Elliptic Problem Solvers - 1st Edition - ISBN: 9780121005603, 9781483263397

Elliptic Problem Solvers

1st Edition

Volume II

Editors: Garrett Birkhoff Arthur Schoenstadt
eBook ISBN: 9781483263397
Imprint: Academic Press
Published Date: 28th January 1984
Page Count: 588
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Elliptic Problem Solvers, II covers the proceedings of the Elliptic Problem Solvers Conference, held at the Naval Postgraduate School in Monterey, California from January 10 to 12, 1983. The book focuses on various aspects of the numerical solution of elliptic boundary value problems.

The selection first offers information on building elliptic problem solvers with ELLPACK; presentation and evolution of the club module; and a fourth order accurate fast direct method for the Helmholtz equation. The text then examines the ITPACK project, CMMPAK, solving elliptic problems on an array processor system, and parallel architectures for iterative methods on adaptive, block structured grids. Topics include adaptive solution algorithm, data structure, elliptic problem solvers, input data, and vector ITPACK.

The publication ponders on conjugate gradient preconditioners for vector and parallel processors; an algebra for systolic computation; and an incomplete-Cholesky factorization by a matrix partition algorithm. The book also tackles the numerical solution of a model equation near the onset of the Rayleigh-Benard instability; numerical methods for solving coupled semiconductor equations on a minicomputer; and analysis of nonlinear elliptic systems arising in reaction/diffusion modeling.

The selection is highly recommended for researchers interested in elliptic problem solvers.

Table of Contents



I Software Packages

Building Elliptic Problem Solvers with ELLPACK

Presentation and Evolution of the Club Modulef: A Library of Computer Procedures for Finite Element Analysis

A Fourth-Order Accurate Fast Direct Method for the Helmholtz Equation

The (New) Yale Sparse Matrix Package

The ITPACK Project: Past, Present, and Future

CMMPAK—The Capacitance Matrix Software Package

II Vector and Parallel Processing

Solving Elliptic Problems on an Array Processor System

Parallel Architectures for Iterative Methods on Adaptive, Block Structured Grids

Highly Concurrent Algorithms for Solving Linear Systems of Equations

Conjugate Gradient Preconditioners for Vector and Parallel Processors

An Algebra for Systolic Computation

An Incomplete-Cholesky Factorization by a Matrix Partition Algorithm

A Fast Poisson Solver for Multiprocessors

Systolic Arrays: High Performance Parallel Machines for Matrix Computation

III Iterative Equation Solving

A Survey of Recent Results on Iterative Methods for Solving Large Sparse Linear Systems

Numerical Algorithms for Indefinite Problems

Preconditioned Conjugate Gradient Methods for the Helmholtz Equation

Solving Elliptic Problems on Regions Partitioned into Substructures

The Ad Hoc SOR Method: A Local Relaxation Scheme

Iterative Methods for Non-Self-Adjoint Elliptic Problems

Implicit Block Explicit Overrelaxation Schemes

Dynamic Acceleration of Nonlinear Iterations

Navier-Stokes Pressure Equation Iteration

Accelerating Nonsymmetrizable Iterative Methods

IV Finite Element and Multigrid Methods

Adaptive Finite Element Processes in Structural Mechanics

Finite Element Approximations to Compressible Flow Problems

Solving Elliptic Problems by Domain Decomposition Methods with Applications

Computing Added Mass Coefficients

A Priori Local Grid Refinement in the Multigrid Method

Abstract Multi-Grid with Applications to Elliptic Boundary Value Problems

A New Ordering Scheme for the Hermite Bicubic Collocation Equations

Solution Methods for the Finite Element Equations in Nonlinear Shell Analysis

V Advances in Modeling and Physical Applications

Discretization and Multilevel Solution Techniques for Nonlinear Elliptic Systems

Analysis of Nonlinear Elliptic Systems Arising in Reaction/Diffusion Modeling

Numerical Methods for Solving Coupled Semiconductor Equations on a Minicomputer

Numerical Solution of a Model Equation Near the Onset of the Rayleigh-Bénard Instability

Approximation of a Nonsymmetric, Singularly Perturbed Problem

Numerical Solution of a Confined Laminar Diffusion Flame



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© Academic Press 1984
Academic Press
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About the Editor

Garrett Birkhoff

Arthur Schoenstadt

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