ALGEBRAIC MULTIGRID FOR MODERATE ORDER FINITE ELEMENTS

摘要: We investigate the use of algebraic multigrid (AMG) methods for solution large sparse linear systems arising from discretization scalar elliptic partial differential equations with Lagrangian finite elements order at most 4. The resulting system matrices do not have M-matrix property that is required by standard analyses classical AMG and aggregation-based methods. A unified approach presented allows us to extend these analyses. It uses an intermediate highlights role spectral equivalence constant relates this matrix original matrix. This shown be bounded independently problem size jumps in coefficients equations, provided are located elements' boundaries. For two-dimensional problems, it further uniformly if angles triangulation also satisfy a uniform bound. analysis validates application the...