Volume 1: Fundamentals – Part 1 Contributors to Volume 1 ix Preface xi 1 Fundamentals: Introduction and Survey 1Erwin Stein 2 Finite Difference Methods 15Owe Axelsson 3 Interpolation and Quasi-Interpolation in h- and hp-Version Finite Element Spaces 67Thomas Apel/Jens M. Melenk 4 Finite Element Methods 101Susanne C. Brenner/Carsten Carstensen 5 Mixed Finite Element Methods 149Ferdinando Auricchio/L. Beirão da Veiga/F. Brezzi/C. Lovadina 6 Spectral Methods 203Claudio Canuto/Alfio Quarteroni 7 Mesh Generation and Mesh Adaptivity: Theory and Techniques 219Paul Louis George/H. Borouchaki/F. Alauzet/P. Laug/A. Loseille/D. Marcum/L. Maréchal 8 Plates and Shells: Asymptotic Expansions and Hierarchical Models 271Monique Dauge/Erwan Faou/Zohar Yosibash 9 Iterative Solutions of Nonlinear Systems, Solution Manifolds, and Bifurcations 311Werner C. Rheinboldt 10 Arbitrary Lagrangian–Eulerian Methods 339Jean Donea/Antonio Huerta/Jean-Philippe Ponthot/Antonio Rodríguez-Ferran 11 Mathematical Foundations of Elastoplastic Deformations in Solids 363B. Daya Reddy 12 Predictive Computational Science: Computer Predictions in the Presence of Uncertainty 391John Tinsley Oden/Ivo Babuška/Danial Faghihi 13 Uncertainty Quantification and Bayesian Inversion 417Hermann 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 589Thomas J. R. Hughes/Giancarlo Sangalli 15 Isogeometric Analysis: Representation of Geometry 629Michael Haberleitner/Bert Jüttler/Michael A. Scott/Derek C. Thomas 16 Meshfree Methods 653Antonio Huerta/Ted Belytschko/Sonia Fernández-Méndez/Timon Rabczuk/Xiaoying Zhuang/Marino Arroyo 17 Reproducing Kernel Particle Method for Solving Partial Differential Equations 691Jiun-Shyan Chen/Wing Kam Liu/Michael C. Hillman/Sheng-Wei Chi/Yanping Lian/Miguel A. Bessa 18 Adaptive Wavelet Techniques in Numerical Simulation 735Albert Cohen/Wolfgang Dahmen/Ronald DeVore 19 Discontinuous Petrov–Galerkin (DPG) Method 777Leszek Demkowicz/Jay Gopalakrishnan 20 Finite Element Methods for Maxwell’s Equations 793Leszek Demkowicz 21 Adaptive Computational Methods for Parabolic Problems 813Kenneth Eriksson/Claes Johnson/A. Logg 22 Boundary Element Methods: Foundation and Error Analysis 841George C. Hsiao/O. Steinbach/W. L. Wendland 23 Coupling of Boundary Element Methods and Finite Element Methods 903Ernst P. Stephan 24 Time-Dependent Problems with the Boundary Integral Equation Method 943Martin Costabel/Francisco-Javier Sayas 25 Linear Algebraic Solvers and Eigenvalue Analysis 967Henk A. van der Vorst/Cornelis Vuik 26 Multigrid Methods for FEM and BEM Applications 995Wolfgang Hackbusch 27 Panel Clustering Techniques and Hierarchical Matrices for BEM and FEM 1013Wolfgang Hackbusch 28 Domain Decomposition Methods and Preconditioning 1031Vadim 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 1René de Borst 2 Finite Element Methods for Elasticity with Error-Controlled Discretization and Model Adaptivity 5Erwin Stein/Marcus Olavi Rüter 3 Model Reduction Methods 101Francisco Chinesta/Antonio Huerta/Gianluigi Rozza/Karen Willcox 4 The p-Version of the Finite Element and Finite Cell Methods 137Alexander Düster/Ernst Rank/Barna Szabó 5 Extended Finite Element Methods 173Nicolas Moës/J. E. Dolbow/N. Sukumar 6 Models and Finite Elements for Thin-Walled Structures 195Manfred Bischoff/E. Ramm/J. Irslinger 7 Computing with Rotations: Algorithms and Applications 281Ignacio Romero/Martin Arnold 8 Buckling 309Eduard Riks 9 Computational Structural Dynamics 339Gregory M. Hulbert 10 Computational Contact Mechanics with the Finite Element Method 365L. De Lorenzis/Peter Wriggers/C. Weißenfels 11 Discrete Element Methods 411Nenad Bićanić 12 Elastoplastic and Viscoplastic Deformations in Solids and Structures 449Francisco Armero 13 Crystal Plasticity and Evolution of Polycrystalline Microstructure 491Christian Miehe/Jan Schotte 14 Computational Modeling of Forming Processes 515D. Perić/D. R. J. Owen 15 Explicit Finite Element Methods for Large Deformation Problems in Solid Mechanics 567David 