Comparison of Several Iterative Techniques in the Solution of Symmetric Banded Equations on a Two-Pipe Cyber 205

Abstract

The effectiveness of several iterative techniques for solving matrix equations resulting from finite difference approximations to self-adjoint parabolic and elliptic partial differential equations is reviewed. The techniques include Stone's Strongly Implicit Procedure (SIP) and several conjugate gradient algorithms with varying preconditioners. The comparison is made on a vector machine (two-pipe Cyber 205) where vectorization of the code is done primarily by the vector machine compiler available. It is found that of the methods studied, POLCG (Polynominal Preconditioned Conjugate Gradient Method) and MICCG (Modified Incomplete Cholesky Conjugate Gradient Method) appear to require the least amount of central processing time. An advantage of MICCG and POLCG is that it is less sensitive to increasing matrix size. Its disadvantages are that it requires an iteration parameter, has a greater set-up time, and needs more storage than POLCG.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1988
Accession Number
ADA204164

Entities

People

  • Clyde Scandrett

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Compilers
  • Differential Equations
  • Equations
  • Groundwater
  • Iterations
  • Mathematics
  • Parallel Computing
  • Parallel Processing
  • Partial Differential Equations
  • Polynomials
  • Three Dimensional
  • Two Dimensional
  • Water
  • Water Resources

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Geospatial Intelligence and Artificial Intelligence Analytics

Technology Areas

  • Cyber
  • Cyber - Cryptography