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Domain Decomposition Methods in Scientific and Engineering Computing
Edited by: David E. Keyes and Jinchao Xu

Contemporary Mathematics
1994; 546 pp; softcover
Volume: 180
ISBN-10: 0-8218-5171-3
ISBN-13: 978-0-8218-5171-5
List Price: US$98
Member Price: US$78.40
Order Code: CONM/180
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This book contains proceedings from the Seventh International Conference on Domain Decomposition Methods, held at Pennsylvania State University in October 1993. The term "domain decomposition" has for nearly a decade been associated with the partly iterative, partly direct algorithms explored in the proceedings of this conference. Noteworthy trends in the current volume include progress in dealing with so-called "bad parameters" in elliptic partial differential equation problems, as well as developments in partial differential equations outside of the elliptically-dominated framework. Also described here are convergence and complexity results for novel discretizations, which bring with them new challenges in the derivation of appropriate operators for coarsened spaces. Implementations and architectural considerations are discussed, as well as partitioning tools and environments. In addition, the book describes a wide array of applications, from semiconductor device simulation to structural mechanics to aerodynamics. Presenting many of the latest results in the field, this book offers readers an up-to-date guide to the many facets of the theory and practice of domain decomposition.


Research mathematicians.

Table of Contents

Part I. Theory
  • F. A. Bornemann -- Interpolation spaces and optimal multilevel preconditioners
  • S. C. Brenner -- Two-level additive Schwarz preconditioners for nonconforming finite elements
  • H.-J. Bungartz, M. Griebel, D. Röschke, and C. Zenger -- Two proofs of convergence for the combination technique for the efficient solution of sparse grid problems
  • X.-C. Cai and M. Dryja -- Domain decomposition methods for monotone nonlinear elliptic problems
  • P. Deuflhard -- Cascadic conjugate gradient methods for elliptic partial differential equations: Algorithm and numerical results
  • M. Dryja -- Multilevel methods for elliptic problems with discontinuous coefficients in three dimensions
  • R. Kornhuber and H. Yserentant -- Multilevel methods for elliptic problems on domains not resolved by the coarse grid
  • P. Le Tallec, T. Sassi, and M. Vidrascu -- Three-dimensional domain decomposition methods with nonmatching grids and unstructured coarse solvers
  • S. V. Nepomnyaschikh -- Domain decomposition for elliptic problems with large condition numbers
  • P. Oswald -- Stable subspace splittings for Sobolev spaces and domain decomposition algorithms
  • L. F. Pavarino -- A wire basket based method for spectral elements in three dimensions
  • A. Pothen -- An analysis of spectral graph partitioning via quadratic assignment problems
  • U. Rüde -- Error estimators based on stable splittings
  • M. Sarkis -- Multilevel methods for \(P_1\) nonconforming finite elements and discontinuous coefficients in three dimensions
  • K. H. Tan and M. J. A. Borsboom -- On generalized Schwarz coupling applied to advection-dominated problems
  • O. B. Widlund -- Exotic coarse spaces for Schwarz methods for lower order and spectral finite elements
Part II. Algorithms
  • S. F. Ashby, C. T. Kelley, P. E. Saylor, and J. S. Scroggs -- Preconditioning via asymptotically-defined domain decomposition
  • M. Azaiez and A. Quarteroni -- A spectral Stokes solver in domain decomposition methods
  • N. S. Bakhvalov and A. V. Knyazev -- Preconditioned iterative methods in a subspace for linear algebraic equations with large jumps in the coefficients
  • R. E. Bank and J. Xu -- The hierarchical basis multigrid method and incomplete LU decomposition
  • T. F. Chan and B. F. Smith -- Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes
  • C. N. Dawson and M. F. Wheeler -- Two-grid methods for mixed finite element approximations of nonlinear parabolic equations
  • L. Giraud and R. S. Tuminaro -- Domain decomposition algorithms for PDE problems with large scale variations
  • R. Glowinski, T.-W. Pan, and J. Périaux -- A one shot domain decomposition/fictitious domain method for the Navier-Stokes equations
  • M. Griebel -- Domain-oriented multilevel methods
  • M. Holst and F. Saied -- Multigrid and domain decomposition methods for electrostatics problems
  • E. Katzer -- A parallel subspace decomposition method for hyperbolic equations
  • S. Kim -- Numerical treatments for the Helmholtz problem by domain decomposition techniques
