The field of numerical solving of large-scale problems is moving towards the development of more efficient and scalable preconditioning techniques. Recent work has focused on improving the performance of multigrid methods, with a particular emphasis on structured grid problems. New methods have been proposed to reduce grid complexity, operator complexity, and implementation effort, leading to significant speedups and improved convergence rates. Additionally, researchers have explored the use of parallel-in-time preconditioning and block triangular preconditioning to accelerate and stabilize the solution of time-dependent and inverse source problems. These innovative approaches have shown great promise in achieving fast convergence, high parallel efficiency, and robustness across a wide range of problems. Noteworthy papers include:

• StructMG, which presents a fast and scalable algebraic multigrid that constructs hierarchical grids automatically, achieving significant speedups over existing methods.
• Accelerating MPGP-type Methods Through Preconditioning, which introduces an approximate variant of preconditioning in face that computes the inner preconditioner only once, leading to very large speedups.
• Parallel-in-Time Preconditioning for Time-Dependent Variational Mean Field Games, which proposes a general class of parallel-in-time preconditioners based on diagonalization techniques, enabling efficient and scalable iterative solvers.
• Block triangular preconditioning for inverse source problems in time-space fractional diffusion equations, which develops and analyzes a block triangular preconditioning strategy that improves convergence rates, robustness, and accuracy.