The DOI matches its Crossref record; 117 of the 117 references it cites were found in a registry or an index.
A review of nonlinear FFT-based computational homogenization methods
Open accessAbstract
Since their inception, computational homogenization methods based on the fast Fourier transform (FFT) have grown in popularity, establishing themselves as a powerful tool applicable to complex, digitized microstructures. At the same time, the understanding of the underlying principles has grown, in terms of both discretization schemes and solution methods, leading to improvements of the original approach and extending the applications. This article provides a condensed overview of results scattered throughout the literature and guides the reader to the current state of the art in nonlinear computational homogenization methods using the fast Fourier transform.
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Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
Iterative Methods for Sparse Linear Systems
Saad, Y. (2003) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898718003 · Cited by 13,790
(2021) · A First Course in Statistical Programming with R · doi:10.1017/9781108993456.011 · Cited by 13,724
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
Saad, Y., & Schultz, M. H. (1986) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0907058 · Cited by 11,154
(1999) · Springer Series in Operations Research and Financial Engineering · doi:10.1007/b98874 · Cited by 9,482
Methods of conjugate gradients for solving linear systems
Hestenes, M. R., & Stiefel, E. (1952) · Journal of Research of the National Bureau of Standards · doi:10.6028/jres.049.044 · Cited by 8,132
Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
Harlow, F. H., & Welch, J. E. (1965) · The Physics of Fluids · doi:10.1063/1.1761178 · Cited by 5,977
A variational approach to the theory of the elastic behaviour of multiphase materials
Hashin, Z., & Shtrikman, S. (1963) · Journal of the Mechanics and Physics of Solids · doi:10.1016/0022-5096(63)90060-7 · Cited by 5,882
Micromechanics of defects in solids
Mura, T. (1987) · Mechanics of Elastic and Inelastic Solids · doi:10.1007/978-94-009-3489-4 · Cited by 5,539
van der Vorst, H. A. (1992) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0913035 · Cited by 5,308
Metadata
- Authors
- Schneider, M.
- Venue
- Acta Mechanica
- Published
- 2021-03-24
- Volume
- 232
- Issue
- 6
- Pages
- 2051-2100
- ISSN
- 0001-5970 (ISSN-L)
- 1619-6937
- OpenAlex
- W3135925085
- Cited by
- 265
- References
- 117
- FWCI
- 18.78
- Type
- journal article
- Language
- en
- Open access
- hybrid
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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