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 method 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.

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