Evaluation of the Action of Finite Element Operators

Robert Kirby; Matt Knepley; L. Ridgway Scott. 23 October, 2010.
Communicated by L. Ridgway Scott.


The Krylov methods frequently used to solve linear systems associated with finite element discretizations of PDE rely only on the matrix-vector product. We consider the relative costs, in terms both of floating point operations and memory traffic, of several approaches to computing the matrix action. These include forming and using a global sparse matrix, building local element matrices and using them with a local-to-global indexing, and computing the action of the local matrices directly by numerical quadrature. Which approach is most efficient depends on several factors, including the relative cost of computation to memory access, how quickly local element matrices may be formed, and how quickly a function expressed in a finite element basis may be differentiated at the quadrature points.

Original Document

The original document is available in PDF (uploaded 23 October, 2010 by L. Ridgway Scott).