This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem of its spurious-free approximations. Treatment of unbounded domains by Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML) is described and analyzed in a separate chapter. The two last chapters deal with time approximation including local time-stepping and with the study of some complex models, i.e. acoustics in flow, gravity waves and vibrating thin plates. Throughout, emphasis is put on the accuracy and computational efficiency of the methods, with attention brought to their practical aspects.
This monograph also covers in details the theoretical foundations and numerical analysis of these methods. As a result, this monograph will be of interest to practitioners, researchers, engineers and graduate students involved in the numerical simulation
Описание: Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations.
Автор: Jan S. Hesthaven; Tim Warburton Название: Nodal Discontinuous Galerkin Methods ISBN: 1441924639 ISBN-13(EAN): 9781441924636 Издательство: Springer Рейтинг: Цена: 9083.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Mathematicsisplayinganevermoreimportantroleinthephysicalandbiol- ical sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and tea- ing, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose ofthistextbookseriesistomeetthecurrentandfutureneedsoftheseadvances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mat- matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden Providence, Rhode Island L. Sirovich College Park, Maryland S.S. Antman Preface The algorithms, methods, and Matlab implementations described in this text have been developed during almost a decade of collaboration. During this time we have worked to simplify the basic methods and make the ideas more accessible to a broad audience. Many people, both students and colleagues, have helped during the development of this project and we are grateful for all their suggestions and input.
Описание: The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering.
Описание: Offers an introduction to the discontinuous finite element method. This book provides a review of the fundamental laws and equations governing thermal and fluid systems. It also explains mesh generation and adaptivity, parellelization algorithms and error analysis.
Автор: Qingjie Cao; Alain L?ger Название: A Smooth and Discontinuous Oscillator ISBN: 3662530929 ISBN-13(EAN): 9783662530924 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Background: Nonlinear Systems.- An Smooth and Discontinuous (SD) Oscillator.- Bifurcation Behaviour.- Periodic Motions of the Perturbed SD Oscillator.- The Exact Solutions.- Chaotic Motions of the SD Oscillator.- Experimental Investigation of the SD Oscillator.- Applications in Structural Dynamics.- Applications in Engineering Isolation.- Challenges and the Open Problems.
Автор: Yury V. Orlov Название: Discontinuous Systems ISBN: 1849968098 ISBN-13(EAN): 9781849968096 Издательство: Springer Рейтинг: Цена: 20896.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book devoted to the theory of discontinuous dynamic systems requires no background in the field. It develops nonsmooth stability analysis and discontinuous control synthesis based on novel modeling of discontinuous dynamic systems.
Описание: 1 INTRODUCTION.- 1.1 Geological and computational background.- 1.2 Outline.- 2 DISCONTINUOUS GALERKIN METHODS.- 2.1 Preliminaries.- 2.2 Construction of IPG Methods.- 2.3 Computation Tools for Integral Terms.- 2.4 Effect of Penalty Parameter.- 2.5 Problems with Convection.- 3 ELLIPTIC PROBLEMS WITH ADAPTIVITY.- 3.1 Model Elliptic Problem.- 3.2 Adaptivity.- 3.3 Solution of Linearized Systems.- 3.4 Comparison with Galerkin Least Squares FEM (GLSFEM).- 3.5 Numerical Examples.- 4 PARABOLIC PROBLEMS WITH TIME-SPACE ADAPTIVITY.- 4.1 Preliminaries and Model Equation.- 4.2 Semi-Discrete and Fully Discrete Formulations.- 4.3 Time-Space Adaptivity for Non-Stationary Problems.- 4.4 Solution of Fully Discrete System.- 4.5 Numerical Examples.-REFERENCES.
Автор: Bernardo Cockburn; George E. Karniadakis; Chi-Wang Название: Discontinuous Galerkin Methods ISBN: 3642640982 ISBN-13(EAN): 9783642640988 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing.
Автор: Marat Akhmet; Enes Y?lmaz Название: Neural Networks with Discontinuous/Impact Activations ISBN: 1461485657 ISBN-13(EAN): 9781461485650 Издательство: Springer Рейтинг: Цена: 18284.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This monograph examines a wide range of neural networks models with discontinuities, including impulsive differential equations, differential equations with piecewise constant arguments, and models of mixed type.
Автор: V?t Dolej??; Miloslav Feistauer Название: Discontinuous Galerkin Method ISBN: 3319192663 ISBN-13(EAN): 9783319192666 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations.
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