Developed in the context of investigating multi-physics simulations on heterogeneous unit-cells following the seminal work of Moulinec and Suquet [1], Fast Fourier Transform (FFT)-based iterative approach is intrinsically limited to periodic boundary conditions (BCs). The present work aims to overcome the limitation of periodic BCs. The novel approach is implemented in the solver AMITEX, a new version of the massively parallel (MPI) Fortran solver AMITEX ([2], open-source) based on the high-performance computing library 2DECOMP&FFT [3]. In this work, we present a natural description of non-periodic BCs (Dirichlet and Neumann types). The main idea of the new approach relies on the link between the BCs and the symmetry properties of the fields. In this case, it is then possible to establish connection between discrete trigonometric transforms (DTT) [4] and discrete Fourier transform (computed with a FFT algorithm). Leveraging on this relation, one can preserve the overall FFT-based approach while applying non-periodic BCs. It is noteworthy that to account for the DTT in a MPI context, a significant modification of 2DECOMP&FFT has been carried out. To solve (thermo-)mechanical problems, we propose a simple and versatile iterative (temperature-)displacement-based fixed-point algorithm coupled with Anderson’s convergence acceleration procedure. We introduce various pre-conditioners and finite difference schemes allowing to compute the discrete Green’s operators. In this regard, the recently proposed tetrahedron-based discretization scheme [5] is compared to the hexahedral-based finite difference scheme in the context of non-periodic BCs. The current progresses help to close the gap between standard finite element (FE) codes and FFT-based ones while preserving the latter numerical performances. Several examples of boundary value problems (conductivity, non-linear elasticity, crystal plasticity in finite transformation) are discussed to demonstrate the ability of the proposed approach to simulate simple structures that could not be achieved with standard FFT-based solvers. REFERENCES [1] H. Moulinec, P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Methods Appl. Mech. Eng., 157, 69–94, 1998. [2] AMITEX_FFTP, https://amitexfftp.github.io/AMITEX/index.html [3] S. Rolfo, C. Flageul, P. Bartholomew, F. Spiga, S. Laizet, The 2DECOMP&FFT library: an update with new CPU/GPU capabilities, J.