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The Global ETD Search service is a free service for researchers
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Showing 221 to 226 of 226 (0.099 seconds)Spelling suggestions: "subject:"[een] DISCRETIZATION"" "subject:"[enn] DISCRETIZATION""
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Development of High-order CENO Finite-volume Schemes with Block-based Adaptive Mesh Refinement (AMR)Ivan, Lucian 31 August 2011 (has links)
A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares
reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction
procedure is used for cells in which the solution is fully resolved. Switching in the
hybrid procedure is determined by a solution smoothness indicator. The hybrid approach
avoids the complexity associated with other ENO schemes that require reconstruction on
multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional
compressible gaseous flows as well as for advection-diffusion problems characterized
by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent
solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.
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Development of High-order CENO Finite-volume Schemes with Block-based Adaptive Mesh Refinement (AMR)Ivan, Lucian 31 August 2011 (has links)
A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares
reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction
procedure is used for cells in which the solution is fully resolved. Switching in the
hybrid procedure is determined by a solution smoothness indicator. The hybrid approach
avoids the complexity associated with other ENO schemes that require reconstruction on
multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional
compressible gaseous flows as well as for advection-diffusion problems characterized
by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent
solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.
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Studies on two specific inverse problems from imaging and financeRückert, Nadja 20 July 2012 (has links) (PDF)
This thesis deals with regularization parameter selection methods in the context of Tikhonov-type regularization with Poisson distributed data, in particular the reconstruction of images, as well as with the identification of the volatility surface from observed option prices.
In Part I we examine the choice of the regularization parameter when reconstructing an image, which is disturbed by Poisson noise, with Tikhonov-type regularization. This type of regularization is a generalization of the classical Tikhonov regularization in the Banach space setting and often called variational regularization. After a general consideration of Tikhonov-type regularization for data corrupted by Poisson noise, we examine the methods for choosing the regularization parameter numerically on the basis of two test images and real PET data.
In Part II we consider the estimation of the volatility function from observed call option prices with the explicit formula which has been derived by Dupire using the Black-Scholes partial differential equation. The option prices are only available as discrete noisy observations so that the main difficulty is the ill-posedness of the numerical differentiation. Finite difference schemes, as regularization by discretization of the inverse and ill-posed problem, do not overcome these difficulties when they are used to evaluate the partial derivatives. Therefore we construct an alternative algorithm based on the weak formulation of the dual Black-Scholes partial differential equation and evaluate the performance of the finite difference schemes and the new algorithm for synthetic and real option prices.
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Studies on two specific inverse problems from imaging and financeRückert, Nadja 16 July 2012 (has links)
This thesis deals with regularization parameter selection methods in the context of Tikhonov-type regularization with Poisson distributed data, in particular the reconstruction of images, as well as with the identification of the volatility surface from observed option prices.
In Part I we examine the choice of the regularization parameter when reconstructing an image, which is disturbed by Poisson noise, with Tikhonov-type regularization. This type of regularization is a generalization of the classical Tikhonov regularization in the Banach space setting and often called variational regularization. After a general consideration of Tikhonov-type regularization for data corrupted by Poisson noise, we examine the methods for choosing the regularization parameter numerically on the basis of two test images and real PET data.
In Part II we consider the estimation of the volatility function from observed call option prices with the explicit formula which has been derived by Dupire using the Black-Scholes partial differential equation. The option prices are only available as discrete noisy observations so that the main difficulty is the ill-posedness of the numerical differentiation. Finite difference schemes, as regularization by discretization of the inverse and ill-posed problem, do not overcome these difficulties when they are used to evaluate the partial derivatives. Therefore we construct an alternative algorithm based on the weak formulation of the dual Black-Scholes partial differential equation and evaluate the performance of the finite difference schemes and the new algorithm for synthetic and real option prices.
