Download or read book Multidimensional Hyperbolic Problems and Computations written by James Glimm and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems written by Sergey I. Kabanikhin and published by Walter de Gruyter. This book was released on 2013-04-09 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finite Volume Methods for Hyperbolic Problems written by Randall J. LeVeque and published by Cambridge University Press. This book was released on 2002-08-26 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Approximation of Hyperbolic Systems of Conservation Laws written by Edwige Godlewski and published by Springer Nature. This book was released on 2021-08-28 with total page 846 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.
Download or read book Hyperbolic Problems written by Michael Fey and published by Springer Science & Business Media. This book was released on 1999 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hyperbolic Problems Theory Numerics and Applications written by Eitan Tadmor and published by American Mathematical Soc.. This book was released on 2009 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hyperbolic Problems Theory Numerics Applications written by Rolf Jeltsch and published by Birkhäuser. This book was released on 2012-12-06 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analytical Approaches to Multidimensional Balance Laws written by Olga S. Rozanova and published by Nova Publishers. This book was released on 2006 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is difficult to overestimate the importance of mathematical investigation of balance laws. They arise in many areas of physics, mechanics, chemistry, biology, social sciences. In this collective book we concentrate in particular on the equations of continuous medium and related to them. As a rule, they are very complicated in their primitive form. An important feature of such equations is a possible formation of singularities even in initially smooth solution within a finite time. The structure of the singularities can be very complex. A natural step in the approach to this problem is the transition, despite the three-dimensionality of our world, to spatially one-dimensional model. Significant progress has been achieved in this direction. Unfortunately, the methods of the one-dimensional theory, as usual, cannot be adapted to a case of many spatial variables. However, there are many attempts to deal with multidimensional problems. We would like to present some of them. All of the papers are written by outstanding experts, representing various schools in mathematics and mechanics. Each paper is organised as follows: it contains an elementary (as far as it is possible) introduction to a problem, a brief review of previously published results, and then original results of the authors are presented.
Download or read book Nonlinear Hyperbolic Problems Theoretical Applied and Computational Aspects written by Andrea Donato and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hyperbolic Problems Theory Numerics Applications Proceedings Of The Fifth International Conference written by James Glimm and published by World Scientific. This book was released on 1996-03-14 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hyperbolic Problems Theory Numerics And Applications In 2 Volumes written by Li Ta-tsien and published by World Scientific. This book was released on 2012-09-28 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of Differential Equations Evolutionary Equations written by C.M. Dafermos and published by Gulf Professional Publishing. This book was released on 2005-11-30 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations. The main objective is to present clear, rigorous, and in depth surveys on the most important aspects of the present theory.
Download or read book Shock capturing and high order methods for hyperbolic conservation laws written by Jan Glaubitz and published by Logos Verlag Berlin GmbH. This book was released on 2020-03-20 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the numerical treatment of hyperbolic conservation laws. These play an important role in describing many natural phenomena. Challenges in their theoretical as well as numerical study stem from the fact that spontaneous shock discontinuities can arise in their solutions, even in finite time and smooth initial states. Moreover, the numerical treatment of hyperbolic conservations laws involves many different fields from mathematics, physics, and computer science. As a consequence, this thesis also provides contributions to several different fields of research - which are still connected by numerical conservation laws, however. These contributions include, but are not limited to, the construction of stable high order quadrature rules for experimental data, the development of new stable numerical methods for conservation laws, and the investigation and design of shock capturing procedures as a means to stabilize high order numerical methods in the presence of (shock) discontinuities. Jan Glaubitz was born in Braunschweig, Germany, in 1990 and completed his mathematical studies (B.Sc., 2014, M.Sc., 2016, Dr. rer. nat., 2019) at TU Braunschweig. In 2016, he received awards from the German Mathematical Society (DMV) for his master's thesis as well as from the Society of Financial and Economic Mathematics of Braunschweig (VBFWM). In 2017, he was honored with the teaching award "LehrLEO" for the best tutorial at TU Braunschweig. Since 2020, he holds a position as a postdoctoral researcher at Dartmouth College, NH, USA.
Download or read book Nonlinear Hyperbolic Problems Theoretical Applied and Computational Aspects written by Andrea Donato and published by Notes on Numerical Fluid Mechanics and Multidisciplinary Design. This book was released on 1993 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains original papers presented at the Fourth International Conference on Hyperbolic Problems which was held on April 3-8, 1992 in Taormina (Sicily), Italy. The aim of the Conferences in this cycle is to bring together scientists with interest in theo retical, applied and computational aspects of hyperbolic partial differential equations. The contributions, well balanced among these three aspects, deal with: mathematical theory of wave propagation, kinetic theory, existence, uniqueness and stabil ity of solutions, mathematical modeling of physical phenomena, stability and convergence of numerical schemes, multidimensional computational applications, etc. The papers are printed in the authors' alphabetic order following the idea both of mixing together topics of interest to different areas and of considering either theoretical results connected with applied problems or new applications with an essential mathemat ical approach. The Proceedings from the previous Conferences held in St. Etienne (1986), Aachen (1988) and Uppsala (1990) appeared respectively as: * Lecture Notes in Mathematics, 1270, P. Carasso, P. A. Raviart & D. Serre (Eds.), Springer-Verlag (1987) * Notes on Numerical Fluid Mechanics, 24, J. Ballmann & R. Jeltsch (Eds.), Vieweg (1989 ) * Third International Conference on Hyperbolic Problems, B. Engquist & B. Gustafs son (Eds.), Vol. I, II, Studentlitteratur, Uppsala University (1991). The organizers and the editors of the Conference would like to thank the Scientific Committee for the generous support, for suggesting the invited lectures, and for selecting the contributed papers.
Download or read book Handbook of Mathematical Fluid Dynamics written by S. Friedlander and published by Elsevier. This book was released on 2002-07-09 with total page 829 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.
Download or read book Mathematics of Computation 1943 1993 A Half Century of Computational Mathematics written by Walter Gautschi and published by American Mathematical Soc.. This book was released on 1994 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of an International Conference held in Vancouver, B.C., August 1993, to commemorate the 50th anniversary of the founding of the journal Mathematics of Computation. It consisted of a Symposium on Numerical Analysis and a Minisymposium of Computational Number Theory. This proceedings contains 14 invited papers, including two not presented at the conference--an historical essay on integer factorization, and a paper on componentwise perturbation bounds in linear algebra. The invited papers present surveys on the various subdisciplines covered by Mathematics of Computation, in a historical perspective and in a language accessible to a wide audience. The 46 contributed papers address contemporary specialized work. Annotation copyright by Book News, Inc., Portland, OR
Download or read book Hyperbolic Problems Theory Numerics Applications written by Heinrich Freistühler and published by Birkhäuser. This book was released on 2012-12-06 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed. This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.
