Speaker
Description
The predictive accuracy of computational multiscale methods depends on detailed microstructural representations and sophisticated material models for microscale constituents. However, with increasing (physical) complexity of the cell problem, the computational cost keeps increasing as well. This stipulates the development of tailored solution approaches among which FFT-based spectral methods have emerged as particularly promising options.
Against this background, we focus on a critical limitation of current FFT-based approaches: their reliance on regular, structured grids. To overcome this, we exploit the hierarchical structure and inherent adaptivity of wavelets. By representing the governing fields in a wavelet basis and by utilizing wavelet transforms, we derive higher-order stress approximations in a nested set of approximation spaces. This enables the precise detection and resolution of localized features while significantly reducing the number of material model evaluations. Because the computational cost of the wavelet transforms scales linearly in the number of voxels and the per-voxel overhead is negligible compared to typical material model evaluations, substantial gains in computational efficiency are thus achieved.
We use a wavelet-enhanced version of the classic Moulinec-Suquet basic scheme as our point of departure and validate the proposed approach through detailed studies of representative boundary value problems in one- and two-dimensional settings. Notably, we demonstrate that the numerical grid in the hybrid wavelet-FFT approach naturally adapts to the solution profile based on a predefined refinement tolerance which results in a 95% reduction in the number of material model evaluations.
[1] T. Kaiser, T. Raasch, J.J.C. Remmers and M.G.D. Geers: A wavelet-enhanced adaptive hierarchical FFT-based approach for the efficient solution of microscale boundary value problems, Computer Methods in Applied Mechanics and Engineering, 409, 115959, 2023, https://doi.org/10.1016/j.cma.2023.11595}
