Expression templates implementation of continuous and discontinuous Galerkin methods

Efficiency and flexibility are often mutually exclusive features in a code. This still prompts a large part of the Scientific Computing community to use traditional procedural languages. In the last years, however, new programming techniques have been introduced allowing for a high level of abstract...

Full description

Saved in:
Bibliographic Details
Published inComputing and visualization in science Vol. 12; no. 8; pp. 421 - 436
Main Authors Di Pietro, Daniele Antonio, Veneziani, Alessandro
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.11.2009
Springer
Springer Verlag
Subjects
Algorithms
Applied sciences
Calculus of Variations and Optimal Control; Optimization
Computational Mathematics and Numerical Analysis
Computer Applications in Chemistry
Computer science; control theory; systems
Exact sciences and technology
Mathematics
Mathematics and Statistics
Numerical Analysis
Regular Article
Software
Software engineering
Visualization
Expression templates
Galerkin methods
Finite elements implementation
Object-Oriented programming
Compiler
Procedural language
Metaprogramming
Syntactic analysis
Abstraction
Galerkin-Petrov method
Finite element method
Mathematical formula
Scientific computation
Object oriented
Galerkin method
Online AccessGet full text

Cover

More Information
Summary:Efficiency and flexibility are often mutually exclusive features in a code. This still prompts a large part of the Scientific Computing community to use traditional procedural languages. In the last years, however, new programming techniques have been introduced allowing for a high level of abstraction without loss of performance. In this paper we present an application of the Expression Templates technique introduced in (Veldhuizen in Expression templates. C++ Report magazine, vol 7, pp 26–31, 1995) to the assembly step of a finite element computation. We show that a suitable implementation, such that the compiler has the role of parsing abstract operations, allows for user-friendliness. Moreover, it gains in performance with respect to more traditional techniques for achieving this kind of abstraction. Both the cases of conforming and discontinuous Galerkin finite element discretization are considered. The proposed implementation is finally applied to a number of problems entailing different kind of complications.
ISSN:1432-9360
1433-0369
DOI:10.1007/s00791-008-0117-x