Domain Decomposition Methods in Scientific and Engineering Computing

by Keyes, David E.; Xu, Jinchao

• ISBN13: 9780821851715
• ISBN10: 0821851713
• Format: Paperback
• Copyright: 1994-12-01
• Publisher: Amer Mathematical Society

Summary

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.

Table of Contents

Theory: Interpolation spaces and optimal multilevel preconditioners

Two-level additive Schwarz preconditioners for nonconforming finite elements

Two proofs of convergence for the combination technique for the efficient solution of sparse grid problems

Domain decomposition methods for monotone nonlinear elliptic problems

Cascadic conjugate gradient methods for elliptic partial differential equations: Algorithm and numerical results

Multilevel methods for elliptic problems with discontinuous coefficients in three dimensions

Multilevel methods for elliptic problems on domains not resolved by the coarse grid

Three-dimensional domain decomposition methods with nonmatching grids and unstructured coarse solvers

Domain decomposition for elliptic problems with large condition numbers

Stable subspace splittings for Sobolev spaces and domain decomposition algorithms

A wire basket based method for spectral elements in three dimensions

An analysis of spectral graph partitioning via quadratic assignment problems

Error estimators based on stable splittings

Multilevel methods for $P_1$ nonconforming finite elements and discontinuous coefficients in three dimensions

On generalized Schwarz coupling applied to advection-dominated problems

Exotic coarse spaces for Schwarz methods for lower order and spectral finite elements

Algorithms: Preconditioning via asymptotically-defined domain decomposition

A spectral Stokes solver in domain decomposition methods

Preconditioned iterative methods in a subspace for linear algebraic equations with large jumps in the coefficients

The hierarchical basis multigrid method and incomplete LU decomposition

Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes

Two-grid methods for mixed finite element approximations of nonlinear parabolic equations

Domain decomposition algorithms for PDE problems with large scale variations

A one shot domain decomposition/fictitious domain method for the Navier-Stokes equations

Domain-oriented multilevel methods

Multigrid and domain decomposition methods for electrostatics problems

A parallel subspace decomposition method for hyperbolic equations

Numerical treatments for the Helmholtz problem by domain decomposition techniques

Schwarz methods for obstacle problems with convection-diffusion operators

On domain decomposition and shooting methods for two-point boundary value problems

Robust methods for highly nonsymmetric problems

Domain decomposition via the Sinc-Galerkin method for second order differential equations

A bisection method to find all solutions of a system of nonlinear equations

Preconditioning cell-centered finite difference equations on grids with local refinement

Outflow boundary conditions and domain decomposition method

Domain decomposition for adaptive $hp$ finite element methods

Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers

Elliptic preconditioners using fast summation techniques

The modified vertex space domain decomposition method for Neumann boundary value problems

A multi-color splitting method and convergence analysis for local grid refinement

Boundary elements in domain decomposition methods

An overdetermined Schwarz alternating method

Domain decomposition for linear and nonlinear elliptic problems via function or space decomposition

ELLAM-based domain decomposition and local refinement techniques for advection-diffusion equations with interfaces

Parallelism: Parallel domain decomposition applied to coupled transport equations

MENUS-PGG: A mapping environment for unstructured and structured numerical parallel grid generation

A comparison of three iterative algorithms based on domain decomposition methods

IBLU preconditioners for massively parallel computers

Tailoring domain decomposition methods for efficient parallel coarse grid solution and for systems with many right hand sides

Analysis and implementation of DD methods for parallel FE computations

Finite-element/Newton method for solution of nonlinear problems in transport processes using domain decomposition and nested dissection on MIMD parallel computers

Modeling with collaborating PDE solvers: Theory and practice

Parallelization of a multigrid solver via domain decomposition method

A compiler for parallel finite element methods with domain-decomposed unstructured meshes

Applications: A $\chi$-formulation of the viscous-inviscid domain decomposition for the Euler/Navier-Stokes equations

Domain decomposition and computation of two dimensional detonation waves

Parallel implicit methods for aerodynamics

Parallel domain-decomposed preconditioners in finite element shallow water flow modeling

A domain decomposition method for Bellman equations

Domain decomposition for the shallow water equations

Domain decomposition methods for device modelling

An efficient computational method for the flow past an airfoil

Newton-Krylov-Schwarz techniques applied to the two-dimensional incompressible Navier-Stokes and energy equations

Direct numerical simulation of jet flow via a multi-block technique

Balancing domain decomposition for plates

Nonlinear block iterative solution of semiconductor device equations by a domain decomposition method

A direct Chebyshev multidomain method for flow computation with application to rotating systems

Multi-domain Fourier algorithms for parallel solution of the Navier-Stokes equations

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