GRMES Iterative Solution of Matrix Systems Derived from Boundary Element Techniques

Abstract

We apply the Generalized Minimal Residual (GMRES) iterative equation solution technique to a set of full, unsymmetric matrix systems generated by a standard boundary element method. The test problems chosen produced well conditioned matrices. The GMRES technique, when used without preconditioning and with a sufficient number of trial vectors, solved the matrix system using as few as 23% of the operations required by a direct Gauss reduction. The class of partial LU decomposition preconditioners tested degraded the condition number of the matrices, and consequently did not reduce the GMRES solution time. In general, the GMRES technique does not appear to be of practical interest compared to the direct reduction unless other factors (availability of a good approximation to the final solution, etc.) intervene.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1989
Accession Number
ADA250961

Entities

People

  • Lorraine G. Olson

Organizations

  • University of Michigan

Tags

Communities of Interest

  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mechanics
  • Boundaries
  • Boundary Element Methods
  • Convergence
  • Engineering
  • Equations
  • Floating Point Operations
  • Integral Equations
  • Integrals
  • Iterations
  • Marine Engineering
  • Mechanical Engineering
  • Mechanics
  • Naval Architecture
  • Procedures (Computers)
  • Residuals

Readers

  • Linear Algebra
  • Systems Analysis and Design