Elliptic Problem Solvers

Elliptic Problem Solvers

1st Edition - January 28, 1981

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  • Editor: Martin H. Schultz
  • eBook ISBN: 9781483259123

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Elliptic Problem Solvers provides information pertinent to some aspects of the numerical solution of elliptic partial differential equations. This book presents the advances in developing elliptic problem solvers and analyzes their performance. Organized into 40 chapters, this book begins with an overview of the approximate solution of using a standard Galerkin method employing piecewise linear triangular finite elements. This text then defines the types of vector architecture and discusses the variation in performance that can occur on a vector processor as a function of algorithm and implementation. Other chapters consider the implementation of techniques for elliptical problems. This book discusses as well the six techniques for the solution of nonsymmetric linear systems arising from finite difference discretization of the convection-diffusion equation. The final chapter deals with the basic semiconductor device equations. This book is a valuable resource for electrical and computer engineers, scientists, computer programmers, pure mathematicians, and research workers.

Table of Contents

  • Contributors


    Invited Papers

    A Multi-Level Iterative Method for Nonlinear Elliptic Equations

    Solving Elliptic Problems: 1930-1980

    Multigrid Solvers on Parallel Computers

    Implementing Techniques for Elliptic Problems on Vector Processors

    On Some Trends in Elliptic Problem Solvers

    Co-Energy Methods for Elliptic Flow and Related Problems

    ELLPACK: Progress and Plans

    The ITPACK Package for Large Sparse Linear Systems

    Contributed Papers

    Efficient Fortran Subprograms for the Solution of Elliptic Partial Differential Equations

    Iterative Methods for Finite Element Equations

    Predictor-Corrector Methods for the Solution of Time-Dependent Parabolic Problems on Parallel Processors

    Efficient Solution of the Biharmonic Equation

    Attainable Accuracy of Compact Discretizations of the Poisson Equation

    The Concept of Rigidity and Its Implementation

    Theorems of Stein-Rosenberg Type II. Optimal Paths of Relaxation in the Complex Plane

    Sparse Vectorized Direct Solution of Elliptic Problems

    Multi-Grid and ICCG for Problems with Interfaces

    An Ad Hoc Sor Method

    On Preconditioned Iterative Methods for Elliptic Partial Differential Equations

    Block Relaxation Strategies

    On the Numerical Solution of Nonlinear Elliptic PDEs Arising from Semiconductor Device Modeling

    Non-Standard Multigrid Techniques Using Checkered Relaxation and Intermediate Grids

    Some Experiments in Solving Stiff Oscillatory Ordinary Differential Equations

    A Numerical Method for Solving Elliptic Boundary Value Problems in Unbounded Domains

    Applications of Transfinite ("Blending-Function") Interpolation to the Approximate Solution of Elliptic Problems

    Application of Parallel Processor to the Solution of Finite Difference Problems

    Vector Algorithms for Elliptic Partial Differential Equations Based on the Jacobi Method

    Adapting Iterative Algorithms Developed for Symmetric Systems to Nonsymmetric Systems

    Comparison of Methods of Solution of the Finite Element Equations for the Large Displacement Analysis of Arches

    Mesh Generation by Conformai and Quasiconformal Mappings

    Block Iterative Methods

    A Mesh-Parameter-Continuation Method

    Capacitance Matrix Methods—A Brief Survey

    Gem Solutions of Elliptic and Mixed Problems with Non-Separable 5- and 9-Point Operators

    A Parallel Block Stiefel Method for Solving Positive Definite Systems

    Numerical Solution of Coupled Systems of Partial Differential Equations in One Spatial Variable Time

    On the Choice of Discretization for Solving PDEs on a Multi-Processor

    A Software Package for Elliptic Partial Differential Equations

    An Empirical Investigation of Methods for Nonsymmetric Linear Systems

    Semiconductor Device Simulation


Product details

  • No. of pages: 458
  • Language: English
  • Copyright: © Academic Press 1981
  • Published: January 28, 1981
  • Imprint: Academic Press
  • eBook ISBN: 9781483259123

About the Editor

Martin H. Schultz

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