Featuring numerous in-depth and thoroughly cross-referenced articles on key topics, each volume of the Encyclopedia focuses on a specific aspect of the discipline.

Relevant links to chapters on industrial applications are also included.

Volume 1: Fundamentals

Volume 1, Fundamentals, of this prestigious three volume work, introduces the basic methodological, analytical, algorithmic and implementation topics and aspects of computational mechanics. Featuring numerous practical algorithms and tools for students, researchers and practitioners, it provides basic knowledge as well as background information for Volumes 2 and 3, which are devoted to solid and structural mechanics and fluid dynamics. Comprising 26 chapters, Volume 1 provides a sound theoretical base to key areas including discretization methods, geometrical modelling, mesh generation and visualization, solvers of algebraic equation systems and time-dependent problems.
View Sample Article: Volume 1 Chapter 14

Volume 2: Solids and Structures

Volume 2, Solids and Structures, examines the numerical analysis of solids and structures in the broadest possible sense. Utilizing basic methods outlined in Volume 1, it begins with a comprehensive picture of finite element methods for solids and structures in the linear regime, before moving on to discuss a wide variety of non-linear theories, encompassing structural stabilityproblems as well as instabilities which stem from the properties of the constituent materials. This volume also features chapters that address computational problems specific for particular materials such as concrete, soils, composites, biomaterials and for forming processes. Problems where interaction between fluids and solids play a role are also covered (for example multi-phase media, fluid-structure interaction and structural acoustics). Other important topics that are treated include stochastic finite elements, parameter identification, contact and the analysis of structural problems using boundary element methods.
View Sample Article: Volume 2 Chapter 3 (extract)

Volume 3: Fluids

Volume 3 focuses on fluid dynamics, with chapters falling into four main groupings. The first describes additional basic methodologies used in computational fluid dynamics, such as, stabilized and multiscale methods, discontinuous Galerkin methods, spectral and hp-methods, and vortex methods. The second grouping is comprised of chapters on various aspects of incompressible viscous flows, including adaptivity and computability, multilevel methods in turbulence, direct and large eddy simulation, Reynolds-average turbulence modeling, non-Newtonian fluids, and blood flow. Grouping three focuses on compressible fluid dynamics. Chapters cover widely used techniques in aerodynamics, recent progress in aeroelasticity, and combustion. The fourth and final grouping relates to problems involving moving domains and free surfaces, including ship hydrodynamics.
View Sample Article: Volume 3 Chapter 11 (extract)

