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Contents of the Handbook
Contents of the Handbook
Volume I Finite Difference Methods (Part 1) Introduction, G.I. Marchuk Finite Difference Methods for Linear Parabolic Equations, V. Thomée Splitting and Alternating Direction Methods, G.I. Marchuk
3 5 197
Solution of Equations in Rn (Part 1) Least Squares Methods, Å. Björck
465
Volume II Finite Element Methods (Part 1) Finite Elements: An Introduction, J.T. Oden Basic Error Estimates for Elliptic Problems, P.G. Ciarlet Local Behavior in Finite Element Methods, L.B. Wahlbin Mixed and Hybrid Methods, J.E. Roberts, J.-M. Thomas Eigenvalue Problems, I. Babuška, J. Osborn Evolution Problems, H. Fujita, T. Suzuki
3 17 353 523 641 789
Volume III Techniques of Scientific Computing (Part 1) Historical Perspective on Interpolation, Approximation and Quadrature, C. Brezinski Padé Approximations, C. Brezinski, J. van Iseghem Approximation and Interpolation Theory, Bl. Sendov, A. Andreev
3 47 223
Numerical Methods for Solids (Part 1) Numerical Methods for Nonlinear Three-Dimensional Elasticity, P. Le Tallec ix
465
x
Contents of the Handbook
Solution of Equations in Rn (Part 2) Numerical Solution of Polynomial Equations, Bl. Sendov, A. Andreev, N. Kjurkchiev
625
Volume IV Finite Element Methods (Part 2) Origins, Milestones and Directions of the Finite Element Method – A Personal View, O.C. Zienkiewicz Automatic Mesh Generation and Finite Element Computation, P.L. George
3 69
Numerical Methods for Solids (Part 2) Limit Analysis of Collapse States, E. Christiansen Numerical Methods for Unilateral Problems in Solid Mechanics, J. Haslinger, I. Hlaváˇcek, J. Neˇcas Mathematical Modeling of Rods, L. Trabucho, J.M. Viano ˜
193 313 487
Volume V Techniques of Scientific Computing (Part 2) Numerical Path Following, E.L. Allgower, K. Georg Spectral Methods, C. Bernardi, Y. Maday Numerical Analysis for Nonlinear and Bifurcation Problems, G. Caloz, J. Rappaz Wavelets and Fast Numerical Algorithms, Y. Meyer Computer Aided Geometric Design, J.-J. Risler
3 209 487 639 715
Volume VI Numerical Methods for Solids (Part 3) Iterative Finite Element Solutions in Nonlinear Solid Mechanics, R.M. Ferencz, T.J.R. Hughes Numerical Analysis and Simulation of Plasticity, J.C. Simo
3 183
Numerical Methods for Fluids (Part 1) Navier–Stokes Equations: Theory and Approximation, M. Marion, R. Temam
503
Contents of the Handbook
xi
Volume VII Solution of Equations in Rn (Part 3) Gaussian Elimination for the Solution of Linear Systems of Equations, G. Meurant
3
Techniques of Scientific Computing (Part 3) The Analysis of Multigrid Methods, J.H. Bramble, X. Zhang Wavelet Methods in Numerical Analysis, A. Cohen Finite Volume Methods, R. Eymard, T. Gallouët, R. Herbin
173 417 713
Volume VIII Solution of Equations in Rn (Part 4) Computational Methods for Large Eigenvalue Problems, H.A. van der Vorst
3
Techniques of Scientific Computing (Part 4) Theoretical and Numerical Analysis of Differential–Algebraic Equations, P.J. Rabier, W.C. Rheinboldt
183
Numerical Methods for Fluids (Part 2) Mathematical Modeling and Analysis of Viscoelastic Fluids of the Oldroyd Kind, E. Fernández-Cara, F. Guillén, R.R. Ortega
543
Volume IX Numerical Methods for Fluids (Part 3) Finite Element Methods for Incompressible Viscous Flow, R. Glowinski
3
Volume X Special Volume: Computational Chemistry Computational Quantum Chemistry: A Primer, E. Cancès, M. Defranceschi, W. Kutzelnigg, C. Le Bris, Y. Maday The Modeling and Simulation of the Liquid Phase, J. Tomasi, B. Mennucci, P. Laug An Introduction to First-Principles Simulations of Extended Systems, F. Finocchi, J. Goniakowski, X. Gonze, C. Pisani
