Electronic ISBN:  9780821877487 
Product Code:  CONM/157.E 
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Book DetailsContemporary MathematicsVolume: 157; 1994; 484 ppMSC: 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 costeffective way. Containing contributions by international experts in this area, this book reports on the stateoftheart in the growing field of domain decomposition.
ReadershipApplied 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 threefield domain decomposition method [ MR 1262602 ]

Claudio Canuto and Alessandro Russo  Selfadaptive 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 twogrid finite element methods [ MR 1262608 ]

Contributed Lectures [ MR 1262599 ]

Gloria Aguilar and Francisco Lisbona  Interface conditions for a kind of nonlinear elliptichyperbolic 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 FrançoisXavier Roux  The dual Schur complement method with wellposed 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 elementbyelement 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 finiteelement 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 convectiondiffusion 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/BEequations 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 elementbyelement method for largescale 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, TsorngWhay Pan and Jacques Periaux  A fictitious domain method for unsteady incompressible viscous flow modelled by NavierStokes equations

Contributed Lectures [ MR 1262599 ]

M. C. Ciccoli, J. A. Desideri and J. Périaux  Introduction of domain decomposition techniques in timedependent 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 NavierStokes flows via domain decomposition by the modified discrete vector potential model [ MR 1262648 ]


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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 costeffective way. Containing contributions by international experts in this area, this book reports on the stateoftheart in the growing field of domain decomposition.
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 threefield domain decomposition method [ MR 1262602 ]

Claudio Canuto and Alessandro Russo  Selfadaptive 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 twogrid finite element methods [ MR 1262608 ]

Contributed Lectures [ MR 1262599 ]

Gloria Aguilar and Francisco Lisbona  Interface conditions for a kind of nonlinear elliptichyperbolic 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 FrançoisXavier Roux  The dual Schur complement method with wellposed 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 elementbyelement 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 finiteelement 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 convectiondiffusion 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/BEequations 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 elementbyelement method for largescale 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, TsorngWhay Pan and Jacques Periaux  A fictitious domain method for unsteady incompressible viscous flow modelled by NavierStokes equations

Contributed Lectures [ MR 1262599 ]

M. C. Ciccoli, J. A. Desideri and J. Périaux  Introduction of domain decomposition techniques in timedependent 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 NavierStokes flows via domain decomposition by the modified discrete vector potential model [ MR 1262648 ]