An Improved Method for Solving Systems of Linear Equations in Frequency Response Problems

Abstract

Vibration and acoustics problems that require solving matrix equations for many frequencies have solutions that vary very little from one frequency to the next. This suggests that an iterative method using the solution at one frequency could be used to obtain the next frequency solution. In this report, the matrix inverse at the first frequency serves as the preconditioner for the preconditioned conjugate gradient method to obtain subsequent frequencies. For the problem examined in this report, in which the matrix comes from the finite-element analysis of a cube, the iterative method is more than an order of magnitude faster than Gaussian elimination.

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Document Details

Document Type
Technical Report
Publication Date
Apr 15, 2004
Accession Number
ADA422723

Entities

People

  • Martin H. Marcus

Organizations

  • United States Naval Research Laboratory

Tags

DTIC Thesaurus Topics

  • Acoustics
  • Bandwidth
  • Computations
  • Contrast
  • Convergence
  • Decomposition
  • Eigenvalues
  • Elimination
  • Equations
  • Finite Element Analysis
  • Frequency
  • Frequency Response
  • Iterations
  • Military Research
  • Modulus Of Elasticity
  • Sparse Matrix
  • Underwater Acoustics

Readers

  • Operations Research
  • Structural Dynamics.