3 271 377
xii
Contents of the Handbook
Computational Approaches of Relativistic Models in Quantum Chemistry, J.P. Desclaux, J. Dolbeault, M.J. Esteban, P. Indelicato, E. Séré Quantum Monte Carlo Methods for the Solution of the Schrödinger Equation for Molecular Systems, A. Aspuru-Guzik, W.A. Lester, Jr. Linear Scaling Methods for the Solution of Schrödinger’s Equation, S. Goedecker Finite Difference Methods for Ab Initio Electronic Structure and Quantum Transport Calculations of Nanostructures, J.-L. Fattebert, M. Buongiorno Nardelli Using Real Space Pseudopotentials for the Electronic Structure Problem, J.R. Chelikowsky, L. Kronik, I. Vasiliev, M. Jain, Y. Saad Scalable Multiresolution Algorithms for Classical and Quantum Molecular Dynamics Simulations of Nanosystems, A. Nakano, T.J. Campbell, R.K. Kalia, S. Kodiyalam, S. Ogata, F. Shimojo, X. Su, P. Vashishta Simulating Chemical Reactions in Complex Systems, M.J. Field Biomolecular Conformations Can Be Identified as Metastable Sets of Molecular Dynamics, C. Schütte, W. Huisinga Theory of Intense Laser-Induced Molecular Dissociation: From Simulation to Control, O. Atabek, R. Lefebvre, T.T. Nguyen-Dang Numerical Methods for Molecular Time-Dependent Schrödinger Equations – Bridging the Perturbative to Nonperturbative Regime, A.D. Bandrauk, H.-Z. Lu Control of Quantum Dynamics: Concepts, Procedures and Future Prospects, H. Rabitz, G. Turinici, E. Brown
453 485 537
571 613
639 667 699 745
803 833
Volume XI Special Volume: Foundations of Computational Mathematics On the Foundations of Computational Mathematics, B.J.C. Baxter, A. Iserles Geometric Integration and its Applications, C.J. Budd, M.D. Piggott Linear Programming and Condition Numbers under the Real Number Computation Model, D. Cheung, F. Cucker, Y. Ye Numerical Solution of Polynomial Systems by Homotopy Continuation Methods, T.Y. Li Chaos in Finite Difference Scheme, M. Yamaguti, Y. Maeda Introduction to Partial Differential Equations and Variational Formulations in Image Processing, G. Sapiro
3 35 141 209 305 383
Contents of the Handbook
xiii
Volume XII Special Volume: Computational Models for the Human Body Mathematical Modeling and Numerical Simulation of the Cardiovascular System, A. Quarteroni, L. Formaggia Computational Methods for Cardiac Electrophysiology, M.E. Belik, T.P. Usyk, A.D. McCulloch Mathematical Analysis, Controllability and Numerical Simulation of a Simple Model of Avascular Tumor Growth, J.I. Díaz, J.I. Tello Human Models for Crash and Impact Simulation, E. Haug, H.-Y. Choi, S. Robin, M. Beaugonin Soft Tissue Modeling for Surgery Simulation, H. Delingette, N. Ayache Recovering Displacements and Deformations from 3D Medical Images Using Biomechanical Models, X. Papademetris, O. Škrinjar, J.S. Duncan Methods for Modeling and Predicting Mechanical Deformations of the Breast under External Perturbations, F.S. Azar, D.N. Metaxas, M.D. Schnall
3 129 189 231 453
551
591
Volume XIII Special Volume: Numerical Methods in Electromagnetics Introduction to Electromagnetism, W. Magnus, W. Schoenmaker Discretization of Electromagnetic Problems: The “Generalized Finite Differences” Approach, A. Bossavit Finite-Difference Time-Domain Methods, S.C. Hagness, A. Taflove, S.D. Gedney Discretization of Semiconductor Device Problems (I), F. Brezzi, L.D. Marini, S. Micheletti, P. Pietra, R. Sacco, S. Wang Discretization of Semiconductor Device Problems (II), A.M. Anile, N. Nikiforakis, V. Romano, G. Russo Modeling and Discretization of Circuit Problems, M. Günther, U. Feldmann, J. ter Maten Simulation of EMC Behaviour, A.J.H. Wachters, W.H.A. Schilders Solution of Linear Systems, O. Schenk, H.A. van der Vorst Reduced-Order Modeling, Z. Bai, P.M. Dewilde, R.W. Freund
