Andreas prohl (45 Ergebnisse)
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Paperback. Zustand: new. Paperback. This book is on the construction and convergence analysis of implementable algorithms to approximate the optimal control of a stochastic linear-quadratic optimal control problem (SLQ problem, for short) subject to a stochastic PDE. If compared to finite dimensional stochastic control theory, t…he increased complexity due to high-dimensionality requires new numerical concepts to approximate SLQ problems; likewise, well-established discretization and numerical optimization strategies from infinite dimensional deterministic control theory need fundamental changes to properly address the optimality system, where to approximate the solution of a backward stochastic PDE is conceptually new. The linear-quadratic structure of SLQ problems allows two equivalent analytical approaches to characterize its minimum: open loop is based on Pontryagins maximum principle, and closed loop utilizes the stochastic Riccati equation in combination with the feedback control law. The authors will discuss why, in general, complexities of related numerical schemes differ drastically, and when which direction should be given preference from an algorithmic viewpoint. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
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Softcover. Zustand: gut. Auflage: 1 (2001). The objective of this monograph is a numerical analysis of the well-accepted models of Landau, Lifhitz an Gilbert for (electrically conducting) ferromagnets. Part I discusses convergence behavior of different finite element schemes for solving the stationary problem. Part II deals with… numerical analyses of different penalization projection strategies in nonstationary micromagnetism; it closes with a chapter on nematic liquid crystals to show applicability of these new methods to further applications. Content: I: Numerical Stationary Micromagnetism - Direct Minimization - Convexified Micromagnetism - Relaxed Micromagnetism using Young Measures - II: Numerical Nonstationary Micromagnetism - The Landau-Lifshitz-Gilbert Equation - The Maxwell-Landau-Lifshitz-Gilbert Equation - Nematic Liquid Crystals - Summary and Outlook Reihe/Serie Advances in Numerical Mathematics Zusatzinfo XVIII, 304 p. 93 illus. Verlagsort Wiesbaden Sprache englisch Maße 170 x 244 mm Mathematik Informatik Mathe Wahrscheinlichkeit Kombinatorik Technik Advances in Numerical Mathematics Direct Minimization Finite Element Method Wahrscheinlichkeitstheorie Stochastik Mathematische Statistik magnetic material magnetism Magnetismus Micromagnetism Model Nematic Liquid Crystals Numerical Mathematics Numerical Nonstationary Numerical Stationary Relaxed Micromagnetism ISBN-10 3-519-00358-9 3519003589 ISBN-13 978-3-519-00358-8 9783519003588 Computational Micromagnetism Advances in Numerical Mathematics Andreas Prohl In englischer Sprache. 304 pages. 23,8 x 17 x 1,6 cm.
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Taschenbuch. Zustand: Neu. Numerical Methods for Optimal Control Problems with SPDEs | Andreas Prohl (u. a.) | Taschenbuch | SpringerBriefs on PDEs and Data Science | x | Englisch | 2026 | Springer | EAN 9789819544684 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hart…mann[at]springer[dot]com | Anbieter: preigu.
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Projection methods had been introduced in the late sixties by A. Chorin and R. Teman to decouple the computation of velocity and pressure within the time-stepping for solving the nonstationary Navier-Stokes equations. Despite the good performance of…projection methods in practical computations, their success remained somewhat mysterious as the operator splitting implicitly introduces a nonphysical boundary condition for the pressure. The objectives of this monograph are twofold. First, a rigorous error analysis is presented for existing projection methods by means of relating them to so-called quasi-compressibility methods (e.g. penalty method, pressure stabilzation method, etc.). This approach highlights the intrinsic error mechanisms of these schemes and explains the reasons for their limitations. Then, in the second part, more sophisticated new schemes are constructed and analyzed which are exempted from most of the deficiencies of the classical projection and quasi-compressibility methods. '. this book should be mandatory reading for applied mathematicians specializing in computational fluid dynamics.' J.-L.Guermond. Mathematical Reviews, Ann Arbor.
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - In this work, we study numerical issues related to a common mathematical model which describes ferromagnetic materials, both in a stationary and non stationary context. Electromagnetic effects are accounted for in an extended model to study nonstatio…nary magneto-electronics. The last part deals with the numerical analysis of the commonly used Ericksen-Leslie model to study the fluid flow of nematic liquid crystals which find applications in display technologies, for example. All these mathematical models to describe different microstructural phe nomena share common features like (i) strong nonlinearities, and (ii) non convex side constraints (i.e., I m I = 1, almost everywhere in w C JRd, for the order parameter m : w -+ JRd). One key issue in numerical modeling of such problems is to make sure that the non-convex constraint is fulfilled for computed solutions. We present and analyze different solution strategies to deal with the variational problem of stationary micromagnetism, which builds part I of the book: direct minimization, convexification, and relaxation using Young measure-valued solutions. In particular, we address the following points: - Direct minimization: A spatial triangulation 'generates an artificial exchange energy contribution' in the discretized minimizing problem which may pollute physically relevant exchange energy contributions; its minimizers exhibit multiple scales (with branching structures near the boundary of the ferromagnet) and are difficult to be computed efficiently. We exploit this observation to construct an adaptive scheme which better resolves multiple scale structures (cubic ferromagnets).
