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Calibri 83ffff̙̙3f3fff3f3f33333f33333.-TU Delft Repositoryg =uuidrepository linktitleauthorcontributorpublication yearabstract
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departmentresearch group programmeprojectcoordinates)uuid:b1024bc5-46ad-450e-a3d3-090a166a67a7Dhttp://resolver.tudelft.nl/uuid:b1024bc5-46ad-450e-a3d3-090a166a67a7ZFast Iterative Solution of the Time-Harmonic Elastic Wave Equation at Multiple Frequencies+Baumann, M.M. (TU Delft Numerical Analysis)pVuik, C. (promotor); van Gijzen, M.B. (copromotor); Delft University of Technology (degree granting institution)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.Krylov subspace methods; Preconditioning; Shifted linear systems; Time-harmonic elastic wave equation; MSSS matrix computations; Spectral analysisendoctoral thesis978-94-6295-827-2)uuid:ed57b9db-66b1-44f9-9903-9cd12b49b17cDhttp://resolver.tudelft.nl/uuid:ed57b9db-66b1-44f9-9903-9cd12b49b17csAn MSSS-preconditioned matrix equation approach for the time-harmonic elastic wave equation at multiple frequenciesGBaumann, M.M. (TU Delft Numerical Analysis); Astudillo Rengifo, R.A. (TU Delft Numerical Analysis); Qiu, Y. (Max Planck Institute for Dynamics of Complex Technical Systems); Ang, Y.M.E. (Nanyang Technological University); van Gijzen, M.B. (TU Delft Numerical Analysis); Plessix, R.E. (Shell Global Solutions International B.V.)In this work, we present a new numerical framework for the efficient solution of the time-harmonic elastic wave equation at multiple frequencies. We show that multiple frequencies (and multiple right-hand sides) can be incorporated when the discretized problem is written as a matrix equation. This matrix equation can be solved efficiently using the preconditioned IDR(s) method. We present an efficient and robust way to apply a single preconditioner using MSSS matrix computations. For 3D problems, we present a memory-efficient implementation that exploits the solution of a sequence of 2D problems. Realistic examples in two and three spatial dimensions demonstrate the performance of the new algorithm.Induced dimension reduction (IDR) method; Multilevel sequentially semiseparable (MSSS) matrices; Multiple frequencies; Preconditioned matrix equations; Time-harmonic elastic wave equationjournal articleNumerical Analysis)uuid:b3810eb3-8314-4f08-b173-baeeeec62efbDhttp://resolver.tudelft.nl/uuid:b3810eb3-8314-4f08-b173-baeeeec62efb]Efficient iterative methods for multi-frequency wave propagation problems: A comparison study[Baumann, M.M. (TU Delft Numerical Analysis); van Gijzen, M.B. (TU Delft Numerical Analysis)5In this paper we present a comparison study for three different iterative Krylov methods that we have recently developed for the simultaneous numerical solution of wave propagation problems at multiple frequencies. The three approaches have in common that they require the application of a single shift-and-invert preconditioner at a suitable seed frequency. The focus of the present work, however, lies on the performance of the respective iterative method. We conclude wi< th numerical examples that provide guidance concerning the suitability of the three methods.Time-harmonic elastic wave equation; global GMRES; multi-shift GMRES; shifted Neumann preconditioner; nested multi-shift Krylov methodsconference paperElsevier)uuid:242e3440-535a-4143-8036-5af5495d60bdDhttp://resolver.tudelft.nl/uuid:242e3440-535a-4143-8036-5af5495d60bdWNonlinear Model Order Reduction using POD/DEIM for Optimal Control of Burgers' Equation
Baumann, M.M.-Van Gijzen, M.B. (mentor); Rojas, M. (mentor)The model-order reduction techniques Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM) have been applied for the optimal control of Burgers' equation. Accuracy and performance of the reduced models have been studied in detail for different values of the viscosity parameter and different sizes of the discretization. Therefore, the three different optimization algorithms Newton-type, BFGS and SPG have been taken into account.model-order reduction; nonlinear dynamical systems; Burgers' equation; proper orthogonal decomposition; discrete empirical interpolation method; optimal control
master thesis
2013-07-158Electrical Engineering, Mathematics and Computer ScienceErasmus Mundus COSSE
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