Multidimensional Hyperbolic Problems and Computations

Multidimensional Hyperbolic Problems and Computations PDF

Author: James Glimm

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 399

ISBN-13: 1461391210

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This IMA Volume in Mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAVES. We are grateful to the Scientific Commit tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the Work shop Organizers, Andrew Majda and James Glimm, for bringing together many of the major figures in a variety of research fields connected with multidimensional hyperbolic problems. A vner Friedman Willard Miller PREFACE A primary goal of the IMA workshop on Multidimensional Hyperbolic Problems and Computations from April 3-14, 1989 was to emphasize the interdisciplinary nature of contemporary research in this field involving the combination of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation, and experiments. The twenty-six papers in this volume span a wide cross-section of this research including some papers on the kinetic theory of gases and vortex sheets for incompressible flow in addition to many papers on systems of hyperbolic conservation laws. This volume includes several papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves.

Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems

Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems PDF

Author: Sergey I. Kabanikhin

Publisher: Walter de Gruyter

Published: 2013-04-09

Total Pages: 188

ISBN-13: 3110960710

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The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection method and prove theorems of convergence, conditional stability, and other properties of the mentioned methods.

Finite Volume Methods for Hyperbolic Problems

Finite Volume Methods for Hyperbolic Problems PDF

Author: Randall J. LeVeque

Publisher: Cambridge University Press

Published: 2002-08-26

Total Pages: 582

ISBN-13: 1139434187

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This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.

Hyperbolic Problems: Theory, Numerics And Applications (In 2 Volumes)

Hyperbolic Problems: Theory, Numerics And Applications (In 2 Volumes) PDF

Author: Tatsien Li

Publisher: World Scientific

Published: 2012-09-28

Total Pages: 793

ISBN-13: 9814417106

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This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and related numerical algorithms.This book contains 80 original research and review papers which are written by leading researchers and promising young scientists, which cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of ';Hyperbolic Partial Differential Equations';. It is aimed at mathematicians, researchers in applied sciences and graduate students.

Lecture Notes on Numerical Methods for Hyperbolic Equations

Lecture Notes on Numerical Methods for Hyperbolic Equations PDF

Author: Elena Vázquez-Cendón

Publisher: CRC Press

Published: 2011-05-23

Total Pages: 0

ISBN-13: 9780415683883

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This volume contains the lecture notes of the Short Course on Numerical Methods for Hyperbolic Equations (Faculty of Mathematics, University of Santiago de Compostela, Spain, 2-4 July 2011). The course was organized in recognition of Prof. Eleuterio Toro’s contribution to education and training on numerical methods for partial differential equations and was organized prior to the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications, which honours Professor Toro in the month of his 65th birthday. These lecture notes on selected topics in numerical methods for hyperbolic equations are from renowned academics in both theoretical and applied fields, and include contributions on: Nonlinear hyperbolic conservation laws First order schemes for the Euler equations High-order accuracy: monotonicity and non-linear methods High-order schemes for multidimensional hyperbolic problems A numerical method for the simulation of turbulent mixing and its basis in mathematical theory Lectures Notes on Numerical Methods for Hyperbolic Equations is intended primarily for research students and post-doctoral research fellows. Some background knowledge on the basics of the theoretical aspects of the partial differential equations, their physical meaning and discretization methods is assumed.

Hyperbolic Problems: Theory, Numerics, Applications - Proceedings Of The Fifth International Conference

Hyperbolic Problems: Theory, Numerics, Applications - Proceedings Of The Fifth International Conference PDF

Author: James Glimm

Publisher: World Scientific

Published: 1996-03-14

Total Pages: 510

ISBN-13: 9814548588

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The intellectual center of this proceedings volume is the subject of conservation laws. Conservation laws are the most basic model of many continuum processes, and for this reason they govern the motion of fluids, solids, and plasma. They are basic to the understanding of more complex modeling issues, such as multiphase flow, chemically reacting flow, and non-equilibrium thermodynamics. Equations of this type also arise in novel and unexpected areas, such as the pattern recognition and image processing problem of edge enhancement and detection. The articles in this volume address the entire range of the study of conservation laws, including the fundamental mathematical theory, familiar and novel applications, and the numerical problem of finding effective computational algorithms for the solution of these problems.

Hyperbolic Problems: Theory, Numerics and Applications

Hyperbolic Problems: Theory, Numerics and Applications PDF

Author: Eitan Tadmor

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 361

ISBN-13: 0821847295

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The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 'HYP2008', was held at the University of Maryland from June 9-13, 2008. This book, the first in a two-part volume, contains nineteen papers based on plenary and invited talks presented at the conference.

Theory, Numerics and Applications of Hyperbolic Problems I

Theory, Numerics and Applications of Hyperbolic Problems I PDF

Author: Christian Klingenberg

Publisher: Springer

Published: 2018-06-23

Total Pages: 706

ISBN-13: 3319915452

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The first of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.

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