3 105 199 317 443 523 661 755 825
xiv
Contents of the Handbook
Volume XIV Special Volume: Computational Methods for the Atmosphere and the Oceans Finite-Volume Methods in Meteorology, Bennert Machenhauer, Eigil Kaas, Peter Hjort Lauritzen Computational Kernel Algorithms for Fine-Scale, Multiprocess, Longtime Oceanic Simulations, Alexander F. Shchepetkin, James C. McWilliams Bifurcation Analysis of Ocean, Atmosphere, and Climate Models, Eric Simonnet, Henk A. Dijkstra, Michael Ghil Time-Periodic Flows in Geophysical and Classical Fluid Dynamics, R. M. Samelson Momentum Maps for Lattice EPDiff, Colin J. Cotter, Darryl D. Holm Numerical Generation of Stochastic Differential Equations in Climate Models, Brian Ewald, Cécile Penland Large-eddy Simulations for Geophysical Fluid Dynamics, Marcel Lesieur, Olivier Metais Two Examples from Geophysical and Astrophysical Turbulence on Modeling Disparate Scale Interactions, Pablo Mininni, Annick Pouquet, Peter Sullivan Data Assimilation for Geophysical Fluids, Jacques Blum, François-Xavier Le Dimet, I. Michael Navon Energetic Consistency and Coupling of the Mean and Covariance Dynamics, Stephen E. Cohn Boundary Value Problems for the Inviscid Primitive Equations in Limited Domains, Antoine Rousseau, Roger M. Temam, Joseph J. Tribbia Some Mathematical Problems in Geophysical Fluid Dynamics, Madalina Petcu, Roger M. Temam, Mohammed Ziane
3
121 187 231 247 279 309
339 385 443
481 577
Volume I Finite Difference Methods (Part 1) Introduction, G.I. Marchuk Finite Difference Methods for Linear Parabolic Equations, V. Thomée Splitting and Alternating Direction Methods, G.I. Marchuk
3 5 197
Solution of Equations in Rn (Part 1) Least Squares Methods, Å. Björck
465
Volume II Finite Element Methods (Part 1) Finite Elements: An Introduction, J.T. Oden Basic Error Estimates for Elliptic Problems, P.G. Ciarlet Local Behavior in Finite Element Methods, L.B. Wahlbin Mixed and Hybrid Methods, J.E. Roberts, J.-M. Thomas Eigenvalue Problems, I. Babuška, J. Osborn Evolution Problems, H. Fujita, T. Suzuki
3 17 353 523 641 789
Volume III Techniques of Scientific Computing (Part 1) Historical Perspective on Interpolation, Approximation and Quadrature, C. Brezinski Padé Approximations, C. Brezinski, J. van Iseghem Approximation and Interpolation Theory, Bl. Sendov, A. Andreev
3 47 223
Numerical Methods for Solids (Part 1) Numerical Methods for Nonlinear Three-Dimensional Elasticity, P. Le Tallec ix
465
x
Contents of the Handbook
Solution of Equations in Rn (Part 2) Numerical Solution of Polynomial Equations, Bl. Sendov, A. Andreev, N. Kjurkchiev
625
Volume IV Finite Element Methods (Part 2) Origins, Milestones and Directions of the Finite Element Method – A Personal View, O.C. Zienkiewicz Automatic Mesh Generation and Finite Element Computation, P.L. George
3 69
Numerical Methods for Solids (Part 2) Limit Analysis of Collapse States, E. Christiansen Numerical Methods for Unilateral Problems in Solid Mechanics, J. Haslinger, I. Hlaváˇcek, J. Neˇcas Mathematical Modeling of Rods, L. Trabucho, J.M. Viano ˜
193 313 487
