## Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and EngineeringThis refereed volume arose from the editors' recognition that physical scientists, engineers, and applied mathematicians are developing, in parallel, solutions to problems of parallelization. The cross-disciplinary field of scientific computation is bringing about better communication between heterogeneous computational groups, as they face this common challenge. This volume is one attempt to provide cross-disciplinary communication. Problem decomposition and the use of domain-based parallelism in computational science and engineering was the subject addressed at a workshop held at the University of Minnesota Supercomputer Institute in April 1994. The authors were subsequently able to address the relationships between their individual applications and independently developed approaches. |

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### Contents

Q Chapter 1 | 1 |

Q Chapter 3 | 39 |

Q Chapter 4 | 57 |

Q Chapter 5 | 75 |

Q Chapter 6 | 97 |

Q Chapter 7 | 107 |

Q Chapter 8 | 125 |

Q Chapter 9 | 141 |

Q Chapter 11 | 177 |

Q Chapter 12 | 193 |

QChapterl3 | 217 |

Q Chapter 14 | 239 |

Q Chapter 15 | 263 |

a Chapter 16 | 279 |

Q Chapter 17 | 303 |

Q Chapter 10 | 161 |

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### Common terms and phrases

active space additive Schwarz applied approach approximation basis functions basis set boundary conditions calculations Chem coarse grid coefficients configuration conjugate gradient convergence coordinates coupling cube data structure defined denote density described diagonal direct Dirichlet discretization domain decomposition algorithms Domain Decomposition Methods dynamics efficient eigenvalues eigenvectors electronic structure elliptic problems energy evaluation expansion finite element formulation global Glowinski GMRES Hamiltonian implementation integral Intel iPSC/860 interaction interface iterative methods Jacobian Krylov linear systems Markov chain matrix-free memory mesh molecular multigrid multiple multipole expansion Newton nodes nonlinear nonsymmetric number of processors obtained optical potential optimal orbitals orthogonal overlap panel parallel computer parameters Partial Differential Equations partitioning Periaux Phys plasma preconditioner preconditioning quantum reconjugation representation residual Schur complement Schwarz algorithms SIAM simulation Slater determinants solution solver solving sparse sparse matrix step subdomain subspace techniques theory time-dependent transformation unstructured updated vector wave operator wavefunction