Parallel Methods for Solving Nonlinear Block Bordered Systems of Equations

Abstract

A group of parallel algorithms, and their implementation is discussed, for solving a special class of large sparse nonlinear equations. The type of sparsity occurring in these problems, which arise in VLSI design, structural engineering and many other areas, is called a block bordered structure. An explicit method and several implicit methods are described for solving block bordered nonlinear problems, and a mathematical analysis and computational comparisons are made for the two types of methods. Several variations and globally convergent modifications of the implicit method are also presented. Parallel algorithms for solving block bordered nonlinear equations are described and experimental results presented on the Intel hypercube that show the effectiveness of the parallel implicit algorithms. These experiments include a fairly large circuit simulation that leads to a multi-level block bordered system of nonlinear equations. Keywords: Nonlinear equations; Block bordered; Parallel; Implicit methods; Circuit simulation.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 31, 1989
Accession Number
ADA217062

Entities

People

  • Richard H. Byrd
  • Robert B. Schnabel
  • Xiaodong Zhang

Organizations

  • University of Colorado Boulder

Tags

Communities of Interest

  • Advanced Electronics
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Civil Engineering
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Computer Science
  • Differential Equations
  • Engineering
  • Equations
  • Linear Systems
  • Mathematical Analysis
  • Nonlinear Systems
  • Numerical Analysis
  • Parallel Computing
  • Simulations
  • Structural Engineering
  • Theorems

Readers

  • Calculus or Mathematical Analysis
  • Environmental Impact Assessment (EIA) of Proposed Air Force Base Actions.
  • Parallel and Distributed Computing.