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Space-Time Methods for Acoustic Waves with Applications to Full Waveform Inversion

Ernesti, Johannes

Abstract (englisch):
Classically, wave equations are considered as evolution equations where the derivative with respect to time is treated in a stronger way than the spatial differential operators. This results in an ordinary differential equation (ODE) with values in a function space, e.g. in a Hilbert space, with respect to the spatial variable.
For instance, acoustic waves in a spatial domain $\Omega \subset \mathbb{R}^d$ for a given right-hand side $\mathbf b$ can be considered in terms of the following ODE
\begin{equation*}
\partial_t \mathbf y = A\mathbf y + \mathbf b\quad \text{ in }[0,T]\,,\quad
\mathbf y(0) = \mathbf 0\,,
\qquad
A = \begin{pmatrix} 0 & \operatorname{div} \\ \nabla & 0 \end{pmatrix},
\end{equation*}
where the solution $\mathbf y = (p, \mathbf v)$ is an element of the space $\mathrm C^0\big(0,T; \mathcal D(A)\big) \cap \mathrm C^1\big(0,T; \mathrm L_2(\Omega)\big)$ with $\mathcal D(A) \subset \mathrm H^1(\Omega) \times H(\operatorname{div}, \Omega)$. In order to analyze this ODE, space and time are treated separately and hence tools for partial differential equations are used in space and tools for ODEs are used in time. ... mehr

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Volltext §
DOI: 10.5445/IR/1000082807
Veröffentlicht am 17.05.2018
Coverbild
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Hochschulschrift
Jahr 2018
Sprache Englisch
Identifikator urn:nbn:de:swb:90-828075
KITopen-ID: 1000082807
Verlag KIT, Karlsruhe
Umfang 168 S.
Abschlussart Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Angewandte und Numerische Mathematik (IANM)
Prüfungsdatum 20.12.2017
Referent/Betreuer Prof. C. Wieners
Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagworte Space-Time Discretizations, Discontinuous Petrov Galerkin, DPG, Full Waveform Inversion, FWI, Inverse Problems, Least-Squares Methods, High Performance Computing
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