Numerical analysis of several FFT-based schemes for computational homogenization
arXiv:2201.01916 · doi:10.1007/s10543-023-00950-6
Abstract
We study the convergences of several FFT-based schemes that are widely applied in computational homogenization for deriving effective coefficients, and the term "convergence" here means the limiting behaviors as spatial resolutions going to infinity. Those schemes include Moulinec-Suquent's scheme [Comput Method Appl M, 157 (1998), pp. 69-94], Willot's scheme [Comptes Rendus Mécanique, 343 (2015), pp. 232-245], and the FEM scheme [Int J Numer Meth Eng, 109 (2017), pp. 1461-1489]. Under some reasonable assumptions, we prove that the effective coefficients obtained by those schemes are all convergent to the theoretical ones. Moreover, for the FEM scheme, we can present several convergence rate estimates under additional regularity assumptions.
References in corpus (10)
- A numerical method for computing the overall response of nonlinear composites with complex microstructure
- Generalized Multiscale Finite Element Methods (GMsFEM)
- Fourier-based schemes for computing the mechanical response of composites with accurate local fields
- Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients
- P3DFFT: a framework for parallel computations of Fourier transforms in three dimensions
- Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
- Constraint Energy Minimizing Generalized Multiscale Finite Element Method
- An FFT-based Galerkin Method for Homogenization of Periodic Media
- Computational Homogenization of Polycrystals
- Guaranteed upper-lower bounds on homogenized properties by FFT-based Galerkin method