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Methodenentwicklung zur Simulation von Strömungen mit freier Oberfläche unter dem Einfluss elektromagnetischer WechselfelderBeckstein, Pascal 16 February 2018 (has links) (PDF)
Im Bereich der industriellen Metallurgie und Kristallzüchtung treten bei zahlreichen Anwendungen, wo magnetische Wechselfelder zur induktiven Beeinflussung von leitfähigen Werkstoffen eingesetzt werden, auch Strömungen mit freier Oberfläche auf. Das Anwendungsspektrum reicht dabei vom einfachen Aufschmelzen eines Metalls in einem offenen Tiegel bis hin zur vollständigen Levitation. Auch der sogenannte RGS-Prozess, ein substratbasiertes Kristallisationsverfahren zur Herstellung siliziumbasierter Dünnschichtmaterialien, ist dafür ein Beispiel. Um bei solchen Prozessen die Interaktion von Magnetfeld und Strömung zu untersuchen, ist die numerische Simulationen ein wertvolles Hilfsmittel. Für beliebige dreidimensionale Probleme werden entsprechende Berechnungen bisher durch eine externe Kopplung kommerzieller Programme realisiert, die für Magnetfeld und Strömung jeweils unterschiedliche numerische Techniken nutzen. Diese Vorgehensweise ist jedoch im Allgemeinen mit unnötigem Rechenaufwand verbunden. In dieser Arbeit wird ein neu entwickelter Methodenapparat auf Basis der FVM vorgestellt, mit welchem sich diese Art von Berechnungen effizient durchführen lassen. Mit der Implementierung dieser Methoden in foam-extend, einer erweiterten Version der quelloffenen Software OpenFOAM, ist daraus ein leistungsfähiges Werkzeug in Form einer freien Simulationsplattform entstanden, welches sich durch einen modularen Aufbau leicht erweitern lässt. Mit dieser Plattform wurden in foam-extend auch erstmalig dreidimensionale Induktionsprozesse im Frequenzraum gelöst.
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Methodenentwicklung zur Simulation von Strömungen mit freier Oberfläche unter dem Einfluss elektromagnetischer WechselfelderBeckstein, Pascal 08 January 2018 (has links)
Im Bereich der industriellen Metallurgie und Kristallzüchtung treten bei zahlreichen Anwendungen, wo magnetische Wechselfelder zur induktiven Beeinflussung von leitfähigen Werkstoffen eingesetzt werden, auch Strömungen mit freier Oberfläche auf. Das Anwendungsspektrum reicht dabei vom einfachen Aufschmelzen eines Metalls in einem offenen Tiegel bis hin zur vollständigen Levitation. Auch der sogenannte RGS-Prozess, ein substratbasiertes Kristallisationsverfahren zur Herstellung siliziumbasierter Dünnschichtmaterialien, ist dafür ein Beispiel. Um bei solchen Prozessen die Interaktion von Magnetfeld und Strömung zu untersuchen, ist die numerische Simulationen ein wertvolles Hilfsmittel. Für beliebige dreidimensionale Probleme werden entsprechende Berechnungen bisher durch eine externe Kopplung kommerzieller Programme realisiert, die für Magnetfeld und Strömung jeweils unterschiedliche numerische Techniken nutzen. Diese Vorgehensweise ist jedoch im Allgemeinen mit unnötigem Rechenaufwand verbunden. In dieser Arbeit wird ein neu entwickelter Methodenapparat auf Basis der FVM vorgestellt, mit welchem sich diese Art von Berechnungen effizient durchführen lassen. Mit der Implementierung dieser Methoden in foam-extend, einer erweiterten Version der quelloffenen Software OpenFOAM, ist daraus ein leistungsfähiges Werkzeug in Form einer freien Simulationsplattform entstanden, welches sich durch einen modularen Aufbau leicht erweitern lässt. Mit dieser Plattform wurden in foam-extend auch erstmalig dreidimensionale Induktionsprozesse im Frequenzraum gelöst.
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