A model order reduction technique for FFT‐based microstructure simulation using a geometrically adapted reduced set of frequencies

PAMM, vol. 21

Abstract

Abstract The FFT‐based method introduced by Moulinec and Suquet [9] serves as an alternative for the classical finite element based simulation of periodic microstructures. This simulation approach makes use of fast Fourier transforms (FFT) as well as fixed‐point iterations to solve the microscopic boundary value problem which is captured by the Lippmann‐Schwinger equation. Kochmann et al. [5] introduced a model order reduction technique using a reduced set of frequencies to decrease the computational effort of solving the Lippmann‐Schwinger equation in Fourier space. This earlier proposed method is based on a fixed sampling pattern, which determines the reduced set of frequencies. Instead of the fixed sampling pattern, we propose to use a geometrically adapted choice of frequencies, which corresponds to the representation of phases within the considered microstructure.

Authors 4

1. Christian Gierden corresponding Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Straße 1 D-52074 Aachen Germany

   Christian Gierden

   Email: [email protected]

   Telephone: +49 241 80 25014

2. Johanna Waimann Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Straße 1 D-52074 Aachen Germany

3. Bob Svendsen Aachen Material Mechanics

   RWTH Aachen University · Max-Planck-Institut für Nachhaltige Materialien

   Affiliation as printed

   Material Mechanics RWTH Aachen University Schinkelstraße 2 D-52062 Aachen Germany

   Microstructure Physics and Alloy Design Max-Planck-Institut für Eisenforschung GmbH Max-Planck-Straße 1 D-40237 Düsseldorf Germany

4. Stefanie Reese Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Straße 1 D-52074 Aachen Germany