Speaker
Description
Multigrid (MG) methods are efficient and scalable for solving sparse linear systems arising from the discretization of partial differential equations (PDEs). However, the performance of standard V- and W-cycle MG methods often deteriorates as the physical and geometric complexity of the PDEs increases. To remedy this, the Algebraic Multilevel Iteration (AMLI)-cycle was developed, utilizing Chebyshev polynomials to define the coarse-level solver. Despite its theoretical strength, AMLI is not widely used in practice because it requires accurate estimations of extreme eigenvalues and can be difficult to implement.
In this talk, inspired by recent acceleration techniques, we propose new accelerated MG cycles that do not require estimating extreme eigenvalues. We prove that these resulting cycles achieve convergence rates comparable to the Chebyshev-based AMLI-cycle. Furthermore, our approach is more straightforward to implement, making it practical for real-world applications. Numerical experiments are presented to validate our theoretical results.