Lattice structures are cellular architected materials that provide, among others, exceptional weight reduction while preserving stiffness and strength. Traditional multiscale methods based on homogenization are often inadequate for lattice structures due to insufficient scale separa- tion. On the contrary, we focus here on high-fidelity, fine-scale simulations using isogeometric (spline-based) volumetric models at the architectural scale. The main challenge lies in the prohibitive computational cost of simulating the vast number of complex cells. Although iso- geometric analysis (IGA) provides superior accuracy per degree of freedom compared to tradi- tional finite element methods (FEM), it poses significant computational challenges, particularly in forming operators and solving the resulting linear systems. In this work, we introduce a high-performance solver tailored for the IGA of lattice structures [1], designed to harness the inherent characteristics of lattices (periodicity, multiscale) to over- come these computational barriers. The solver employs a two-level geometric preconditioner, combining a fine-level smoother based on overlapping domain decomposition with a coarse- level correction using an algebraic multigrid method. By leveraging the multiscale properties of lattice structures, the fine-level computations utilize a matrix-free approach for matrix-vector products and transfer operators. Additionally, the structural similarities of the lattice cells are exploited through a reduced-order modeling strategy [2] applied locally within each subdomain, enabling efficient local solves within the fine-level smoother. We evaluate the solver’s performance through extensive 2D and 3D numerical experiments, demonstrating its efficiency in terms of memory usage, computational time, and robustness under varying mesh refinements, spline degrees, and problem sizes. Notably, we simulate an industrially representative spiral channel regenerative cooling thrust chamber lattice struc- ture—comprising over 66,000 cells—in just minutes using thousands of processes. Finally, we will also present numerical simulations accounting for geometric and material nonlinearities, highlighting the attractiveness of IGA discretizations for such problems [3].