An extensively expanded and revised edition of the leading major reference work in computational engineering
The completely updated and extended second edition of Encyclopedia of Computational Mechanics, Second Edition has, once again, been prepared under the guidance of three of the world's foremost experts in the field. It follows the same structure as the first edition, yet has been expanded from three to six full volumes to give readers a more in-depth and complete understanding of the topic.
Volumes 1 & 2 (Fundamentals) contain contributions related to mathematics, mechanics, and computer science, and are structured as discretization methods, treating approximations with finite differences, discrete variational forms, boundary integral equations and further problem-oriented techniques, mesh-based and meshfree discretizations and the generation and visualization of geometry; Isogeometric analysis as well as various direct and iterative solvers; time-dependent parabolic problems and FEMs for the Maxwell equation; further, new chapters on uncertainty quantification and related stochastic solution methods are included.
Volumes 3 & 4 (Solids and Structures) are organized into five different parts, namely, structural behavior; constitutive theories and their implementation; materials and processing; interaction problems; and identification, stochastics, and optimization.
Volumes 5 & 6 (Fluids) build on the fundamentals of the first volumes, and offer four main groups that describe additional basic methodologies used in computational fluid dynamics; cover the various aspects of incompressible viscous flows; focus on compressible fluid dynamics; and address problems involving moving domains and free surfaces, and application areas.
- The single most comprehensive reference on computational mechanics
- 18 new chapters added representing a more than 20% increase over current edition
- Extensive revision plan with major updates to the majority of existing articles
- Covers solid and fluid mechanics, with extensive treatment of FEA and CFD techniques
With contributions from leading experts around the globe, this is an essential and comprehensive reference for any university engineering department or corporation, and contains invaluable, up-to-date content for researchers, students, and practitioners alike.
Table of Contents:
Volume 1: Fundamentals – Part 1
Contributors to Volume 1 ix
Preface xi
1 Fundamentals: Introduction and Survey 1
Erwin Stein
2 Finite Difference Methods 15
Owe Axelsson
3 Interpolation and Quasi-Interpolation in h- and hp-Version Finite Element Spaces 67
Thomas Apel/Jens M. Melenk
4 Finite Element Methods 101
Susanne C. Brenner/Carsten Carstensen
5 Mixed Finite Element Methods 149
Ferdinando Auricchio/L. Beirão da Veiga/F. Brezzi/C. Lovadina
6 Spectral Methods 203
Claudio Canuto/Alfio Quarteroni
7 Mesh Generation and Mesh Adaptivity: Theory and Techniques 219
Paul Louis George/H. Borouchaki/F. Alauzet/P. Laug/A. Loseille/D. Marcum/L. Maréchal
8 Plates and Shells: Asymptotic Expansions and Hierarchical Models 271
Monique Dauge/Erwan Faou/Zohar Yosibash
9 Iterative Solutions of Nonlinear Systems, Solution Manifolds, and Bifurcations 311
Werner C. Rheinboldt
10 Arbitrary Lagrangian–Eulerian Methods 339
Jean Donea/Antonio Huerta/Jean-Philippe Ponthot/Antonio Rodríguez-Ferran
11 Mathematical Foundations of Elastoplastic Deformations in Solids 363
B. Daya Reddy
12 Predictive Computational Science: Computer Predictions in the Presence of Uncertainty 391
John Tinsley Oden/Ivo Babuška/Danial Faghihi
13 Uncertainty Quantification and Bayesian Inversion 417
Hermann G. Matthies
Contents for Volumes 2–6 469
Subject Index 481
Volume 2: Fundamentals – Part 2
Contributors to Volume 2 ix
Preface xi
14 Mathematics of Isogeometric Analysis: A Conspectus 589