Volume V Techniques of Scientific Computing (Part 2) Numerical Path Following, E.L. Allgower, K. Georg Spectral Methods, C. Bernardi, Y. Maday Numerical Analysis for Nonlinear and Bifurcation Problems, G. Caloz, J. Rappaz Wavelets and Fast Numerical Algorithms, Y. Meyer Computer Aided Geometric Design, J.-J. Risler
3 209 487 639 715
Volume VI Numerical Methods for Solids (Part 3) Iterative Finite Element Solutions in Nonlinear Solid Mechanics, R.M. Ferencz, T.J.R. Hughes Numerical Analysis and Simulation of Plasticity, J.C. Simo
3 183
Numerical Methods for Fluids (Part 1) Navier–Stokes Equations: Theory and Approximation, M. Marion, R. Temam
503
Contents of the Handbook
xi
Volume VII Solution of Equations in Rn (Part 3) Gaussian Elimination for the Solution of Linear Systems of Equations, G. Meurant
3
Techniques of Scientific Computing (Part 3) The Analysis of Multigrid Methods, J.H. Bramble, X. Zhang Wavelet Methods in Numerical Analysis, A. Cohen Finite Volume Methods, R. Eymard, T. Gallouët, R. Herbin
173 417 713
Volume VIII Solution of Equations in Rn (Part 4) Computational Methods for Large Eigenvalue Problems, H.A. van der Vorst
3
Techniques of Scientific Computing (Part 4) Theoretical and Numerical Analysis of Differential–Algebraic Equations, P.J. Rabier, W.C. Rheinboldt
183
Numerical Methods for Fluids (Part 2) Mathematical Modeling and Analysis of Viscoelastic Fluids of the Oldroyd Kind, E. Fernández-Cara, F. Guillén, R.R. Ortega
543
Volume IX Numerical Methods for Fluids (Part 3) Finite Element Methods for Incompressible Viscous Flow, R. Glowinski
3
Volume X Special Volume: Computational Chemistry Computational Quantum Chemistry: A Primer, E. Cancès, M. Defranceschi, W. Kutzelnigg, C. Le Bris, Y. Maday The Modeling and Simulation of the Liquid Phase, J. Tomasi, B. Mennucci, P. Laug An Introduction to First-Principles Simulations of Extended Systems, F. Finocchi, J. Goniakowski, X. Gonze, C. Pisani
3 271 377
xii
Contents of the Handbook
Computational Approaches of Relativistic Models in Quantum Chemistry, J.P. Desclaux, J. Dolbeault, M.J. Esteban, P. Indelicato, E. Séré Quantum Monte Carlo Methods for the Solution of the Schrödinger Equation for Molecular Systems, A. Aspuru-Guzik, W.A. Lester, Jr. Linear Scaling Methods for the Solution of Schrödinger’s Equation, S. Goedecker Finite Difference Methods for Ab Initio Electronic Structure and Quantum Transport Calculations of Nanostructures, J.-L. Fattebert, M. Buongiorno Nardelli Using Real Space Pseudopotentials for the Electronic Structure Problem, J.R. Chelikowsky, L. Kronik, I. Vasiliev, M. Jain, Y. Saad Scalable Multiresolution Algorithms for Classical and Quantum Molecular Dynamics Simulations of Nanosystems, A. Nakano, T.J. Campbell, R.K. Kalia, S. Kodiyalam, S. Ogata, F. Shimojo, X. Su, P. Vashishta Simulating Chemical Reactions in Complex Systems, M.J. Field Biomolecular Conformations Can Be Identified as Metastable Sets of Molecular Dynamics, C. Schütte, W. Huisinga Theory of Intense Laser-Induced Molecular Dissociation: From Simulation to Control, O. Atabek, R. Lefebvre, T.T. Nguyen-Dang Numerical Methods for Molecular Time-Dependent Schrödinger Equations – Bridging the Perturbative to Nonperturbative Regime, A.D. Bandrauk, H.-Z. Lu Control of Quantum Dynamics: Concepts, Procedures and Future Prospects, H. Rabitz, G. Turinici, E. Brown
453 485 537
571 613
639 667 699 745
803 833
