Numerical Laplace inversion in problems of elastodynamics: Comparison of four algorithms

•Four numerical algorithms tested for Laplace transform inversion in elastodynamics.•Some methods can reach nearly arbitrary precision using multi-precision computations.•The combination of FFT and Wynns algorithm seems to be the most powerful.•Results of numerical inversion need to be always verifi...

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Bibliographic Details
Published in:Advances in engineering software (1992) Vol. 113; pp. 120 - 129
Main Authors: Adamek, Vitezslav, Vales, Frantisek, Cerv, Jan
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.11.2017
Subjects:
Inverse Laplace transform
Maple code
Multi-precision computation
Numerical algorithm
Wave propagation
Multi-precision computation
Wave propagation
Maple code
Inverse Laplace transform
Numerical algorithm
ISSN:0965-9978
Online Access:Get full text
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Summary:•Four numerical algorithms tested for Laplace transform inversion in elastodynamics.•Some methods can reach nearly arbitrary precision using multi-precision computations.•The combination of FFT and Wynns algorithm seems to be the most powerful.•Results of numerical inversion need to be always verified by another method.•Presented Maple codes can be directly applied to particular problems. The objective of this work is to find a suitable algorithm for numerical Laplace inversion which could be used for effective and precise solution of elastodynamic problems. For this purpose, the capabilities of four algorithms are studied using three transforms resulted from analytical solutions of longitudinal waves in a thin rod, flexural waves in a thin beam and plane waves in a strip. In particular, the Gaver–Stehfest algorithm, the Gaver–Wynn’s rho algorithm, the Fixed-Talbot algorithm and the FFT algorithm combined with Wynn’s epsilon accelerator are tested. The codes written in Maple 16 employing multi-precision computations are presented for each method. Given the results obtained, the last mentioned algorithm proves to be the best. It is most efficient and it gives results of reasonable accuracy nearly for all tested times ranging from 3×10−7s to 3 × 103 s.
ISSN:0965-9978
DOI:10.1016/j.advengsoft.2016.10.006