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High performance computational kernels for selected segments of a p finite element code
Author(s) -
Barragy E.,
Van De Geijn R.
Publication year - 1995
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620380806
Subject(s) - computer science , parallel computing , finite element method , supercomputer , computational science , conjugate gradient method , tensor product , algorithm , mathematics , engineering , structural engineering , pure mathematics
A high performance implementation is presented for three kernel routines commonly found in element‐byelement preconditioned conjugate gradient finite element codes. These routines include forming the element stiffness matrices and loading vectors, or in the case of a non‐linear problem, element residual vectors; and routines for applying element matrix–vector products. The present study considers tensor product elements of arbitrary mapping in 2‐D, although the generalization to triangular elements and serendipity elements is straightforward. The implementation presented is most appropriate for high p type finite element methods, where the element matrices are relatively large and dense. This results in a set of high performance kernels for superscalar architectures, which otherwise may be memory bandwidth limited. Performance studies are presented for a representative superscalar microprocessor, the Intel i860. As these types of microprocessors are at the heart of modern workstations as well as several parallel supercomputing systems, this work is relevant across a variety of platforms. The resulting kernels yield both high performance on a variety of sequential architectures as well as a high degree of code portability through the basic linear algebra subprograms mechanism.