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Domain Decomposition Methods in Science and Engineering
 
Edited by: Alfio Quarteroni Polytechnic Institute of Milan, Milan, Italy
Jacques Periaux Dussault Aviatiation, St. Cloud, France
Yuri A. Kuznetsov Russian Academy of Sciences, Moscow, Russia
Olof B. Widlund New York University-Courant Institute of Mathematical Sciences, New York, NY
Front Cover for Domain Decomposition Methods in Science and Engineering
Available Formats:
Softcover ISBN: 978-0-8218-5158-6
Product Code: CONM/157
484 pp 
List Price: $48.00
MAA Member Price: $43.20
AMS Member Price: $38.40
Electronic ISBN: 978-0-8218-7748-7
Product Code: CONM/157.E
484 pp 
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $36.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
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Front Cover for Domain Decomposition Methods in Science and Engineering
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  • Front Cover for Domain Decomposition Methods in Science and Engineering
  • Back Cover for Domain Decomposition Methods in Science and Engineering
Domain Decomposition Methods in Science and Engineering
Edited by: Alfio Quarteroni Polytechnic Institute of Milan, Milan, Italy
Jacques Periaux Dussault Aviatiation, St. Cloud, France
Yuri A. Kuznetsov Russian Academy of Sciences, Moscow, Russia
Olof B. Widlund New York University-Courant Institute of Mathematical Sciences, New York, NY
Available Formats:
Softcover ISBN:  978-0-8218-5158-6
Product Code:  CONM/157
484 pp 
List Price: $48.00
MAA Member Price: $43.20
AMS Member Price: $38.40
Electronic ISBN:  978-0-8218-7748-7
Product Code:  CONM/157.E
484 pp 
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $36.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $57.60
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1571994
    MSC: Primary 65;

    This book contains the proceedings of the Sixth International Conference on Domain Decomposition, held in June 1992 in Como, Italy. Developments in this area are driven by advances in computer technology as well as by a strengthening in the mathematical foundations of the subject. Compared to just a few years ago, experts have much more experience with difficult applications and have accumulated solid evidence that these methods provide valuable tools for solving problems in science and engineering. Much of the work in this field focuses on developing numerical methods for large algebraic systems, methods central to producing efficient codes for computational fluid dynamics, elasticity, and other core problems of continuum mechanics. These methods hold the promise of allowing simulations of very high resolution with relative ease. This approach allows for the flexibility of using different numerical methods and different models, each appropriate for the subregion at hand, to solve large problems in a cost-effective way. Containing contributions by international experts in this area, this book reports on the state-of-the-art in the growing field of domain decomposition.

    Readership

    Applied mathematicians, numerical analysts, computer scientists, engineers, graduate students, and researchers.

