Finite element and discontinuous Galerkin methods for transient wave equations
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...
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| Main Authors | , |
|---|---|
| Format | Electronic eBook |
| Language | English |
| Published |
Dordrecht :
Springer,
[2016]
|
| Series | Scientific computation.
|
| Subjects | |
| Online Access | Full text |
| ISBN | 9789401777612 9789401777599 |
| ISSN | 1434-8322 |
| Physical Description | 1 online resource (xvii, 381 pages) : illustrations (some color) |
Cover
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| 100 | 1 | |a Cohen, Gary C., |d 1952- |e author. | |
| 245 | 1 | 0 | |a Finite element and discontinuous Galerkin methods for transient wave equations / |c Gary Cohen, Sébastien Pernet. |
| 264 | 1 | |a Dordrecht : |b Springer, |c [2016] | |
| 264 | 4 | |c ©2017 | |
| 300 | |a 1 online resource (xvii, 381 pages) : |b illustrations (some color) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a počítač |b c |2 rdamedia | ||
| 338 | |a online zdroj |b cr |2 rdacarrier | ||
| 490 | 1 | |a Scientific computation, |x 1434-8322 | |
| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a Foreword; Preface; Contents; 1 Classical Continuous Models and Their Analysis; 1.1 The Basic Equations; 1.1.1 The Acoustics Equation; 1.1.2 Maxwell's Equations; 1.1.3 The Linear Elastodynamics System; 1.1.4 Boundary Conditions; 1.2 Functional Issues; 1.2.1 Some Functional Spaces; 1.2.2 Variational Formulations; 1.2.3 Energy Identities; 1.2.4 Well-Posedness Results of Waves Equations; 1.3 Plane Wave Solutions; 1.3.1 A General Solution of the Homogeneous Wave Equation; 1.3.2 Application to Maxwell's Equations; 1.3.3 The 2D Case; 1.3.4 Application to the Isotropic Linear Elastodynamics System. | |
| 505 | 8 | |a 2.5 Tetrahedral and Triangular Edge Elements2.5.1 Mixed Formulation; 2.5.2 A First Family; 2.5.3 A Second Family; 2.5.4 Tetrahedral Mass-Lumped Edge Elements; 2.5.5 Triangular Mass-Lumped Edge Elements; 2.6 Hexahedral and Quadrilateral Edge Elements; 2.6.1 First Family; 2.6.2 Second Family; 2.7 H(div) Finite Elements; 2.7.1 Tetrahedral and Triangular Elements; 2.7.2 Hexahedral and Quadrilateral Elements; 2.8 Other Mixed Elements; 2.8.1 Pyramidal and Prismatic Edge Elements; 2.8.2 Pyramidal and Prismatic H(div) Elements; References. | |
| 505 | 8 | |a 3 Hexahedral and Quadrilateral Spectral Elements for Acoustic Waves3.1 Second-Order Formulation of the Acoustics Equation; 3.1.1 The Continuous and Approximate Problem; 3.1.2 Discretization of the Integrals; 3.2 First-Order Formulation of the Acoustics Equation; 3.2.1 The Mixed Formulation; 3.2.2 The Mass Matrices; 3.2.3 The Stiffness Matrices; 3.3 Comparison of the Methods; 3.3.1 Matrix Formulation; 3.3.2 A Theorem of Equivalence; 3.3.3 Comparison of the Costs; 3.4 Dispersion Relation; 3.4.1 The Continuous Equation; 3.4.2 A Didactic Case: The P1 Approximation. | |
| 505 | 8 | |a 3.4.3 The Concept of Numerical Dispersion3.4.4 P2 Approximation; 3.4.5 P3 and Higher-Order Approximations; 3.4.6 Extension to Higher Dimensions; 3.5 Reflection-Transmission by a Discontinuous Interface; 3.5.1 The Continuous Problem; 3.5.2 FEM Approximation of the Heterogeneous Wave Equation; 3.5.3 Taylor Expansion of the Wavenumber; 3.5.4 Interface Between Two Elements; 3.5.5 Interface at an Interior Point; 3.5.6 Extension to Higher-Order Approximations; 3.5.7 A Two-Layer Experiment; 3.6 hp-a priori Error Estimates; 3.6.1 Some Properties of Meshes. | |
| 506 | |a Plný text je dostupný pouze z IP adres počítačů Univerzity Tomáše Bati ve Zlíně nebo vzdáleným přístupem pro zaměstnance a studenty | ||
| 520 | |a 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 of waves. | ||
| 590 | |a SpringerLink |b Springer Complete eBooks | ||
| 650 | 0 | |a Finite element method. | |
| 650 | 0 | |a Galerkin methods. | |
| 655 | 7 | |a elektronické knihy |7 fd186907 |2 czenas | |
| 655 | 9 | |a electronic books |2 eczenas | |
| 700 | 1 | |a Pernet, Sébastien, |e author. | |
| 776 | 0 | 8 | |i Erscheint auch als: |n Druck-Ausgabe |t Cohen, Gary. Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations |
| 830 | 0 | |a Scientific computation. | |
| 856 | 4 | 0 | |u https://proxy.k.utb.cz/login?url=https://link.springer.com/10.1007/978-94-017-7761-2 |
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