  • Yu. A. Kuznetsov, P. Neittaanmäki, and P. Tarvainen -- Schwarz methods for obstacle problems with convection-diffusion operators
  • C.-H. Lai -- On domain decomposition and shooting methods for two-point boundary value problems
  • W. Layton, J. Maubach, and P. Rabier -- Robust methods for highly nonsymmetric problems
  • N. J. Lybeck and K. L. Bowers -- Domain decomposition via the Sinc-Galerkin method for second order differential equations
  • P. Mejzlík -- A bisection method to find all solutions of a system of nonlinear equations
  • I. D. Mishev -- Preconditioning cell-centered finite difference equations on grids with local refinement
  • F. Nataf and F. Rogier -- Outflow boundary conditions and domain decomposition method
  • J. T. Oden, A. Patra, and Y. Feng -- Domain decomposition for adaptive \(hp\) finite element methods
  • M. Pernice -- Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers
  • L. R. Scott -- Elliptic preconditioners using fast summation techniques
  • J. P. Shao -- The modified vertex space domain decomposition method for Neumann boundary value problems
  • T.-m. Shih, C.-b. Liem, T. Lu, and A. Zhou -- A multi-color splitting method and convergence analysis for local grid refinement
  • O. Steinbach -- Boundary elements in domain decomposition methods
  • V. H. Sun and W.-P. Tang -- An overdetermined Schwarz alternating method
  • X.-C. Tai -- Domain decomposition for linear and nonlinear elliptic problems via function or space decomposition
  • H. Wang, H. K. Dahle, R. E. Ewing, T. Lin, and J. E. Vå g -- ELLAM-based domain decomposition and local refinement techniques for advection-diffusion equations with interfaces
Part III. Parallelism
  • P. E. Bjørstad, W. M. Coughran, Jr., and E. Grosse -- Parallel domain decomposition applied to coupled transport equations
  • N. Chrisochoides, G. Fox, and J. Thompson -- MENUS-PGG: A mapping environment for unstructured and structured numerical parallel grid generation
  • P. Ciarlet, Jr. -- A comparison of three iterative algorithms based on domain decomposition methods
  • E. D. Sturler -- IBLU preconditioners for massively parallel computers
  • C. Farhat and P.-S. Chen -- Tailoring domain decomposition methods for efficient parallel coarse grid solution and for systems with many right hand sides
  • H. X. Lin -- Analysis and implementation of DD methods for parallel FE computations
  • M. R. Mehrabi and R. A. Brown -- Finite-element/Newton method for solution of nonlinear problems in transport processes using domain decomposition and nested dissection on MIMD parallel computers
  • M. Mu and J. R. Rice -- Modeling with collaborating PDE solvers: Theory and practice
  • F.-X. Roux and D. Tromeur-Dervout -- Parallelization of a multigrid solver via domain decomposition method
  • J. R. Shewchuk and O. Ghattas -- A compiler for parallel finite element methods with domain-decomposed unstructured meshes
Part IV. Applications
  • R. Arina and C. Canuto -- A \(\chi\)-formulation of the viscous-inviscid domain decomposition for the Euler/Navier-Stokes equations
  • W. Cai -- Domain decomposition and computation of two dimensional detonation waves
  • X.-C. Cai, W. D. Gropp, D. E. Keyes, and M. D. Tidriri -- Parallel implicit methods for aerodynamics
  • Y. Cai and I. M. Navon -- Parallel domain-decomposed preconditioners in finite element shallow water flow modeling
  • F. Camilli, M. Falcone, P. Lanucara, and A. Seghini -- A domain decomposition method for Bellman equations
  • J. G. Chefter, C. K. Chu, and D. E. Keyes -- Domain decomposition for the shallow water equations
  • R. K. Coomer and I. G. Graham -- Domain decomposition methods for device modelling
  • G. C. Hsiao, M. D. Marcozzi, and S. Zhang -- An efficient computational method for the flow past an airfoil
  • P. G. Jacobs, V. A. Mousseau, P. R. McHugh, and D. A. Knoll -- Newton-Krylov-Schwarz techniques applied to the two-dimensional incompressible Navier-Stokes and energy equations
  • H. C. Ku, H. E. Gilreath, R. Raul, and J. C. Sommerer -- Direct numerical simulation of jet flow via a multi-block technique
  • P. Le Tallec, J. Mandel, and M. Vidrascu -- Balancing domain decomposition for plates
  • S. Micheletti, A. Quarteroni, and R. Sacco -- Nonlinear block iterative solution of semiconductor device equations by a domain decomposition method
  • I. Raspo, J. Ouazzani, and R. Peyret -- A direct Chebyshev multidomain method for flow computation with application to rotating systems
  • L. Vozovoi, M. Israeli, and A. Averbuch -- Multi-domain Fourier algorithms for parallel solution of the Navier-Stokes equations
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