Multiscale modelling plays an important role in understanding the behaviour of heterogeneous materials with complex internal architectures, such as woven composites. Conventional first-order homogenisation (1OH) methods bridge fine and coarse scales, but are limited to cases where the two length scales are orders of magnitudes apart, failing to capture length-scale and size effects when the unit cell dimensions become comparable to macro-scale dimensions, as seen in woven composites. Second-order homogenisation (2OH) methods address this by incorporating higher-order deformation gradients and length-scale effects in the RVE boundary value formulations, both of which are absent in 1OH. This study addresses the computational challenges specific to second-order homogenisation of large-scale RVE models with large degrees of freedom, demonstrated using a 2OH shell-element based framework[1], [2] to model 3D woven composites. In downscaling, a predictor-corrector scheme[3], [4] based on Broyden’s algorithm[5] is used to replace the direct displacement (DD) method to solve for dense constraint equations. In upscaling, several instances of densely populated matrix equations are addressed through an adaptive algorithm which allows the user to choose between the direct condensation (DC) method supported by dask libraries[6] and the forward difference method[7], based on the computational resources available. Application of these strategies to 3D woven RVEs significantly reduces runtime and memory usage without compromising accuracy. For downscaling at the maximum mesh density solvable by DD (5488 elements), the predictor-corrector scheme is nearly 100x faster, while for upscaling at the limit of DC (31250 elements), dask libraries improve runtime by 1.5x, and the perturbation method by 10x. The updated algorithm enables solving finer RVE models and applying 2OH frameworks to large-scale, complex models, particularly relevant for aerospace industries using woven composites. The findings also support ongoing research on second-order homogenisation using higher-order solid elements, enabling efficient analysis of thick composites like 3D weaves.