Domain Decomposition Methods in Scientific and Engineering Computing

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