  • Table of Contents
     
     
    • Part I: Theory [ MR 1262599 ]
    • Invited Lectures [ MR 1262599 ]
    • V. I. Agoshkov - Domain decomposition methods using modified basis functions [ MR 1262600 ]
    • James H. Bramble and Joseph E. Pasciak - Uniform convergence estimates for multigrid $V$-cycle algorithms with less than full elliptic regularity [ MR 1262601 ]
    • F. Brezzi and L. D. Marini - A three-field domain decomposition method [ MR 1262602 ]
    • Claudio Canuto and Alessandro Russo - Self-adaptive coupling of mathematical models and/or numerical methods [ MR 1262603 ]
    • Clint N. Dawson and Todd F. Dupont - Noniterative domain decomposition for second order hyperbolic problems [ MR 1262604 ]
    • Maksymilian Dryja and Olof B. Widlund - Some recent results on Schwarz type domain decomposition algorithms [ MR 1262605 ]
    • Yu. A. Kuznetsov - Overlapping domain decomposition methods for parabolic problems [ MR 1262606 ]
    • Jia Chang Sun - Domain decomposition and multilevel PCG method for solving $3$-D fourth order problems [ MR 1262607 ]
    • Jinchao Xu - Some two-grid finite element methods [ MR 1262608 ]
    • Contributed Lectures [ MR 1262599 ]
    • Gloria Aguilar and Francisco Lisbona - Interface conditions for a kind of nonlinear elliptic-hyperbolic problems [ MR 1262609 ]
    • Lucia Gastaldi - A domain decomposition for the transport equation
    • Jan Mandel - Hybrid domain decomposition with unstructured subdomains [ MR 1262611 ]
    • Luca F. Pavarino - Some Schwarz algorithms for the $p$-version finite element method [ MR 1262612 ]
    • U. Rüde - On the robustness and efficiency of the fully adaptive multigrid method [ MR 1262613 ]
    • J.-M. Thomas and D. Trujillo - Finite volume variational formulation. Application to domain decomposition methods [ MR 1262614 ]
    • Part II: Algorithms [ MR 1262599 ]
    • Invited Lectures [ MR 1262599 ]
    • Achi Brandt and Boris Diskin - Multigrid solvers on decomposed domains [ MR 1262615 ]
    • Tony F. Chan and Tarek P. Mathew - Domain decomposition preconditioners for convection diffusion problems [ MR 1262616 ]
    • Oliver Ernst and Gene H. Golub - A domain decomposition approach to solving the Helmholtz equation with a radiation boundary condition [ MR 1262617 ]
    • Charbel Farhat and François-Xavier Roux - The dual Schur complement method with well-posed local Neumann problems [ MR 1262618 ]
    • William D. Gropp, David E. Keyes and Jon S. Mounts - Implicit domain decomposition algorithms for steady, compressible aerodynamics [ MR 1262619 ]
    • T. E. Tezduyar, M. Behr, S. K. Aliabadi, S. Mittal and S. E. Ray - A new mixed preconditioning method based on the clustered element-by-element preconditioners
    • Contributed Lectures [ MR 1262599 ]
    • J.-D. Benamou and Y. Brenier - A domain decomposition method for the polar factorization of vector fields [ MR 1262622 ]
    • B. Bialecki, X.-C. Cai, M. Dryja and G. Fairweather - An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation [ MR 1262623 ]
    • Mark C. Curran - An iterative finite-element collocation method for parabolic problems using domain decomposition [ MR 1262624 ]
    • Michael Griebel - A domain decomposition method using sparse grids [ MR 1262625 ]
    • Wilhelm Heinrichs - Domain decomposition for the Stokes equations in streamfunction formulation [ MR 1262626 ]
    • Yu. A. Kuznetsov, P. Neittaanmäki and P. Tarvainen - Overlapping domain decomposition methods for the obstacle problem [ MR 1262627 ]
    • C.-H. Lai - An iteration scheme for nonsymmetric interface operator [ MR 1262628 ]
    • F. Nataf and F. Rogier - Factorization of the convection-diffusion operator and a (possibly) nonoverlapping Schwarz method [ MR 1262629 ]
    • C. R. Schneidesch, M. O. Deville and E. H. Mund - Domain decomposition method coupling finite elements and preconditioned Chebyshev collocation to solve elliptic problems [ MR 1262630 ]
    • Tsi Min Shih, Chin Bo Liem and Tao Lü - Additive Schwarz methods and acceleration with variable weights [ MR 1262631 ]
    • Part III: Parallelism [ MR 1262599 ]
    • Invited Lectures [ MR 1262599 ]
    • Paul F. Fischer - Parallel domain decomposition for incompressible fluid dynamics [ MR 1262632 ]
    • William D. Gropp and Barry F. Smith - Experiences with domain decomposition in three dimensions: overlapping Schwarz methods [ MR 1262633 ]
    • U. Langer - Parallel iterative solution of symmetric coupled FE/BE-equations via domain decomposition [ MR 1262634 ]
    • Contributed Lectures [ MR 1262599 ]
    • A. Brambilla, C. Carlenzoli, G. Gazzaniga, P. Gervasio and G. Sacchi - Implementation of domain decomposition techniques on nCUBE2 parallel machine [ MR 1262635 ]
    • Patrick Ciarlet, Jr. and Gérard Meurant - A class of domain decomposition preconditioners for massively parallel computers [ MR 1262636 ]
    • F. Dellagiacoma, S. Paoletti, F. Poggi and M. Vitaletti - A domain decomposition environment for local time dependent problems [ MR 1262637 ]
    • S. Foresti, S. Hassanzadeh and V. Sonnad - A parallel element-by-element method for large-scale computations with $h$-$p$-finite elements [ MR 1262638 ]
    • Part IV: Applications [ MR 1262599 ]
    • Invited Lectures [ MR 1262599 ]
    • J.-F. Bourgat, P. Le Tallec, B. Perthame and Y. Qiu - Coupling Boltzmann and Euler equations without overlapping [ MR 1262639 ]
    • M. O. Bristeau, R. Glowinski and J. Periaux - On the numerical solution of the Helmholtz equation at large wave numbers using exact controllability methods. Applications to scattering
    • Roland Glowinski, Tsorng-Whay Pan and Jacques Periaux - A fictitious domain method for unsteady incompressible viscous flow modelled by Navier-Stokes equations
    • Contributed Lectures [ MR 1262599 ]
    • M. C. Ciccoli, J. A. Desideri and J. Périaux - Introduction of domain decomposition techniques in time-dependent flow problems
    • Zdeněk Dostál - The Schur complement algorithm for the solution of contact problems [ MR 1262643 ]
    • E. Faccioli, A. Quarteroni and A. Tagliani - Spectral multidomain methods for the simulation of wave propagation in heterogeneous media [ MR 1262644 ]
    • Adam Gersztenkorn and J. C. Díaz - Domain decomposition preconditioning for faulted geological blocks [ MR 1262645 ]
    • J.-L. Guermond and W.-Z. Shen - A domain decomposition method for simulating $2$D external viscous flows [ MR 1262646 ]
    • Ivar Lie - Interface conditions for heterogeneous domain decomposition: coupling of different hyperbolic systems [ MR 1262647 ]
    • Daniela Mansutti and Francesca Pitolli - Simulation of $3$D Navier-Stokes flows via domain decomposition by the modified discrete vector potential model [ MR 1262648 ]
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Volume: 1571994
MSC: Primary 65;