Volume XI Special Volume: Foundations of Computational Mathematics On the Foundations of Computational Mathematics, B.J.C. Baxter, A. Iserles Geometric Integration and its Applications, C.J. Budd, M.D. Piggott Linear Programming and Condition Numbers under the Real Number Computation Model, D. Cheung, F. Cucker, Y. Ye Numerical Solution of Polynomial Systems by Homotopy Continuation Methods, T.Y. Li Chaos in Finite Difference Scheme, M. Yamaguti, Y. Maeda Introduction to Partial Differential Equations and Variational Formulations in Image Processing, G. Sapiro
3 35 141 209 305 383
Contents of the Handbook
xiii
Volume XII Special Volume: Computational Models for the Human Body Mathematical Modeling and Numerical Simulation of the Cardiovascular System, A. Quarteroni, L. Formaggia Computational Methods for Cardiac Electrophysiology, M.E. Belik, T.P. Usyk, A.D. McCulloch Mathematical Analysis, Controllability and Numerical Simulation of a Simple Model of Avascular Tumor Growth, J.I. Díaz, J.I. Tello Human Models for Crash and Impact Simulation, E. Haug, H.-Y. Choi, S. Robin, M. Beaugonin Soft Tissue Modeling for Surgery Simulation, H. Delingette, N. Ayache Recovering Displacements and Deformations from 3D Medical Images Using Biomechanical Models, X. Papademetris, O. Škrinjar, J.S. Duncan Methods for Modeling and Predicting Mechanical Deformations of the Breast under External Perturbations, F.S. Azar, D.N. Metaxas, M.D. Schnall
3 129 189 231 453
551
591
Volume XIII Special Volume: Numerical Methods in Electromagnetics Introduction to Electromagnetism, W. Magnus, W. Schoenmaker Discretization of Electromagnetic Problems: The “Generalized Finite Differences” Approach, A. Bossavit Finite-Difference Time-Domain Methods, S.C. Hagness, A. Taflove, S.D. Gedney Discretization of Semiconductor Device Problems (I), F. Brezzi, L.D. Marini, S. Micheletti, P. Pietra, R. Sacco, S. Wang Discretization of Semiconductor Device Problems (II), A.M. Anile, N. Nikiforakis, V. Romano, G. Russo Modeling and Discretization of Circuit Problems, M. Günther, U. Feldmann, J. ter Maten Simulation of EMC Behaviour, A.J.H. Wachters, W.H.A. Schilders Solution of Linear Systems, O. Schenk, H.A. van der Vorst Reduced-Order Modeling, Z. Bai, P.M. Dewilde, R.W. Freund
3 105 199 317 443 523 661 755 825
xiv
Contents of the Handbook
Volume XIV Special Volume: Computational Methods for the Atmosphere and the Oceans Finite-Volume Methods in Meteorology, Bennert Machenhauer, Eigil Kaas, Peter Hjort Lauritzen Computational Kernel Algorithms for Fine-Scale, Multiprocess, Longtime Oceanic Simulations, Alexander F. Shchepetkin, James C. McWilliams Bifurcation Analysis of Ocean, Atmosphere, and Climate Models, Eric Simonnet, Henk A. Dijkstra, Michael Ghil Time-Periodic Flows in Geophysical and Classical Fluid Dynamics, R. M. Samelson Momentum Maps for Lattice EPDiff, Colin J. Cotter, Darryl D. Holm Numerical Generation of Stochastic Differential Equations in Climate Models, Brian Ewald, Cécile Penland Large-eddy Simulations for Geophysical Fluid Dynamics, Marcel Lesieur, Olivier Metais Two Examples from Geophysical and Astrophysical Turbulence on Modeling Disparate Scale Interactions, Pablo Mininni, Annick Pouquet, Peter Sullivan Data Assimilation for Geophysical Fluids, Jacques Blum, François-Xavier Le Dimet, I. Michael Navon Energetic Consistency and Coupling of the Mean and Covariance Dynamics, Stephen E. Cohn Boundary Value Problems for the Inviscid Primitive Equations in Limited Domains, Antoine Rousseau, Roger M. Temam, Joseph J. Tribbia Some Mathematical Problems in Geophysical Fluid Dynamics, Madalina Petcu, Roger M. Temam, Mohammed Ziane
3
121 187 231 247 279 309
339 385 443
481 577