Contemporary Mathematics 1994; 484 pp; softcover Volume: 157 Reprint/Revision History: reprinted 1996 ISBN10: 0821851586 ISBN13: 9780821851586 List Price: US$45 Member Price: US$36 Order Code: CONM/157
 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. Readership Applied mathematicians, numerical analysts, computer scientists, engineers, graduate students, and researchers. Table of Contents Part I. Theory: Invited Lectures  V. I. Agoshkov  Domain decomposition methods using modified basis functions
 J. H. Bramble and J. E. Pasciak  Uniform convergence estimates for multigrid Vcycle algorithms with less than full elliptic regularity
 F. Brezzi and L. D. Marini  A threefield domain decomposition method
 C. Canuto and A. Russo  Selfadaptive coupling of mathematical models and/or numerical methods
 C. N. Dawson and T. F. Dupont  Noniterative domain decomposition for second order hyperbolic problems
 M. Dryja and O. B. Widlund  Some recent results on Schwarz type domain decomposition algorithms
 Yu. A. Kuznetsov  Overlapping domain decomposition methods for parabolic problems
 J. Sun  Domain decomposition and multilevel PCG method for solving \(3\)\(\mathrm{D}\) fourth order problems
 J. Xu  Some twogrid finite element methods
 Contributed Lectures
 G. Aguilar and F. Lisbona  Interface conditions for a kind of non linear elliptichyperbolic problems
 L. Gastaldi  A domain decomposition for the transport equation
 J. Mandel  Hybrid domain decomposition with unstructured subdomains
 L. F. Pavarino  Some Schwarz algorithms for the \(p\)version finite element method
 U. Rüde  On the robustness and efficiency of the fully adaptive multigrid method
 J.M. Thomas and D. Trujillo  Finite volume variational formulation. Application to domain decomposition methods
Part II. Algorithms: Invited Lectures  A. Brandt and B. Diskin  Multigrid solvers on decomposed domains
 T. F. Chan and T. P. Mathew  Domain decomposition preconditioners for convection diffusion problems
 O. Ernst and G. H. Golub  A domain decomposition approach to solving the Helmholtz equation with a radiation boundary condition
 C. Farhat and F.X. Roux  The dual Schur complement method with wellposed local Neumann problems
 W. D. Gropp, D. E. Keyes, and J. S. Mounts  Implicit domain decomposition algorithms for steady, compressible aerodynamics
 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
 A. Averbuch, M. Israeli, and L. Vozovoi  Domain decomposition methods with local Fourier basis for parabolic problems
 J.D. Benamou and Y. Brenier  A domain decomposition method for the polar factorization of vector fields
 B. Bialecki, X.C. Cai, M. Dryja, and G. Fairweather  An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation
 M. C. Curran  An iterative finiteelement collocation method for parabolic problems using domain decomposition
 M. Griebel  A domain decomposition method using sparse grids
 W. Heinrichs  Domain decomposition for the Stokes equations in streamfunction formulation
 Yu. A. Kuznetsov, P. Neittaanmäki, and P. Tarvainen  Overlapping domain decomposition methods for the obstacle problem
 C.H. Lai  An iteration scheme for nonsymmetric interface operators
 F. Nataf and F. Rogier  Factorization of the convectiondiffusion operator and a ( possibly) non overlapping Schwarz method
 C. R. Schneidesch, M. O. Deville, and E. H. Mund  Domain decomposition method coupling finite elements and preconditioned Chebyshev collocation to solve elliptic problems
 T.M. Shih, C.B. Liem, and T. Lu  Additive Schwarz methods and acceleration with variable weights
Part III. Parallelism: Invited Lectures  P. F. Fischer  Parallel domain decomposition for incompressible fluid dynamics
 W. D. Gropp and B. F. Smith  Experiences with domain decomposition in three dimensions: Overlapping Schwarz methods
 U. Langer  Parallel iterative solution of symmetric coupled FE/BEequations via domain decomposition
 Contributed Lectures
 A. Brambilla, C. Carlenzoli, G. Gazzaniga, P. Gervasio, and G. Sacchi  Implementation of domain decomposition techniques on nCUBE2 parallel machine
 P. Ciarlet, Jr. and G. Meurant  A class of domain decomposition preconditioners for massively parallel computers
 F. Dellagiacoma, S. Paoletti, F. Poggi, and M. Vitaletti  A domain decomposition environment for local time dependent problems
 S. Foresti, S. Hassanzadeh, and V. Sonnad  A parallel elementbyelement method for largescale computations with \(hp\)finite elements
Part IV. Applications: Invited Lectures  J. F. Bourgat, P. L. Tallec, B. Perthame, and Y. Qiu  Coupling Boltzmann and Euler equations without overlapping
 M. O. Bristeau, R. Glowinski, and J. Périaux  On the numerical solution of the Helmholtz equation at large wave numbers using exact controllability methods. Application to scattering
 R. Glowinski, T.W. Pan, and J. Périaux  A fictitious domain method for unsteady incompressible viscous flow modelled by NavierStokes equations
 Contributed Lectures
 M. C. Ciccoli, J. A. Desideri, and J. Périaux  Introduction of domain decomposition techniques in timedependent flow problems
 Z. Dostál  The Schur complement algorithm for the solution of contact problems
 E. Faccioli, A. Quarteroni, and A. Tagliani  Spectral multidomain methods for the simulation of wave propagation in heterogeneous media
 A. Gersztenkorn and J. C. Diaz  Domain decomposed preconditioning for faulted geological blocks
 J.L. Guermond and W.Z. Shen  A domain decomposition method for simulating 2D external viscous flows
 I. Lie  Interface conditions for heterogeneous domain decomposition: Coupling of different hyperbolic systems
 D. Mansutti and F. Pitolli  Simulation of 3D NavierStokes flows via domain decomposition by the modified discrete vector potential model