This book contains the proceedings of the Sixth International Conference on Domain Decomposition, held in June 1992 in Como, Italy. Developments in this area are driven by advances in computer technology as well as by a strengthening in the mathematical foundations of the subject. Compared to just a few years ago, experts have much more experience with difficult applications and have accumulated solid evidence that these methods provide valuable tools for solving problems in science and engineering. Much of the work in this field focuses on developing numerical methods for large algebraic systems, methods central to producing efficient codes for computational fluid dynamics, elasticity, and other core problems of continuum mechanics. These methods hold the promise of allowing simulations of very high resolution with relative ease. This approach allows for the flexibility of using different numerical methods and different models, each appropriate for the subregion at hand, to solve large problems in a cost-effective way. Containing contributions by international experts in this area, this book reports on the state-of-the-art in the growing field of domain decomposition.

Readership

Applied mathematicians, numerical analysts, computer scientists, engineers, graduate students, and researchers.

  • Part I: Theory [ MR 1262599 ]
  • Invited Lectures [ MR 1262599 ]
  • V. I. Agoshkov - Domain decomposition methods using modified basis functions [ MR 1262600 ]
  • James H. Bramble and Joseph E. Pasciak - Uniform convergence estimates for multigrid $V$-cycle algorithms with less than full elliptic regularity [ MR 1262601 ]
  • F. Brezzi and L. D. Marini - A three-field domain decomposition method [ MR 1262602 ]
  • Claudio Canuto and Alessandro Russo - Self-adaptive coupling of mathematical models and/or numerical methods [ MR 1262603 ]
  • Clint N. Dawson and Todd F. Dupont - Noniterative domain decomposition for second order hyperbolic problems [ MR 1262604 ]
  • Maksymilian Dryja and Olof B. Widlund - Some recent results on Schwarz type domain decomposition algorithms [ MR 1262605 ]
  • Yu. A. Kuznetsov - Overlapping domain decomposition methods for parabolic problems [ MR 1262606 ]
  • Jia Chang Sun - Domain decomposition and multilevel PCG method for solving $3$-D fourth order problems [ MR 1262607 ]
  • Jinchao Xu - Some two-grid finite element methods [ MR 1262608 ]
  • Contributed Lectures [ MR 1262599 ]
  • Gloria Aguilar and Francisco Lisbona - Interface conditions for a kind of nonlinear elliptic-hyperbolic problems [ MR 1262609 ]
  • Lucia Gastaldi - A domain decomposition for the transport equation
  • Jan Mandel - Hybrid domain decomposition with unstructured subdomains [ MR 1262611 ]
  • Luca F. Pavarino - Some Schwarz algorithms for the $p$-version finite element method [ MR 1262612 ]
  • U. Rüde - On the robustness and efficiency of the fully adaptive multigrid method [ MR 1262613 ]
  • J.-M. Thomas and D. Trujillo - Finite volume variational formulation. Application to domain decomposition methods [ MR 1262614 ]
  • Part II: Algorithms [ MR 1262599 ]
  • Invited Lectures [ MR 1262599 ]
  • Achi Brandt and Boris Diskin - Multigrid solvers on decomposed domains [ MR 1262615 ]
  • Tony F. Chan and Tarek P. Mathew - Domain decomposition preconditioners for convection diffusion problems [ MR 1262616 ]
  • Oliver Ernst and Gene H. Golub - A domain decomposition approach to solving the Helmholtz equation with a radiation boundary condition [ MR 1262617 ]
  • Charbel Farhat and François-Xavier Roux - The dual Schur complement method with well-posed local Neumann problems [ MR 1262618 ]
  • William D. Gropp, David E. Keyes and Jon S. Mounts - Implicit domain decomposition algorithms for steady, compressible aerodynamics [ MR 1262619 ]
  • T. E. Tezduyar, M. Behr, S. K. Aliabadi, S. Mittal and S. E. Ray - A new mixed preconditioning method based on the clustered element-by-element preconditioners
