Spectral AMGe (AMGe)

Timothy P. Chartier

Department of Mathematics
University of Washington
P.O. Box 354350
Seattle, Washington 98195


Abstract

Spectral AMGe (AMGe), is a new algebraic multigrid method for solving discretizations that arise in Ritz-type finite element methods for partial difierential equations. The method assumes access to the element stifiness matrices in order to lessen certain presumptions that can limit other algebraic methods. AMGe uses the spectral decomposition of small collections of element stiffness matrices to determine local representations of algebraically "smooth" error components. This decomposition provides the basis for generating a coarse grid and for deflning efiective interpolation. This paper presents a theoretical foundation for AMGe alongwith numerical results that demonstrate the efficiency and robustness of the method.