Fast frequency sweep computations using a multi‐point Padé‐based reconstruction method and an efficient iterative solver |
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| Authors: | Philip Avery Charbel Farhat Garth Reese |
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| Affiliation: | 1. Department of Mechanical Engineering and Institute for Computational and Mathematical Engineering, Stanford University, Mail Code 3035, Stanford, CA 94305, U.S.A.;2. Department of Mechanical Engineering and Institute for Computational and Mathematical Engineering, Stanford University, Mail Code 3035, Stanford, CA 94305, U.S.A.Department of Mechanical Engineering and Institute for Computational and Mathematical Engineering, Stanford University, Mail Code 3035, Stanford, CA 94305, U.S.A.;3. Sandia National Laboratories, Albuquerque, New Mexico 87185, U.S.A. |
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| 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. |
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| Keywords: | FETI‐DPH frequency sweep GCR medium frequency regime multi‐frequency multi‐point Padé approximant reconstruction algorithm |
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