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 731Nestor Zouain 17 Damage, Material Instabilities, and Failure 779René de Borst/Clemens V. Verhoosel 18 Computational Fracture Mechanics 829Anthony R. Ingraffea/René de Borst 19 Homogenization Methods and Multiscale Modeling 855Tarek I. Zohdi 20 Homogenization Methods and Multiscale Modeling: Nonlinear Problems 879Marc G. D. Geers/Varvara G. Kouznetsova/Karel Matouš/Julien Yvonnet 21 Computational Concrete Mechanics 913Roman Lackner/Christian Pichler/Roland Traxl/Herbert A. Mang 22 Multifield Problems 965Bernhard A. Schrefler/L. Simoni/B. Markert 23 Fluid–Structure Interaction Problems 1001Roger Ohayon/Jean-Sébastien Schotté 24 Acoustics 1013Lonny L. Thompson/Peter M. Pinsky 25 Computational Geomechanics Including Consolidation 1039John P. Carter/John C. Small 26 Computational Modeling of Damage and Failures in Composite Laminates 1075J. N. Reddy/D. H. Robbins 27 Computational Biomechanics of Soft Biological Tissues: Arterial Walls, Hearts Walls, and Ligaments 1117Gerhard A. Holzapfel 28 Identification of Material Parameters for Constitutive Equations 1165Rolf Mahnken 29 Stochastic Finite Element Methods 1187Miguel A. Gutiérrez/Steen Krenk 30 Shape Optimization 1213Kai-Uwe Bletzinger 31 Topology Optimization 1255Kurt Maute 32 Boundary Integral Equation Methods for Elastic and Plastic Problems 1289Marc Bonnet 33 Boundary Element Methods for the Dynamic Analysis of Elastic, Viscoelastic, and Piezoelectric Solids 1323Lothar 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 1Thomas J. R. Hughes 2 Multiscale and Stabilized Methods 5Thomas J. R. Hughes/Guglielmo Scovazzi/Leopoldo P. Franca 3 Variational Multiscale Methods in Computational Fluid Dynamics 69Ramon Codina/Santiago Badia/Joan Baiges/Javier Principe 4 Spectral Element and hp Methods 97Yue Yu/Robert M. Kirby/George Em Karniadakis 5 Discontinuous Galerkin Methods for Computational Fluid Dynamics 141Bernado A. Cockburn 6 Finite Volume Methods: Foundation and Analysis 205Timothy Barth/Raphaèle Herbin/Mario Ohlberger 7 High-Order Methods for CFD 265R. Abgrall/Mario Ricchiuto 8 Particle Methods in Computational Fluid Dynamics 319Sergio R. Idelsohn/Eugenio Oñate/Pablo Becker 9 Residual Distribution Schemes: Foundations and Analysis 361Herman Deconinck/Mario Ricchiuto 10 Vortex Methods 415G. S. Winckelmans 11 Computational Phase-Field Modeling 439Hector Gomez/Kristoffer G. van der Zee 12 Incompressible Viscous Flows 475Rolf Rannacher 13 Computability and Adaptivity in CFD 503Johan Hoffman/Johan Jansson/Niclas Jansson/Rodrigo Vilela De Abreu/Claes Johnson Contents for Volumes 1–4, 6 525 Subject Index 537Volume 6: Fluids – Part 2 Contributors to Volume 6 ix Preface xi 14 Dynamic Multilevel Methods and Turbulence 645Thierry Dubois/Francois Jauberteau/Roger M. Temam 15 Turbulence Direct Numerical Simulation and Large-Eddy Simulation 721Pierre Sagaut 16 Turbulence Closure Models for Computational Fluid Dynamics 753Paul A. Durbin 17 Aerodynamics 775Freddie D. Witherden/Antony Jameson 18 Industrial Aerodynamics 883Frédéric L. Chalot 19 CFD-Based Nonlinear Computational Aeroelasticity 935Charbel Farhat 20 The Use of Mixed Finite Element Methods for Viscoelastic Fluid Flow Analysis 957Frank P. T. Baaijens/Martien A. Hulsen/Patrick D. Anderson 21 Combustion 975Thierry J. Poinsot/Denis P. Veynante 22 Blood Flow 1005C. Alberto Figueroa/Charles A. Taylor/Alison L. Marsden23 Fluid–Structure Interaction and Flows with Moving Boundaries and Interfaces 1037Tayfun E. Tezduyar/Kenji Takizawa/Yuri Bazilevs 24 Ship Hydrodynamics 1091Eugenio Oñate/Julio García-Espinosa/Sergio R. Idelsohn/Borja Serván-Camas 25 Boundary-Element Methods and Wave Loading on Ships 1137Panagiotis 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

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 mechanics18 new chapters added representing a more than 20% increase over current editionExtensive revision plan with major updates to the majority of existing articlesCovers 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.