Spectral method for evaluating effective rock sample properties based on the fast Fourier transform: algorithm and comparison with the finite element method
https://doi.org/10.22405/2226-8383-2025-26-4-370-382
Abstract
The article considers a spectral method for evaluating the effective properties of composites and rock samples based on the Fast Fourier Transform (FFT). Having limitations on the applied boundary conditions, the method offers high efficiency of stress and strain analysis in a periodic cell due to the asymptotics of FFT in time 𝑂(𝑛 · 𝑙𝑜𝑔(𝑛)). The comparison of the results of homogenization with the Finite Element Method shows the high accuracy of the spectral method in estimating the properties of the rocks. An analysis of the efficiency and convergence of the algorithm for various periodic cells and materials is presented.
About the Authors
Mikhail Nikolaevich Tsybakov
Lomonosov Moscow State University
Russian Federation
Russian Federation
Anatoly Viktorovich Vershinin
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
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Review
For citations:
Tsybakov M.N., Vershinin A.V. Spectral method for evaluating effective rock sample properties based on the fast Fourier transform: algorithm and comparison with the finite element method. Chebyshevskii Sbornik. 2025;26(4):370-382. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-370-382
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