  • Contributed Lectures [ MR 1262599 ]
  • J.-D. Benamou and Y. Brenier - A domain decomposition method for the polar factorization of vector fields [ MR 1262622 ]
  • B. Bialecki, X.-C. Cai, M. Dryja and G. Fairweather - An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation [ MR 1262623 ]
  • Mark C. Curran - An iterative finite-element collocation method for parabolic problems using domain decomposition [ MR 1262624 ]
  • Michael Griebel - A domain decomposition method using sparse grids [ MR 1262625 ]
  • Wilhelm Heinrichs - Domain decomposition for the Stokes equations in streamfunction formulation [ MR 1262626 ]
  • Yu. A. Kuznetsov, P. Neittaanmäki and P. Tarvainen - Overlapping domain decomposition methods for the obstacle problem [ MR 1262627 ]
  • C.-H. Lai - An iteration scheme for nonsymmetric interface operator [ MR 1262628 ]
  • F. Nataf and F. Rogier - Factorization of the convection-diffusion operator and a (possibly) nonoverlapping Schwarz method [ MR 1262629 ]
  • C. R. Schneidesch, M. O. Deville and E. H. Mund - Domain decomposition method coupling finite elements and preconditioned Chebyshev collocation to solve elliptic problems [ MR 1262630 ]
  • Tsi Min Shih, Chin Bo Liem and Tao Lü - Additive Schwarz methods and acceleration with variable weights [ MR 1262631 ]
  • Part III: Parallelism [ MR 1262599 ]
  • Invited Lectures [ MR 1262599 ]
  • Paul F. Fischer - Parallel domain decomposition for incompressible fluid dynamics [ MR 1262632 ]
  • William D. Gropp and Barry F. Smith - Experiences with domain decomposition in three dimensions: overlapping Schwarz methods [ MR 1262633 ]
  • U. Langer - Parallel iterative solution of symmetric coupled FE/BE-equations via domain decomposition [ MR 1262634 ]
  • Contributed Lectures [ MR 1262599 ]
  • A. Brambilla, C. Carlenzoli, G. Gazzaniga, P. Gervasio and G. Sacchi - Implementation of domain decomposition techniques on nCUBE2 parallel machine [ MR 1262635 ]
  • Patrick Ciarlet, Jr. and Gérard Meurant - A class of domain decomposition preconditioners for massively parallel computers [ MR 1262636 ]
  • F. Dellagiacoma, S. Paoletti, F. Poggi and M. Vitaletti - A domain decomposition environment for local time dependent problems [ MR 1262637 ]
  • S. Foresti, S. Hassanzadeh and V. Sonnad - A parallel element-by-element method for large-scale computations with $h$-$p$-finite elements [ MR 1262638 ]
  • Part IV: Applications [ MR 1262599 ]
  • Invited Lectures [ MR 1262599 ]
  • J.-F. Bourgat, P. Le Tallec, B. Perthame and Y. Qiu - Coupling Boltzmann and Euler equations without overlapping [ MR 1262639 ]
  • M. O. Bristeau, R. Glowinski and J. Periaux - On the numerical solution of the Helmholtz equation at large wave numbers using exact controllability methods. Applications to scattering
  • Roland Glowinski, Tsorng-Whay Pan and Jacques Periaux - A fictitious domain method for unsteady incompressible viscous flow modelled by Navier-Stokes equations
  • Contributed Lectures [ MR 1262599 ]
  • M. C. Ciccoli, J. A. Desideri and J. Périaux - Introduction of domain decomposition techniques in time-dependent flow problems
  • Zdeněk Dostál - The Schur complement algorithm for the solution of contact problems [ MR 1262643 ]
  • E. Faccioli, A. Quarteroni and A. Tagliani - Spectral multidomain methods for the simulation of wave propagation in heterogeneous media [ MR 1262644 ]
  • Adam Gersztenkorn and J. C. Díaz - Domain decomposition preconditioning for faulted geological blocks [ MR 1262645 ]
  • J.-L. Guermond and W.-Z. Shen - A domain decomposition method for simulating $2$D external viscous flows [ MR 1262646 ]
  • Ivar Lie - Interface conditions for heterogeneous domain decomposition: coupling of different hyperbolic systems [ MR 1262647 ]
  • Daniela Mansutti and Francesca Pitolli - Simulation of $3$D Navier-Stokes flows via domain decomposition by the modified discrete vector potential model [ MR 1262648 ]
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