Multiscale coupling of FFT-based simulations with the LDC approach

FFT based solvers have proven to be efficient computational methods for the numerical simulations of composite materials with complex microstructures and sophisticated material behavior. Nevertheless, these solvers require a regular discretization of the investigated domain and periodic boundary conditions. Local multi-grid methods appear as an appropriate framework to perform simulations involving local refinement with FFT solvers. A coarse (global) discretization is improved by one or several local refined discretizations defined in subdomains overlapping the global grid. The Local Defect Correction (LDC) method is adapted to couple the resolution on the global coarse grid problem with the resolution of the local grids problems. Numerical tests demonstrate a significant reduction of CPU time and memory consumption with a relatively low loss in accuracy in comparison to the computation on one fully refined global grid. This approach also provides a baseline for extensions to the coupling of FFT codes with other solvers in a multi-scale and multi-physics framework.