Fast Iterative Solution of the Time-Harmonic Elastic Wave Equation at Multiple Frequencies

Manuel Baumann

Research output: ThesisDissertation (TU Delft)

114 Downloads (Pure)


Seismic Full-Waveform Inversion is an imaging technique to better understand the earth's subsurface. Therefore, the reflection intensity of sound waves is measured in a field experiment and is matched with the results from a computer simulation in a least-squares sense. From a computational point-of-view, but also from an economic view point, the efficient numerical solution of the elastic wave equation on current hardware is the main bottleneck of the computations, especially when a large three-dimensional computational domain is considered. In our research, we focused on an alternative problem formulation in frequency-domain. The mathematical challenge then becomes to efficiently solve the time-harmonic elastic wave equation at multiple frequencies. The resulting sequence of shifted linear systems is solved with a new framework of Krylov subspace methods derived for this specific problem formulation. Our numerical analysis gives insight in the theoretical convergence behavior of the new algorithm.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Delft University of Technology
  • Vuik, C., Supervisor
  • van Gijzen, M.B., Advisor
Thesis sponsors
Award date10 Jan 2018
Print ISBNs978-94-6295-827-2
Publication statusPublished - 2018


  • Krylov subspace methods
  • Preconditioning
  • Shifted linear systems
  • Time-harmonic elastic wave equation
  • MSSS matrix computations
  • Spectral analysis


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