Encyclopedia of Computational Mechanics (6Vol Set)

Volume 1: Fundamentals ?Part 1 Contributors to Volume 1 ixVolumes 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. 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. Beir? 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. Mar?hal 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?ulerian Methods 339 Jean Donea/Antonio Huerta/Jean-Philippe Ponthot/Antonio Rodr?uez-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 Babu?a/Danial Faghihi 13 Uncertainty Quantification and Bayesian Inversion 417 Hermann G. Matthies Contents for Volumes 2? 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 J?tler/Michael A. Scott/Derek C. Thomas 16 Meshfree Methods 653 Antonio Huerta/Ted Belytschko/Sonia Fern?dez-M?dez/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?alerkin (DPG) Method 777 Leszek Demkowicz/Jay Gopalakrishnan 20 Finite Element Methods for Maxwell? 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? 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 Ren?de Borst 2 Finite Element Methods for Elasticity with Error-Controlled Discretization and Model Adaptivity 5 Erwin Stein/Marcus Olavi R?er 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 D?ter/Ernst Rank/Barna Szab? 5 Extended Finite Element Methods 173 Nicolas Mo?/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. Wei?nfels 11 Discrete Element Methods 411 Nenad Bi?ani? 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. Peri?/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? 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 Ren?de Borst/Clemens V. Verhoosel 18 Computational Fracture Mechanics 829 Anthony R. Ingraffea/Ren?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 Matou?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?tructure Interaction Problems 1001 Roger Ohayon/Jean-S?astien Schott? 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. Guti?rez/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 K?l/Friedrich Moser/Martin Schanz Contents for Volumes 1?, 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/Rapha?e 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 O?te/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?, 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 Fr??ic 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?tructure Interaction and Flows with Moving Boundaries and Interfaces 1037 Tayfun E. Tezduyar/Kenji Takizawa/Yuri Bazilevs 24 Ship Hydrodynamics 1091 Eugenio O?te/Julio Garc?-Espinosa/Sergio R. Idelsohn/Borja Serv?-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? 1173 Subject Index 1185

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