Contemporary Mathematics 1994; 546 pp; softcover Volume: 180 ISBN10: 0821851713 ISBN13: 9780821851715 List Price: US$98 Member Price: US$78.40 Order Code: CONM/180
 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 socalled "bad parameters" in elliptic partial differential equation problems, as well as developments in partial differential equations outside of the ellipticallydominated 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 uptodate guide to the many facets of the theory and practice of domain decomposition. Readership Research mathematicians. Table of Contents Part I. Theory  F. A. Bornemann  Interpolation spaces and optimal multilevel preconditioners
 S. C. Brenner  Twolevel 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  Threedimensional 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 advectiondominated 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 asymptoticallydefined 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  Twogrid 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 NavierStokes equations
 M. Griebel  Domainoriented 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 convectiondiffusion operators
 C.H. Lai  On domain decomposition and shooting methods for twopoint 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 SincGalerkin 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 cellcentered 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 multicolor 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  ELLAMbased domain decomposition and local refinement techniques for advectiondiffusion 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  MENUSPGG: 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  Finiteelement/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. TromeurDervout  Parallelization of a multigrid solver via domain decomposition method
 J. R. Shewchuk and O. Ghattas  A compiler for parallel finite element methods with domaindecomposed unstructured meshes
Part IV. Applications  R. Arina and C. Canuto  A \(\chi\)formulation of the viscousinviscid domain decomposition for the Euler/NavierStokes 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 domaindecomposed 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  NewtonKrylovSchwarz techniques applied to the twodimensional incompressible NavierStokes and energy equations
 H. C. Ku, H. E. Gilreath, R. Raul, and J. C. Sommerer  Direct numerical simulation of jet flow via a multiblock 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  Multidomain Fourier algorithms for parallel solution of the NavierStokes equations
