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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 ... mehr

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Volltext §
DOI: 10.5445/IR/1000082807
Veröffentlicht am 17.05.2018
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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