4 citations · 5 across the 3 of their papers we have counts for
4 papers
Derivation of higher-order terms in FFT-based numerical homogenization
Felix Dietrich, Dennis Merkert, Bernd Simeon
In this paper, we first introduce the reader to the Basic Scheme of Moulinec and Suquet in the setting of quasi-static linear elasticity, which takes advantage of the fast Fourier…
Approximation of Periodic PDE Solutions with Anisotropic Translation Invariant Spaces
Ronny Bergmann, Dennis Merkert
We approximate the quasi-static equation of linear elasticity in translation invariant spaces on the torus. This unifies different FFT-based discretisation methods into a common fr…
FFT-based homogenization on periodic anisotropic translation invariant spaces
Ronny Bergmann, Dennis Merkert
In this paper we derive a discretisation of the equation of quasi-static elasticity in homogenization in form of a variational formulation and the so-called Lippmann-Schwinger equa…
A Framework for FFT-based Homogenization on Anisotropic Lattices
Ronny Bergmann, Dennis Merkert
In order to take structural anisotropies of a given composite and different shapes of its unit cell into account, we generalize the Basic Scheme in Homogenization by Moulinec and S…