TR-2010-08
Evaluation of the Action of Finite Element Operators
Robert Kirby; Matt Knepley; L. Ridgway Scott. 23 October, 2010.
Communicated by L. Ridgway Scott.
Abstract
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).
