Homogenization Dielectric Permittivity FFT scheme

An efficient method to solve the problem of homogenization of physical properties of heterogeneous media, such as dielectric permittivity, is the implementation of numerical solutions, before estimating the effective properties by spatial average of the solution. The input data is a 3D binary volume or a 2D binary image of the studied sample. The proposed method is taken from the work of [Moulinec and Suquet, 1994] [Moulinec and Suquet, 1998], then [Eyre and Milton, 1999], and [Delarue and Jeulin, 2002]. It consists, knowing the structure of a material as well as the properties of its constituents, of determining the macroscopic equivalent dielectric constant ε*. The calculation uses a formulation based on Fast Fourier Transform to solve the equations of electrostatics in a heterogeneous medium. This method is the one implemented in [Jeulin, Moreaud, 2006]. It is necessary to install the redistribution libraries of Microsoft visual studio 2019 64 bits (x64), for the module to work (see link below).

References

[Delarue et Jeulin, 2002] D. Jeulin, A. Delarue, Numerical homogenization of dielectric properties of random media. Application to nanocomposites, Doctoriales St. Etienne, 2002.
[Eyre et Milton, 1999] D.J. Eyre, G.W. Milton, A fast numerical scheme for computing the response of composites using grid refinement, The European Physical Journal of Applied Physics 6, p.41-47, 1999.
[Jeulin, Moreaud, 2006] D. Jeulin, M. Moreaud . Statistical Representative Volume Element for Predicting the Dielectric Permittivity of Random Media. Progress In Electromagnetics Research Symposium, Tokyo, Japan, 2006.
[Moulinec et Suquet 1994] H. Moulinec, P. Suquet, A fast numerical method for computing the linear and nonlinear mechanical properties of composites, C. R. Acad. Sci. Paris, t. 318, Série II, p. 1417-1423, 1994.
[Moulinec et Suquet, 1998] H. Moulinec, P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Computer Methods in applied Mechanics and Engineering 157, p. 69-94, 1998.

Updates
20201203: addition of configurable stop criteria (handling of oscillating solutions).
20200507: code acceleration.
20200403: added support for 2D binary images.