The hierarchical basis multigrid method and incomplete LU decomposition

Abstract

A new multigrid or incomplete LU technique is developed in this paperfor solving large sparse algebraic systems from discretizing partialdifferential equations. By exploring some deep connection betweenthe hierarchical basis method and incomplete LU decomposition, theresulting algorithm can be effectively applied to problems discretizedon completelyunstructured grids. Numerical experiments demonstratingthe efficiency of the method are also reported.