Global ETD Search

41	Efficient Solvers for the Phase-Field Crystal Equation: Development and Analysis of a Block-Preconditioner Praetorius, Simon 08 December 2015 (has links) A preconditioner to improve the convergence properties of Krylov subspace solvers is derived and analyzed in this work. This method is adapted to linear systems arising from a finite-element discretization of a phase-field crystal equation. info:eu-repo/classification/ddc/510 ddc:510
42	Effiziente Vorkonditionierung von Finite-Elemente-Matrizen unter Verwendung hierarchischer Matrizen Fischer, Thomas 15 September 2010 (has links) Diese Arbeit behandelt die effiziente Vorkonditionierung von Finite-Elemente-Matrizen unter Verwendung hierarchischer Matrizen. info:eu-repo/classification/ddc/518 ddc:518
43	Global stability analysis of three-dimensional boundary layer flows Brynjell-Rahkola, Mattias January 2015 (has links) This thesis considers the stability and transition of incompressible boundary layers. In particular, the Falkner–Skan–Cooke boundary layer subject to a cylindrical surface roughness, and the Blasius boundary layer with applied localized suction are investigated. These flows are of great importance within the aviation industry, feature complex transition scenarios, and are strongly three-dimensional in nature. Consequently, no assumptions regarding homogeneity in any of the spatial directions are possible, and the stability of the flow is governed by an extensive three-dimensional eigenvalue problem. The stability of these flows is addressed by high-order direct numerical simulations using the spectral element method, in combination with a Krylov subspace projection method. Such techniques target the long-term behavior of the flow and can provide lower limits beyond which transition is unavoidable. The origin of the instabilities, as well as the mechanisms leading to transition in the aforementioned cases are studied and the findings are reported. Additionally, a novel method for computing the optimal forcing of a dynamical system is developed. This type of analysis provides valuable information about the frequencies and structures that cause the largest energy amplification in the system. The method is based on the inverse power method, and is discussed in the context of the one-dimensional Ginzburg–Landau equation and a two-dimensional flow case governed by the Navier–Stokes equations. / <p>QC 20151015</p> Hydrodynamic stability transition to turbulence global analysis boundary layers roughness laminar flow control Stokes/Laplace preconditioner optimal forcing crossflow vortices Ginzburg-Landau Falkner-Skan-Cooke Blasius lid-driven cavity Fluid Mechanics and Acoustics Strömningsmekanik och akustik
44	Multi-level extensions for the fast and robust overlapping Schwarz preconditioners Röver, Friederike 14 June 2023 (has links) Der GDSW-Vorkonditionierer ist ein zweistufiges überlappendes Schwarz-Gebietszerlegungsverfahren mit einem energieminimierenden Grobraum, dessen parallele Skalierbarkeit durch das direkt gelöste Grobproblem begrenzt ist. Zur Verbesserung der parallelen Skalierbarkeit wurde hier eine mehrstufige Erweiterung eingeführt. Für den Fall skalarer elliptischer Probleme wurde eine Konditionierungszahlschranke aufgestellt. Die parallele Implementierung wurde in das quelloffene ShyLU/FROSch Paket der Trilinos-Softwarebibliothek (http://trilinos.org) integriert und auf mehreren der leistungsstärksten Supercomputern der Welt (JUQUEEN, Forschungszentrum Jülich; SuperMUC-NG, LRZ Garching; Theta, Argonne Leadership Computing Facility, Argonne National Laboratory, USA) für Modellprobleme (Laplace und lineare Elastizität) getestet. Das angestrebte Ziel einer verbesserten parallelen Skalierbarkeit wurde erreicht, der Bereich der Skalierbarkeit wurde um mehr als eine Größenordnung erweitert. Die größten Rechnungen verwendeten mehr als 200000 Prozessorkerne des Theta Supercomputers. Zudem wurde die Anwendung des GDSW-Vorkonditionierers auf ein vollständig gekoppeltes nichtlineare Deformations-Diffusions Problem in der Chemomechanik betrachtet. info:eu-repo/classification/ddc/510 ddc:510 Gebietszerlegungsmethode Hochleistungsrechnen Parallelrechner Skalierbarkeit
45	Studies on instability and optimal forcing of incompressible flows Brynjell-Rahkola, Mattias January 2017 (has links) This thesis considers the hydrodynamic instability and optimal forcing of a number of incompressible flow cases. In the first part, the instabilities of three problems that are of great interest in energy and aerospace applications are studied, namely a Blasius boundary layer subject to localized wall-suction, a Falkner–Skan–Cooke boundary layer with a localized surface roughness, and a pair of helical vortices. The two boundary layer flows are studied through spectral element simulations and eigenvalue computations, which enable their long-term behavior as well as the mechanisms causing transition to be determined. The emergence of transition in these cases is found to originate from a linear flow instability, but whereas the onset of this instability in the Blasius flow can be associated with a localized region in the vicinity of the suction orifice, the instability in the Falkner–Skan–Cooke flow involves the entire flow field. Due to this difference, the results of the eigenvalue analysis in the former case are found to be robust with respect to numerical parameters and domain size, whereas the results in the latter case exhibit an extreme sensitivity that prevents domain independent critical parameters from being determined. The instability of the two helices is primarily addressed through experiments and analytic theory. It is shown that the well known pairing instability of neighboring vortex filaments is responsible for transition, and careful measurements enable growth rates of the instabilities to be obtained that are in close agreement with theoretical predictions. Using the experimental baseflow data, a successful attempt is subsequently also made to reproduce this experiment numerically. In the second part of the thesis, a novel method for computing the optimal forcing of a dynamical system is developed. The method is based on an application of the inverse power method preconditioned by the Laplace preconditioner to the direct and adjoint resolvent operators. The method is analyzed for the Ginzburg–Landau equation and afterwards the Navier–Stokes equations, where it is implemented in the spectral element method and validated on the two-dimensional lid-driven cavity flow and the flow around a cylinder. / <p>QC 20171124</p> hydrodynamic stability optimal forcing resolvent operator Laplace preconditioner spectral element method eigenvalue problems inverse power method direct numerical simulations Falkner–Skan–Cooke boundary layer localized roughness crossflow vortices Blasius boundary layer localized suction helical vortices lid-driven cavity cylinder flow Fluid Mechanics and Acoustics Strömningsmekanik och akustik
46	CUDA-based Scientific Computing / Tools and Selected Applications Kramer, Stephan Christoph 22 November 2012 (has links) No description available. 510 CUDA C++ Expression Templates Preconditioning Sparse Matrix Indoor Airflow Quantum Hall Effect Magnetic Focussing Hardy Space Infinite Elements Phase Retrieval Optogenetics Object-oriented Design FFT Dielectric Relaxation Spectroscopy Poisson-Nernst-Planck Equations BEM FEM-BEM Coupling Curvilinear Boundaries Boundary Integral Equation Transparent Boundary Conditions Schrödinger Equation Krylov Methods Parallel Computing GPU Computing Sparse Approximate Inverse Faber Polynomials Polynomial Preconditioner Conformational Sampling of Proteins Protein Folding Higher Order Finite Elements Mathematics (PPN61756535X)

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