On Improving the Convergence of the Solution of a System of Linear Equations

Abstract

The computation of electromagnetic scattering from a nanowire requires the solution of a system of linear equations of the form, Ax=b, where the dimension of the matrix A increases with the number of unknowns. Previously, we had implemented a bi-conjugate gradient algorithm to iteratively solve this system of equations. However, this method converges very slowly when the convergence criterion is made stringent. An improved version of the algorithm, namely stabilized bi-conjugate gradient algorithm, is implemented to overcome this drawback. The new version provides very good convergence for convergence factors up to 0.0001 but the convergence is still slow for convergence factor in the 10(to the minus 5th power) - 10(to the minus 8th power) range. In order to accelerate the convergence of the solution, we make use of the Levin transform to accelerate the convergence of the solution. This transform is tested in the numerical solution of three different types of integral equations using the method of moments.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 2005
Accession Number
ADA444371

Entities

People

  • J. M. Elson
  • Klaus Halterman
  • Surendra Singh

Organizations

  • University of Tulsa

Tags

Communities of Interest

  • Advanced Electronics
  • Air Platforms

DTIC Thesaurus Topics

  • Aerial Warfare
  • Algorithms
  • Computational Science
  • Computations
  • Convergence
  • Electric Fields
  • Electromagnetic Scattering
  • Equations
  • Integral Equations
  • Method Of Moments
  • Military Research
  • Precision
  • Procedures (Computers)
  • Residuals
  • Sequences
  • Two Dimensional
  • Warfare

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)