## Fifth International Symposium on Domain Decomposition Methods for Partial Differential EquationsPapers presented at the May 1991 symposium reflect continuing interest in the role of domain decomposition in the effective utilization of parallel systems; applications in fluid mechanics, structures, biology, and design optimization; and maturation of analysis of elliptic equations, with theoretic |

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### Contents

Additive Schwarz Methods for Elliptic Finite Element | 3 |

Some Schwarz Methods for Symmetric and Nonsymmetric | 19 |

Domain Decomposition Method with Nonsymmetric Interface | 37 |

The Schwarz Algorithm and Multilevel Decomposition Iterative | 48 |

Preconditioners for One Class of Elliptic Problems in Not Simply | 56 |

Decomposition and Fictitious Domains Methods for Elliptic | 62 |

Spectral Analysis of the Interface Operators Associated with | 73 |

An Iterative Substructuring Algorithm for Problems in Three | 91 |

Numerical Solution of a Turning Point Problem | 330 |

The Parallel Block Preconditioned Conjugate Gradient Algorithm | 339 |

A Domain Decomposition Preconditioner Based on a Change | 346 |

Domain Decomposition Algorithms of Schwarz Type Designed | 362 |

Parallel Multigrid and Domain Decomposition Algorithms | 376 |

The Performance of an ExplicitImplicit Domain Decomposition | 386 |

Solution of the Stokes Problem on DistributedMemory | 394 |

Parallel Multigrid Methods on Composite Meshes | 401 |

Finite Element Matching Methods | 99 |

Iterative Methods by SPD and Small Subspace Solvers | 106 |

Contents | 119 |

Principles Algorithms | 129 |

Adaptive MultiDomain Spectral Methods | 195 |

Penalty Method Utilized for Parabolic Problems | 204 |

Application of Domain Decomposition Techniques to Modal | 214 |

A Comparison of Some Domain Decomposition Algorithms | 224 |

Fourier and Probe Variants of the Vertex Space Domain | 236 |

Domain Decomposition Method and Slow Passage Through | 250 |

Domain Decomposition and PDE with Periodic Boundary | 258 |

A SaddlePoint Principle Domain Decomposition Method for | 271 |

Domain Decomposition to Solve Layers and Singular | 293 |

A Domain Decomposition Method for Eigenvalue Problems | 306 |

On Adaptive Domain Decomposition with Moving Subdomains | 322 |

Kinematic Domain Decomposition for BoundaryMotionInduced | 411 |

Spectral Domain Decomposition Methods for Compressible | 441 |

Hybrid Domain Decomposition for Configurations with Multiple | 476 |

A Submerged Body Moving in a Stratified Medium Via Domain | 498 |

Solution of DifferentialAlgebraic Equations for Renal AcidBase | 518 |

Pseudospectral Domain Decomposition Techniques for | 531 |

A Domain Decomposition Method for Elliptic Boundary Value | 545 |

A Multiblock Multigrid Solution Procedure for Multielement | 558 |

NonOscillatory Spectral Element Chebyshev Method for Shock | 566 |

Adaptive Multigrid Domain Decomposition Solutions of | 586 |

A Parallel Algorithm for an Investigation of SelfFocusing | 597 |

Composite Grids for Flow Computations on Complex | 605 |

A Multidomain Spectral Collocation Solver for the Elasticity | 614 |

### Common terms and phrases

adaptive additive algorithm analysis applied approach approximation associated assume block bound boundary conditions calculation cell coarse coefficients communication computed consider constant construct continuity convergence corresponding coupling defined definite denote derivatives described direction discrete discussed Domain Decomposition Methods efficient eigenvalues elliptic problems error example Figure finite element flow flux formulation function given global grid implementation increases independent initial interface interior interpolation introduce iterative linear Mathematics matrix mesh multigrid multipliers Navier-Stokes nodes Note obtained operator overlap parallel parameter Partial Differential Equations performance physical points polynomial positive preconditioned preconditioner presented pressure problem procedure processors reduced refer refinement region respectively satisfies scheme Schur complement Schwarz shown SIAM solution solve solver space spectral step structure subdomains subspace substructuring Table technique values variables variational vector Widlund