Strong Stability Preserving Runge Kutta And Multistep Time Discretizations
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Strong Stability Preserving Runge Kutta And Multistep Time Discretizations
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Author : Sigal Gottlieb
language : en
Publisher: World Scientific
Release Date : 2011
Strong Stability Preserving Runge Kutta And Multistep Time Discretizations written by Sigal Gottlieb and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This book captures the state-of-the-art in the field of Strong Stability Preserving (SSP) time stepping methods, which have significant advantages for the time evolution of partial differential equations describing a wide range of physical phenomena. This comprehensive book describes the development of SSP methods, explains the types of problems which require the use of these methods and demonstrates the efficiency of these methods using a variety of numerical examples. Another valuable feature of this book is that it collects the most useful SSP methods, both explicit and implicit, and presents the other properties of these methods which make them desirable (such as low storage, small error coefficients, large linear stability domains). This book is valuable for both researchers studying the field of time-discretizations for PDEs, and the users of such methods.
Spectral And High Order Methods For Partial Differential Equations Icosahom 2014
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Author : Robert M. Kirby
language : en
Publisher: Springer
Release Date : 2015-11-26
Spectral And High Order Methods For Partial Differential Equations Icosahom 2014 written by Robert M. Kirby and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-26 with Computers categories.
The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2014), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of papers will provide the reader with a snapshot of the state-of-the-art and help initiate new research directions through the extensive biography.
Handbook Of Numerical Methods For Hyperbolic Problems
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Author : Remi Abgrall
language : en
Publisher: Elsevier
Release Date : 2016-11-17
Handbook Of Numerical Methods For Hyperbolic Problems written by Remi Abgrall and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-17 with Mathematics categories.
Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations. - Provides detailed, cutting-edge background explanations of existing algorithms and their analysis - Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis - Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications - Written by leading subject experts in each field who provide breadth and depth of content coverage
Numerical Techniques For Global Atmospheric Models
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Author : Peter H. Lauritzen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-29
Numerical Techniques For Global Atmospheric Models written by Peter H. Lauritzen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-29 with Mathematics categories.
This book surveys recent developments in numerical techniques for global atmospheric models. It is based upon a collection of lectures prepared by leading experts in the field. The chapters reveal the multitude of steps that determine the global atmospheric model design. They encompass the choice of the equation set, computational grids on the sphere, horizontal and vertical discretizations, time integration methods, filtering and diffusion mechanisms, conservation properties, tracer transport, and considerations for designing models for massively parallel computers. A reader interested in applied numerical methods but also the many facets of atmospheric modeling should find this book of particular relevance.
Computational Science Iccs 2009
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Author : Gabrielle Allen
language : en
Publisher: Springer
Release Date : 2009-05-21
Computational Science Iccs 2009 written by Gabrielle Allen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-21 with Computers categories.
“There is something fascinating about science. One gets such wholesale returns of conjecture out of such a tri?ing investment of fact. ” Mark Twain, Life on the Mississippi The challenges in succeeding with computational science are numerous and deeply a?ect all disciplines. NSF’s 2006 Blue Ribbon Panel of Simulation-Based 1 Engineering Science (SBES) states ‘researchers and educators [agree]: com- tational and simulation engineering sciences are fundamental to the security and welfare of the United States. . . We must overcome di?culties inherent in multiscale modeling, the development of next-generation algorithms, and the design. . . of dynamic data-driven application systems. . . We must determine better ways to integrate data-intensive computing, visualization, and simulation. - portantly,wemustoverhauloureducationalsystemtofostertheinterdisciplinary study. . . The payo?sformeeting these challengesareprofound. ’The International Conference on Computational Science 2009 (ICCS 2009) explored how com- tational sciences are not only advancing the traditional hard science disciplines, but also stretching beyond, with applications in the arts, humanities, media and all aspects of research. This interdisciplinary conference drew academic and industry leaders from a variety of ?elds, including physics, astronomy, mat- matics,music,digitalmedia,biologyandengineering. Theconferencealsohosted computer and computational scientists who are designing and building the - ber infrastructure necessary for next-generation computing. Discussions focused on innovative ways to collaborate and how computational science is changing the future of research. ICCS 2009: ‘Compute. Discover. Innovate. ’ was hosted by the Center for Computation and Technology at Louisiana State University in Baton Rouge.
An Introduction To Element Based Galerkin Methods On Tensor Product Bases
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Author : Francis X. Giraldo
language : en
Publisher: Springer Nature
Release Date : 2020-10-30
An Introduction To Element Based Galerkin Methods On Tensor Product Bases written by Francis X. Giraldo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-30 with Mathematics categories.
This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.
Recent Developments In The Numerics Of Nonlinear Hyperbolic Conservation Laws
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Author : Rainer Ansorge
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-14
Recent Developments In The Numerics Of Nonlinear Hyperbolic Conservation Laws written by Rainer Ansorge and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Technology & Engineering categories.
In January 2012 an Oberwolfach workshop took place on the topic of recent developments in the numerics of partial differential equations. Focus was laid on methods of high order and on applications in Computational Fluid Dynamics. The book covers most of the talks presented at this workshop.
Computational Aerodynamics
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Author : Antony Jameson
language : en
Publisher: Cambridge University Press
Release Date : 2022-09
Computational Aerodynamics written by Antony Jameson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09 with Science categories.
Learn the design and analysis of numerical algorithms for aerodynamics. Ideal for graduates, researchers, and professionals in the field.
Strong Stability Preserving High Order Time Discretization Methods
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Author : Sigal Gottlieb
language : en
Publisher:
Release Date : 2000
Strong Stability Preserving High Order Time Discretization Methods written by Sigal Gottlieb and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Boundary element methods categories.
In this paper we review and further develop a class of strong-stability preserving (SSP) high-order time discretizations for semi-discrete method-of-lines approximations of partial differential equations. Termed TVD (total variation diminishing) time discretizations before this class of high-order time discretization methods preserves the strong-stability properties of first-order Euler time stepping and has proved very useful especially in solving hyperbolic partial differential equations. The new contributions in this paper include the development of optimal explicit SSP linear Runge-Kutta methods, their application to the strong stability of coercive approximations, a systematic study of explicit SSP multi-step methods, and a study of the strong-stability preserving property of implicit Runge-Kutta and multi-step methods.
Numerical Methods For Conservation Laws
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Author : Jan S. Hesthaven
language : en
Publisher: SIAM
Release Date : 2018-01-30
Numerical Methods For Conservation Laws written by Jan S. Hesthaven and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Science categories.
Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material will be available online at publication.