Thomas J. R. Hughes/Giancarlo Sangalli
15 Isogeometric Analysis: Representation of Geometry 629
Michael Haberleitner/Bert Jüttler/Michael A. Scott/Derek C. Thomas
16 Meshfree Methods 653
Antonio Huerta/Ted Belytschko/Sonia Fernández-Méndez/Timon Rabczuk/Xiaoying Zhuang/Marino Arroyo
17 Reproducing Kernel Particle Method for Solving Partial Differential Equations 691
Jiun-Shyan Chen/Wing Kam Liu/Michael C. Hillman/Sheng-Wei Chi/Yanping Lian/Miguel A. Bessa
18 Adaptive Wavelet Techniques in Numerical Simulation 735
Albert Cohen/Wolfgang Dahmen/Ronald DeVore
19 Discontinuous Petrov–Galerkin (DPG) Method 777
Leszek Demkowicz/Jay Gopalakrishnan
20 Finite Element Methods for Maxwell’s Equations 793
Leszek Demkowicz
21 Adaptive Computational Methods for Parabolic Problems 813
Kenneth Eriksson/Claes Johnson/A. Logg
22 Boundary Element Methods: Foundation and Error Analysis 841
George C. Hsiao/O. Steinbach/W. L. Wendland
23 Coupling of Boundary Element Methods and Finite Element Methods 903
Ernst P. Stephan
24 Time-Dependent Problems with the Boundary Integral Equation Method 943
Martin Costabel/Francisco-Javier Sayas
25 Linear Algebraic Solvers and Eigenvalue Analysis 967
Henk A. van der Vorst/Cornelis Vuik
26 Multigrid Methods for FEM and BEM Applications 995
Wolfgang Hackbusch
27 Panel Clustering Techniques and Hierarchical Matrices for BEM and FEM 1013
Wolfgang Hackbusch
28 Domain Decomposition Methods and Preconditioning 1031
Vadim G. Korneev/Ulrich Langer
Contents for Volumes 1, 3–6 1069
Subject Index 1081
Volume 3: Solids and Structures – Part 1
Contributors to Volume 3 ix
Preface xi
1 Solids and Structures: Introduction and Survey 1
René de Borst
2 Finite Element Methods for Elasticity with Error-Controlled Discretization and Model Adaptivity 5
Erwin Stein/Marcus Olavi Rüter
3 Model Reduction Methods 101
Francisco Chinesta/Antonio Huerta/Gianluigi Rozza/Karen Willcox
4 The p-Version of the Finite Element and Finite Cell Methods 137
Alexander Düster/Ernst Rank/Barna Szabó
5 Extended Finite Element Methods 173
Nicolas Moës/J. E. Dolbow/N. Sukumar
6 Models and Finite Elements for Thin-Walled Structures 195
Manfred Bischoff/E. Ramm/J. Irslinger
7 Computing with Rotations: Algorithms and Applications 281
Ignacio Romero/Martin Arnold
8 Buckling 309
Eduard Riks
9 Computational Structural Dynamics 339
Gregory M. Hulbert
10 Computational Contact Mechanics with the Finite Element Method 365
L. De Lorenzis/Peter Wriggers/C. Weißenfels
11 Discrete Element Methods 411
Nenad Bićanić
12 Elastoplastic and Viscoplastic Deformations in Solids and Structures 449
Francisco Armero
13 Crystal Plasticity and Evolution of Polycrystalline Microstructure 491
Christian Miehe/Jan Schotte
14 Computational Modeling of Forming Processes 515
D. Perić/D. R. J. Owen
15 Explicit Finite Element Methods for Large Deformation Problems in Solid Mechanics 567
David J. Benson
Contents for Volumes 1, 2, 4–6 611
Subject Index 623
Volume 4: Solids and Structures – Part 2
Contributors to Volume 4 ix
Preface xi
16 Shakedown and Safety Assessment 731
Nestor Zouain
17 Damage, Material Instabilities, and Failure 779
René de Borst/Clemens V. Verhoosel
18 Computational Fracture Mechanics 829
Anthony R. Ingraffea/René de Borst
19 Homogenization Methods and Multiscale Modeling 855
Tarek I. Zohdi
20 Homogenization Methods and Multiscale Modeling: Nonlinear Problems 879
Marc G. D. Geers/Varvara G. Kouznetsova/Karel Matouš/Julien Yvonnet
21 Computational Concrete Mechanics 913
Roman Lackner/Christian Pichler/Roland Traxl/Herbert A. Mang
22 Multifield Problems 965
Bernhard A. Schrefler/L. Simoni/B. Markert
23 Fluid–Structure Interaction Problems 1001
Roger Ohayon/Jean-Sébastien Schotté
24 Acoustics 1013
Lonny L. Thompson/Peter M. Pinsky
25 Computational Geomechanics Including Consolidation 1039
John P. Carter/John C. Small
