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High-frequency wave-propagation: error analysis for analytical and numerical approximations

Baumstark, Julian 1
1 Karlsruher Institut für Technologie (KIT)

Abstract (englisch):

In this thesis we investigate a specific type of semilinear hyperbolic systems with highly oscillatory initial data. This type of systems is numerically very challenging to treat since the solutions are highly oscillatory in space and time. The goal is to derive suitable analytical and numerical approximations. Based on the classical slowly varying envelope approximation (SVEA), an improved error estimate is proven for this analytical approximation. The envelope equation avoids oscillations in space, making this approximation attractive for numerical computations. Furthermore, more accurate analytical approximations are obtained by extending the ansatz of the SVEA. In addition to the analytical study of the SVEA two numerical time integrators are constructed and analyzed without any step-size restrictions. Numerical examples are provided to illustrate the theoretical results.
Finally, a complementary approach is presented which address both problems, the oscillations in space and time, simultaneously.


Volltext §
DOI: 10.5445/IR/1000149719
Veröffentlicht am 24.08.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Hochschulschrift
Publikationsdatum 24.08.2022
Sprache Englisch
Identifikator KITopen-ID: 1000149719
Verlag Karlsruher Institut für Technologie (KIT)
Umfang iii, 155 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Angewandte und Numerische Mathematik (IANM)
Prüfungsdatum 06.07.2022
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Schlagwörter High-frequency wave propagation, semilinear wave equation, Maxwell–Lorentz, system, Klein--Gordon system, diffractive geometric optics, slowly varying envelope approximation, error analysis, time integration, modulated Fourier expansion
Relationen in KITopen
Referent/Betreuer Jahnke, Tobias
Hochbruck, Marlis
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