Fast frequency sweep computations using a multi‐point Padé‐based reconstruction method and an efficient iterative solver

Abstract

Problems of the form Z(σ) u(σ)=f(σ), where Z is a given matrix, f is a given vector, and σ is a circular frequency or circular frequency‐related parameter arise in many applications including computational structural and fluid dynamics, and computational acoustics and electromagnetics. The straightforward solution of such problems for fine increments of σ is computationally prohibitive, particularly when Z is a large‐scale matrix. This paper discusses an alternative solution approach based on the efficient computation of u and its successive derivatives with respect to σ at a few sample values of this parameter, and the reconstruction of the solution u(σ) in the frequency band of interest using multi‐point Padé approximants. This computational methodology is illustrated with applications from structural dynamics and underwater acoustic scattering. In each case, it is shown to reduce the CPU time required by the straightforward approach to frequency sweep computations by two orders of magnitude. Copyright © 2006 John Wiley & Sons, Ltd.

Document Details

Document Type
Pub Defense Publication
Publication Date
Sep 05, 2006
Source ID
10.1002/nme.1879

Entities

People

  • Charbel Farhat
  • Garth Reese
  • Philip Avery

Organizations

  • Office of Naval Research
  • Sandia National Laboratories
  • United States Department of Energy

Tags

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design