An Algebraic Programming Style for Numerical Software and its Optimization

The abstract mathematical theory of partial differential equations (PDEs) is formulated in terms of manifolds,scalar fields, tensors, and the like, but these algebraic structures are hardly recognizable in actual PDE solvers. The general aim of the Sophus programming style is to bridge the gap between theory and practice in the domain of PDE solvers. Its main ins are a library of abstract datatypes corresponding to the algebraic structures used in the mathematical theory and an algebraic expression style similar to the expression style used in the mathematical theory. Because of its emphasis on datatypes, Sophus is most naturally combined with object-oriented languages or other languages supporting abstract datatypes. The resulting source code patterns are beyond the scope of current compiler optimizations, but are sufficiently specific for a dedicated source-to-source optimizer. The limited, domain-specific, character of Sophus is the key to success here. This kind of optimization has...

• Type: Journal
• Year: 1999
• Where: CORR
• Authors: T. B. Dinesh, Magne Haveraaen, Jan Heering
• Keywords: Abstract Datatypes, CORR 1999, Education, Mathematical Theory, PDE Solvers