Treffer: Multigrid Methods

Engineering school ; Multigrid methods are a class of efficient and versatile algorithms for solving many types of computational problems involving differential and integral equations. They use a hierarchy of discretizations, from coarse to fine, to accelerate the convergence of traditional iterative solvers. This multilevel approach enables rapid damping of error components at different frequencies, allowing multigrid methods to solve problems with improved efficiency compared to conventional techniques. These methods have been successfully applied to a wide range of mathematical problems, including differential equations, integral equations, and elliptic boundary value problems. They have also been used to accelerate computations in many physical applications, such as optimization, image reconstruction, and computational fluid dynamics. The multigrid philosophy of using global correction from coarse grids to improve fine-grid performance makes these techniques both flexible and broadly applicable to large-scale modeling and simulation problems across science and engineering disciplines.