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Domain Decomposition Methods in Science and Engineering
Edited by: Alfio Quarteroni, Polytechnic Institute of Milan, Italy, Jacques Periaux, Dussault Aviatiation, St. Cloud, France, Yuri A. Kuznetsov, Russian Academy of Sciences, Moscow, Russia, and Olof B. Widlund, New York University-Courant Institute of Mathematical Sciences, NY
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Contemporary Mathematics
1994; 484 pp; softcover
Volume: 157
Reprint/Revision History:
reprinted 1996
ISBN-10: 0-8218-5158-6
ISBN-13: 978-0-8218-5158-6
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 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.

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

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 V-cycle algorithms with less than full elliptic regularity
• F. Brezzi and L. D. Marini -- A three-field domain decomposition method
• C. Canuto and A. Russo -- Self-adaptive 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 two-grid finite element methods
• Contributed Lectures
• G. Aguilar and F. Lisbona -- Interface conditions for a kind of non linear elliptic-hyperbolic 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 well-posed 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 element-by-element 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 finite-element 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 non-symmetric interface operators
• F. Nataf and F. Rogier -- Factorization of the convection-diffusion 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/BE-equations 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 element-by-element method for large-scale computations with $$h-p$$-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 Navier-Stokes equations
• Contributed Lectures
• M. C. Ciccoli, J. A. Desideri, and J. Périaux -- Introduction of domain decomposition techniques in time-dependent 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 Navier-Stokes flows via domain decomposition by the modified discrete vector potential model