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Hardback. Zustand: New. 1st. This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). The first part of the book studies the role of noise in finite ensembles of nanomagnetic particles: we show geometric ergodicity of a unique invari…ant measure of Gibbs type and study related properties of approximations of the SLLG, including time discretization and Ginzburg-Landau type penalization. In the second part we propose an implementable space-time discretization using random walks to construct a weak martingale solution of the corresponding stochastic partial differential equation which describes the magnetization process of infinite spin ensembles. The last part of the book is concerned with a macroscopic deterministic equation which describes temperature effects on macro-spins, i.e. expectations of the solutions to the SLLG. Furthermore, comparative computational studies with the stochastic model are included. We use constructive tools such as e.g. finite element methods to derive the theoretical results, which are then used for computational studies. The numerical experiments motivate an interesting interplay between inherent geometric and stochastic effects of the SLLG which still lack a rigorous analytical understanding: the role of space-time white noise, possible finite time blow-up behavior of solutions, long-time asymptotics, and effective dynamics.
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Hardback. Zustand: New. 1st. This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). The first part of the book studies the role of noise in finite ensembles of nanomagnetic particles: we show geometric ergodicity of a unique invari…ant measure of Gibbs type and study related properties of approximations of the SLLG, including time discretization and Ginzburg-Landau type penalization. In the second part we propose an implementable space-time discretization using random walks to construct a weak martingale solution of the corresponding stochastic partial differential equation which describes the magnetization process of infinite spin ensembles. The last part of the book is concerned with a macroscopic deterministic equation which describes temperature effects on macro-spins, i.e. expectations of the solutions to the SLLG. Furthermore, comparative computational studies with the stochastic model are included. We use constructive tools such as e.g. finite element methods to derive the theoretical results, which are then used for computational studies. The numerical experiments motivate an interesting interplay between inherent geometric and stochastic effects of the SLLG which still lack a rigorous analytical understanding: the role of space-time white noise, possible finite time blow-up behavior of solutions, long-time asymptotics, and effective dynamics.
Sprache: Englisch
Verlag: Vieweg+Teubner Verlag, Vieweg+Teubner Verlag Dez 2001, 2001
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In this work, we study numerical issues related to a common mathematical model which describes ferromagnetic materials, both in a stationary and non stationary context. Electromagnetic effects are accounted for in an extended model to… study nonstationary magneto-electronics. The last part deals with the numerical analysis of the commonly used Ericksen-Leslie model to study the fluid flow of nematic liquid crystals which find applications in display technologies, for example. All these mathematical models to describe different microstructural phe nomena share common features like (i) strong nonlinearities, and (ii) non convex side constraints (i.e., I m I = 1, almost everywhere in w C JRd, for the order parameter m : w -+ JRd). One key issue in numerical modeling of such problems is to make sure that the non-convex constraint is fulfilled for computed solutions. We present and analyze different solution strategies to deal with the variational problem of stationary micromagnetism, which builds part I of the book: direct minimization, convexification, and relaxation using Young measure-valued solutions. In particular, we address the following points: - Direct minimization: A spatial triangulation 'generates an artificial exchange energy contribution' in the discretized minimizing problem which may pollute physically relevant exchange energy contributions; its minimizers exhibit multiple scales (with branching structures near the boundary of the ferromagnet) and are difficult to be computed efficiently. We exploit this observation to construct an adaptive scheme which better resolves multiple scale structures (cubic ferromagnets). 324 pp. Englisch.
Sprache: Englisch
Verlag: Vieweg+Teubner, Vieweg+Teubner Verlag Jan 1997, 1997
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Projection methods had been introduced in the late sixties by A. Chorin and R. Teman to decouple the computation of velocity and pressure within the time-stepping for solving the nonstationary Navier-Stokes equations. Despite the good… performance of projection methods in practical computations, their success remained somewhat mysterious as the operator splitting implicitly introduces a nonphysical boundary condition for the pressure. The objectives of this monograph are twofold. First, a rigorous error analysis is presented for existing projection methods by means of relating them to so-called quasi-compressibility methods (e.g. penalty method, pressure stabilzation method, etc.). This approach highlights the intrinsic error mechanisms of these schemes and explains the reasons for their limitations. Then, in the second part, more sophisticated new schemes are constructed and analyzed which are exempted from most of the deficiencies of the classical projection and quasi-compressibility methods. '. this book should be mandatory reading for applied mathematicians specializing in computational fluid dynamics.' J.-L.Guermond. Mathematical Reviews, Ann Arbor 294 pp. Englisch.
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book is on the construction and convergence analysis of implementable algorithms to approximate the optimal control of a stochastic linear-quadratic optimal control problem (SLQ problem, for short) subject to a stochastic PDE. If… compared to finite dimensional stochastic control theory, the increased complexity due to high-dimensionality requires new numerical concepts to approximate SLQ problems; likewise, well-established discretization and numerical optimization strategies from infinite dimensional deterministic control theory need fundamental changes to properly address the optimality system, where to approximate the solution of a backward stochastic PDE is conceptually new. The linear-quadratic structure of SLQ problems allows two equivalent analytical approaches to characterize its minimum: open loop is based on Pontryagin s maximum principle, and closed loop utilizes the stochastic Riccati equation in combination with the feedback control law. The authors will discuss why, in general, complexities of related numerical schemes differ drastically, and when which direction should be given preference from an algorithmic viewpoint. 142 pp. Englisch.