26 Computational Modeling of Damage and Failures in Composite Laminates 1075
J. N. Reddy/D. H. Robbins
27 Computational Biomechanics of Soft Biological Tissues: Arterial Walls, Hearts Walls, and Ligaments 1117
Gerhard A. Holzapfel
28 Identification of Material Parameters for Constitutive Equations 1165
Rolf Mahnken
29 Stochastic Finite Element Methods 1187
Miguel A. Gutiérrez/Steen Krenk
30 Shape Optimization 1213
Kai-Uwe Bletzinger
31 Topology Optimization 1255
Kurt Maute
32 Boundary Integral Equation Methods for Elastic and Plastic Problems 1289
Marc Bonnet
33 Boundary Element Methods for the Dynamic Analysis of Elastic, Viscoelastic, and Piezoelectric Solids 1323
Lothar Gaul/Martin Kögl/Friedrich Moser/Martin Schanz
Contents for Volumes 1–3, 5, 6 1345
Subject Index 1355
Volume 5: Fluids – Part 1
Contributors to Volume 5 vii
Preface ix
1 Fluids: Introduction and Survey 1
Thomas J. R. Hughes
2 Multiscale and Stabilized Methods 5
Thomas J. R. Hughes/Guglielmo Scovazzi/Leopoldo P. Franca
3 Variational Multiscale Methods in Computational Fluid Dynamics 69
Ramon Codina/Santiago Badia/Joan Baiges/Javier Principe
4 Spectral Element and hp Methods 97
Yue Yu/Robert M. Kirby/George Em Karniadakis
5 Discontinuous Galerkin Methods for Computational Fluid Dynamics 141
Bernado A. Cockburn
6 Finite Volume Methods: Foundation and Analysis 205
Timothy Barth/Raphaèle Herbin/Mario Ohlberger
7 High-Order Methods for CFD 265
R. Abgrall/Mario Ricchiuto
8 Particle Methods in Computational Fluid Dynamics 319
Sergio R. Idelsohn/Eugenio Oñate/Pablo Becker
9 Residual Distribution Schemes: Foundations and Analysis 361
Herman Deconinck/Mario Ricchiuto
10 Vortex Methods 415
G. S. Winckelmans
11 Computational Phase-Field Modeling 439
Hector Gomez/Kristoffer G. van der Zee
12 Incompressible Viscous Flows 475
Rolf Rannacher
13 Computability and Adaptivity in CFD 503
Johan Hoffman/Johan Jansson/Niclas Jansson/Rodrigo Vilela De Abreu/Claes Johnson
Contents for Volumes 1–4, 6 525
Subject Index 537
Volume 6: Fluids – Part 2
Contributors to Volume 6 ix
Preface xi
14 Dynamic Multilevel Methods and Turbulence 645
Thierry Dubois/Francois Jauberteau/Roger M. Temam
15 Turbulence Direct Numerical Simulation and Large-Eddy Simulation 721
Pierre Sagaut
16 Turbulence Closure Models for Computational Fluid Dynamics 753
Paul A. Durbin
17 Aerodynamics 775
Freddie D. Witherden/Antony Jameson
18 Industrial Aerodynamics 883
Frédéric L. Chalot
19 CFD-Based Nonlinear Computational Aeroelasticity 935
Charbel Farhat
20 The Use of Mixed Finite Element Methods for Viscoelastic Fluid Flow Analysis 957
Frank P. T. Baaijens/Martien A. Hulsen/Patrick D. Anderson
21 Combustion 975
Thierry J. Poinsot/Denis P. Veynante
22 Blood Flow 1005
C. Alberto Figueroa/Charles A. Taylor/Alison L. Marsden
23 Fluid–Structure Interaction and Flows with Moving Boundaries and Interfaces 1037
Tayfun E. Tezduyar/Kenji Takizawa/Yuri Bazilevs
24 Ship Hydrodynamics 1091
Eugenio Oñate/Julio García-Espinosa/Sergio R. Idelsohn/Borja Serván-Camas
25 Boundary-Element Methods and Wave Loading on Ships 1137
Panagiotis D. Kaklis/Constantinos G. Politis/Konstantinos A. Belibassakis/Alexandros I. Ginnis/Konstantinos V. Kostas/Theodoros P. Gerostathis
Contents for Volumes 1–5 1173
Subject Index 1185
About the Author :
Erwin Stein, PhD is Professor Emeritus, Curator of the Leibniz Exhibition, Stein Institut für Baumechanik und Numerische Mechanik, Leibniz Universität, Hannover, Germany. Institute of Mechanics and Computational Mechanics.
René de Borst, PhD is Professor, Centenary Professor of Civil Engineering, University of Sheffield, UK.
Thomas J. R. Hughes, PhD is Professor of Aerospace Engineering and Engineering Mechanics, Computational and Applied Mathematics Chair III, The University of Texas at Austin, Institute for Computational Engineering and Sciences, Austin, Texas, USA.
