Smoothed aggregation methods in applications

Abstract:

Smoothed aggregation methods form a class of algebraic multilevel methods for solution of large sparse linear systems. They provide an efficient extension of the classical (geometrical) multigrid methods for problems discretized on unstructured meshes, where the classical approach of mesh refinement is either impractical or impossible. Instead, the hierarchy of grids is constructed by coarsening based on the algebraic input data. In this talk, we will discuss theoretical results and consider practical advantages of the smoothed aggregation approach for solving a variety of problems including elliptic differential equations with jumps in coefficients.