8.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Numerical Accuracy of Principal Geodesic Analyis on the Sphere in Director-Based Dynamics of Hybrid Mechanical Systems
AU - Schubert, Jenny
AU - Steinbach, Marc C.
N1 - Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – SFB1463 – 434502799. Open access funding enabled and organized by Projekt DEAL.
PY - 2023/11/1
Y1 - 2023/11/1
N2 - We aim at nonlinear model order reduction (MOR) in hybrid mechanical systemsby means of Principal Geodesic Analysis (PGA) on the Riemannian manifolds S2(the sphere) and SO(3) (the rotation group). MOR requires highly accurate andefficient implementations of the logarithm maps and the resulting lifts acrossmultiple branches. However, in our cases these maps have singularities due toperiodicity. In this work we focus on the logarithm and lift maps for the sphere S 2 .We conduct detailed numerical experiments on mechanical systems to achievemaximal accuracy in spite of the singularities.
AB - We aim at nonlinear model order reduction (MOR) in hybrid mechanical systemsby means of Principal Geodesic Analysis (PGA) on the Riemannian manifolds S2(the sphere) and SO(3) (the rotation group). MOR requires highly accurate andefficient implementations of the logarithm maps and the resulting lifts acrossmultiple branches. However, in our cases these maps have singularities due toperiodicity. In this work we focus on the logarithm and lift maps for the sphere S 2 .We conduct detailed numerical experiments on mechanical systems to achievemaximal accuracy in spite of the singularities.
U2 - 10.1002/pamm.202300178
DO - 10.1002/pamm.202300178
M3 - Article
VL - 23
SP - 1
EP - 8
JO - PAMM
JF - PAMM
SN - 1617-7061
IS - 3
ER -