Fourier‐based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields

By François Willot, Bassam Abdallah, Y. Pellegrini. 2013

148 citations recorded by the source corpus.

A modified Green operator is proposed as an improvement of Fourier‐based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media. Contrary to other methods, the number of iterations necessary to achieve convergence tends to a finite value when the contrast of properties between the phases becomes infinite. Furthermore, it is shown that the method produces much more accurate local fields inside highly conducting and quasi‐insulating phases, as well as in the vicinity of phase boundaries. These good properties stem from the discretization of Green's function, which is consistent with the pixel grid while retaining the local nature of the operator that acts on the polarization field. Finally, a fast implementation of the ‘direct scheme’ of Moulinec et al. (1994) that allows for parsimonious memory use is proposed. Copyright © 2014 John Wiley & Sons, Ltd.

Subfields: Biomedical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c25b2c61b0d9c1d722620d3b8e45138b120e3b95

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. Dennis Merkert
2. Matthias Kabel
3. Matti Schneider
4. Felix Ospald

In Mechanics of Materials

1. Matti Schneider
2. Dennis Merkert
3. Matthias Kabel
4. Felix Ospald

Citations in the corpus

• Convergence of FFT‐based homogenization for strongly heterogeneous media (2015, background): “Willot [35, 36] explored the benefits of finite difference discretizations.”
• FFT‐based homogenization for microstructures discretized by linear hexahedral elements (2017, methodology): “Willot [31, 57] has provided a reduced algorithm for his finite difference scheme, operating on four displacements, reducing the required storage by 50%.”
• Computational homogenization of elasticity on a staggered grid (2016, methodology): “[51] for computing the electrical response of heterogeneous media.”