The field of numerical methods for complex systems is witnessing significant advancements, driven by the need for efficient and accurate solutions to large-scale problems. Recent developments are focused on improving the performance and robustness of existing methods, such as multigrid and quadrature techniques, through the use of innovative strategies like adaptive domain decomposition, low-rank approximations, and mixed precision formulations. These advancements have the potential to significantly impact various fields, including rarefied gas flows, linear algebra, and numerical simulations. Noteworthy papers include:

• A study on two-dimensional Gauss--Jacobi Quadrature for Multiscale Boltzmann Solvers, which proposes a Gaussian quadrature scheme that improves accuracy and reduces computational cost.
• A paper on Adaptive Multidimensional Quadrature on Multi-GPU Systems, which introduces a distributed adaptive quadrature method that achieves higher efficiency and improved robustness in high dimensions.
• A work on A Low-Rank BUG Method for Sylvester-Type Equations, which presents a low-rank algorithm that efficiently approximates solutions to Sylvester-type equations by exploiting low-rank structure and sparsity.