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Encyclopedia of Computational Mechanics


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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. Beirao 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. Marechal

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 Rodriguez-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 Babuska/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 Juttler/Michael A. Scott/Derek C. Thomas

16 Meshfree Methods 653
Antonio Huerta/Ted Belytschko/Sonia Fernandez-Mendez/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
Rene de Borst

2 Finite Element Methods for Elasticity with Error-Controlled Discretization and Model Adaptivity 5
Erwin Stein/Marcus Olavi Ruter

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 Duster/Ernst Rank/Barna Szabo

5 Extended Finite Element Methods 173
Nicolas Moes/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 Bicanic

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. Peric/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
Rene de Borst/Clemens V. Verhoosel

18 Computational Fracture Mechanics 829
Anthony R. Ingraffea/Rene 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 Matous/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-Sebastien Schotte

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. Gutierrez/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 Koegl/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/Raphaele 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 Onate/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
Frederic 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 Onate/Julio Garcia-Espinosa/Sergio R. Idelsohn/Borja Servan-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 fur Baumechanik und Numerische Mechanik, Leibniz Universitat, Hannover, Germany. Institute of Mechanics and Computational Mechanics. Rene 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.

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