Speaker
Description
FFT-based computational homogenization methods [1, 2] have been shown to efficiently solve multi-scale problems that are discretized on a regular grid. However, due to the grid-like structure, the obtained local solution fields lack accuracy in the vicinity of material interfaces that are not parallel to the grid. Simple workarounds typically comprise the numerical efficiency of the solver. In this contribution, we present a computational homogenization approach that guarantees the accuracy of interface-conforming finite elements while maintaining the computational efficiency of FFT-based computational homogenization methods for two-dimensional thermal conductivity problems. In particular, we propose a discretization by the extended finite element method (X-FEM) with modified absolute enrichment [3] and present an associated fast Lippmann-Schwinger solver that is numerically robust independently of the mesh. We analyze the properties of the corresponding X-FFT solver in a series of computational experiments.
REFERENCES
[1] Moulinec H., Suquet P., A fast numerical method for computing the linear and nonlinear mechanical properties of composites, Comptes Rendus de l’Académie des sciences. Série II. Mécanique, physique, chimie, astronomie, Vol. 318 (11), pp. 1417–1423, 1994.
[2] Moulinec H., Suquet P., A numerical method for computing the overall response of nonlinear composites with complex microstructure, Computer Methods in Applied Mechanics and Engineering, Vol. 157 (1-2), pp. 69–94, 1998.
[3] Moës N., Cloirec M., Cartraud P., Remacle J.-F., A computational approach to handle complex microstructure geometries, Computer Methods in Applied Mechanics and Engineering,Vol. 192 (28-30), pp. 3163–3177, 2003.
