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Fast frequency sweep computations using a multi‐point Padé‐based reconstruction method and an efficient iterative solver
Author(s) -
Avery Philip,
Farhat Charbel,
Reese Garth
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1879
Subject(s) - solver , computation , computational complexity theory , matrix (chemical analysis) , algorithm , iterative method , computer science , point (geometry) , mathematics , mathematical optimization , computational science , geometry , materials science , composite material
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.