Author: Olga Lepsky
Publisher:
ISBN:
Category :
Languages : en
Pages : 224

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Author: Timothy J. Barth
Publisher: Springer Science & Business Media
ISBN: 366203882X
Category : Mathematics
Languages : en
Pages : 594

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The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining chal lenges facing the field of computational fluid dynamics. In structural me chanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the com putation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order ac curacy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence sug gests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Cen ter. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18,1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25,1998 at the NASA Ames Research Center in the United States.

Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 834

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Author: Yves Achdou
Publisher: Springer
ISBN: 3642364330
Category : Mathematics
Languages : en
Pages : 316

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These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).

Author: Adriano Festa
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659140532
Category :
Languages : en
Pages : 128

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Book Description
This book deals with the development and the analysis of numerical methods for the resolution of first order nonlinear differential equations of Hamilton-Jacobi type on irregular data. These equations arises for example in the study of front propagation via the level set methods, the Shape-from-Shading problem and, in general, in Control theory. Our contribution to the numerical approximation of Hamilton-Jacobi equations consists in the proposal of some semiLagrangian schemes for different kind of discontinuous Hamiltonian and in an analysis of their convergence and a comparison of the results on some test problems. In particular we will approach with an eikonal equation with discontinuous coefficients in a well posed case of existence of Lipschitz continuous solutions. Furthermore, we propose a semiLagrangian scheme also for a Hamilton-Jacobi equation of a eikonal type on a ramified space, for example a graph. This is a not classical domain and only in last years there are developed a systematic theory about this. We present, also, some applications of our results on several problems arise from applied sciences.

Author: Roger Temam
Publisher: Elsevier
ISBN: 1483256855
Category : Mathematics
Languages : en
Pages : 539

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Book Description
Navier-Stokes Equations: Theory and Numerical Analysis focuses on the processes, methodologies, principles, and approaches involved in Navier-Stokes equations, computational fluid dynamics (CFD), and mathematical analysis to which CFD is grounded. The publication first takes a look at steady-state Stokes equations and steady-state Navier-Stokes equations. Topics include bifurcation theory and non-uniqueness results, discrete inequalities and compactness theorems, existence and uniqueness theorems, discretization of Stokes equations, existence and uniqueness for the Stokes equations, and function spaces. The text then examines the evolution of Navier-Stokes equations, including linear case, compactness theorems, alternate proof of existence by semi-discretization, and discretization of the Navier-Stokes equations. The book ponders on the approximation of the Navier-Stokes equations by the projection and compressibility methods; properties of the curl operator and application to the steady-state Navier-Stokes equations; and implementation of non-conforming linear finite elements. The publication is a valuable reference for researchers interested in the theory and numerical analysis of Navier-Stokes equations.

Author: Songting Luo
Publisher:
ISBN: 9781109153477
Category :
Languages : en
Pages : 145

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Book Description
Crandall and Lions [23] introduced the concept of viscosity solutions which provides a foundation for studying the Hamilton-Jacobi equations both theoretically and numerically. Ever since then, computing the viscosity solutions numerically has become very important in a variety of applications. A lot of numerical methods have been developed to compute the viscosity solutions. We study the convergence of classical monotone upwind schemes, for example the fast sweeping method, for static convex Hamilton-Jacobi equations by analyzing a contraction property of such schemes. Heuristic error estimate is discussed, and the convergence proof through the Hopf formula in control theory is also studied. Monotone upwind schemes are at most first order [51]. In order to improve the accuracy when there is source singularity, we introduce a new fast sweeping method for the factored Eikonal equation, which improves the accuracy of original fast sweeping method on the Eikonal equation by resolving the source singularity with an underlying correction function. This new factorization idea comes from problems in geosciences. And it provides a possible procedure for source singularity resolution in other problems. Furthermore, high order schemes are also important in many applications, for example the high frequency wave propagation. The ENO or WENO technique seems to be the popular one. But methods based on ENO or WENO are often slower to converge. They are based on direction by direction approximations with wide stencils to capture smoother approximations of second derivatives. We develop a compact upwind second order scheme for the Eikonal equations by observing a superconvergence phenomena of classical monotone upwind schemes: the numerical gradient of such first order schemes is also first order. The new second order scheme combines this phenomena with the Lagrangian structure of the equations. The stencil can be reduced, and it is upwind. As an application of the fast sweeping method, we apply the method in computer vision by introducing a distance-ordered-homotopic thinning algorithm for computing the skeleton of an object represented by point clouds. This algorithm uses the closest point information calculated efficiently by the fast sweeping method. Further possible ideas on developing fast sweeping methods for static non-convex Hamilton-Jacobi equations are also discussed in the conclusion.

Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1460

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Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Author: Roger Temam
Publisher: North-Holland
ISBN:
Category : Navier-Stokes equations
Languages : en
Pages : 522

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Book Description
This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof. It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.

Author: Hiroyoshi Mitake
Publisher: Springer
ISBN: 3319542087
Category : Mathematics
Languages : en
Pages : 233

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Book Description
Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge–Ampère and linearized Monge–Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge–Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry. Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton–Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the nonlinear adjoint method, is introduced. The appendix offers a short introduction to the theory of viscosity solutions of first-order Hamilton–Jacobi equations.