Volume 1: Fundamentals

1 Fundamentals, Introduction and Survey
Erwin Stein

2 Finite Difference Methods
Owe Axelsson

3 Interpolation in h -version Finite Element Spaces
Thomas Apel

4 Finite Element Methods
Susanne C. Brenner/Carsten Carstensen

5 The p -version of the Finite Element Method
Ernst Rank/Barna Szabó/Alexander Düster

6 Spectral Methods
Claudio Canuto/Alfio Quarteroni

7 Adaptive Wavelet Techniques in Numerical Simulation
Wolfgang Dahmen/Ronald DeVore/Albert Cohen

8 Plates and Shells: Asymptotic Expansions and Hierarchic Models
Zohar Yosibash/Monique Dauge/Erwan Faou

9 Mixed Finite Elements Methods
Franco Brezzi/Ferdinando Auricchio/Carlo Lovadina

10 Meshfree Methods
Timon Rabczuk/Ted Belytschko/Sonia Fernández-Méndez/Antonio Huerta

11 Discrete Element Method
Nenad Bićanić

12 Boundary Element Methods: Foundation and Error Analysis
W. L. Wendland/G. C. Hsiao

13 Coupling of Boundary Element Methods and Finite Element Methods
Ernst P. Stephan

14 Arbitrary Lagrangian--Eulerian Methods
J. Donéa/J.-Ph. Ponthot/A. Rodríguez-Ferran/A. Huerta

15 Finite Volume Methods: Foundation and Analysis
Timothy Barth/Mario Ohlberger

16 Geometrical Modeling of Technical Objects
F.-E. Wolter/M. Reuter/N. Peinecke

17 Mesh Generation and Mesh Adaptivity
P. Laug/P. L. George/P. J. Frey/H. Borouchaki/E. Saltel

18 Computational Visualization
William J. Schroeder/Mark S. Shephard

19 Linear Algebraic Solvers and Eigenvalue Analysis
Henk A. van der Vorst

20 Multigrid Methods for FEM and BEM Applications
Wolfgang Hackbusch

21 Panel Clustering Techniques and Hierarchical Matrices for BEM and FEM
Wolfgang Hackbusch

22 Domain Decomposition Methods and Preconditioning
V. G. Korneev/U. Langer

23 Nonlinear Systems and Bifurcations
Werner C. Rheinboldt

24 Adaptive Computational Methods for Parabolic Problems
K. Eriksson/C. Johnson/A. Logg

25 Time-dependent Problems with the Boundary Integral Equation Method
Martin Costabel

26 Finite Element Methods for Maxwell Equations
Leszek Demkowicz

Volume 2: Solids and Structures

1 Solids, Introduction and Survey
René de Borst

2 Finite Element Method for Elasticity with Error-controlled Approximation and Model Adaptivity
Marcus Rüter/Erwin Stein

3 Models and Finite Elements for Thin-walled Structures
W. A. Wall/M. Bischoff/K.-U. Bletzinger/E. Ramm

4 Buckling of Structures
Eduard Riks

5 Linear and Nonlinear Structural Dynamics
Gregory M. Hulbert

6 Computational Contact Mechanics
P. Wriggers/G. Zavarise

7 Elastoplastic and Viscoplastic Deformations in Solids and Structures
F. Armero

8 Crystal Plasticity
Jan Schotte/Christian Miehe

9 Shakedown and Safety Assessment
Nestor Zouain

10 Damage, Material Instabilities, and Failure
René de Borst

11 Computational Fracture Mechanics
Anthony R. Ingraffea

12 Homogenization Methods and Multiscale Modeling
Tarek I. Zohdi

13 Computational Modelling of Damage and Failures in Composite Laminates
J. N. Reddy/D. H. Robbins Jr

14 Computational Modeling of Forming Processes
D. R. J. Owen/D. Perić

15 Computational Concrete Mechanics
Roman Lackner/Herbert A. Mang/Christian Pichler

16 Computational Geomechanics Including Consolidation
John P. Carter/John C. Small

17 Multifield Problems
B. A. Schrefler

18 Computational Biomechanics of Soft Biological Tissue
Gerhard A. Holzapfel

19 Identification of Material Parameters for Constitutive Equations
R. Mahnken

20 Stochastic Finite Element Methods
Steen Krenk/Miguel A. Gutiérrez

21 Fluid-structure Interaction Problems
Roger Ohayon

22 Acoustics
Peter M. Pinsky/Lonny L. Thompson

23 Boundary Integral Equation Methods for Elastic and Plastic Problems
Marc Bonnet

24 Boundary Element Methods for the Dynamic Analysis of Elastic, Viscoelastic, and Piezoelastic Solids
M. Schanz/M. Kögl/L. Gaul/F. Moser

Volume 3: Fluids

1 Fluids, Introduction and Survey
Thomas J. R. Hughes

2 Multiscale and Stabilized Methods
Thomas J. R. Hughes/Leopoldo P. Franca/Guglielmo Scovazzi

3 Spectral Element and hp Methods
Robert M. Kirby/George E.M. Karniadakis

4 Discontinuous Galerkin Methods for Computational Fluid Dynamics
B. Cockburn

5 Vortex Methods
G. S. Winckelmans

6 Incompressible Viscous Flows
Rolf Rannacher

7 Computability and Adaptivity in CFD
J. Hoffman/C. Johnson

8 Dynamic Multilevel Methods and Turbulence
T. Dubois/R. M. Temam/F. Jauberteau

9 Turbulence Direct Numerical Simulation and Large-eddy Simulation
Pierre Sagaut

10 Turbulence Closure Models for Computational Fluid Dynamics
Paul A. Durbin

11 Aerodynamics
Antony Jameson

12 Industrial Aerodynamics
Frédéric L. Chalot

13 CFD-based Nonlinear Computational Aeroelasticity
Charbel Farhat

14 Mixed Finite Element Methods for Non-newtonian Fluid
Patrick D. Anderson/Martien A. Hulsen/Frank P. T. Baaijens

15 Combustion
T. J. Poinsot/D. P. Veynante

16 Blood Flow
Charles A. Taylor

17 Finite Element Methods for Fluid Dynamics with Moving Boundaries and Interfaces
Tayfun E. Tezduyar

18 Ship Hydrodynamics
Sergio R. Idelsohn/Julio Garc í a/Eugenio Oñate