Algebraic Programming Style for Numerical Software and its Optimization. Software211 Engineering

摘要

The abstract mathematical theory of partial differential equations (PDEs) is211u001eformulated in terms of manifolds, scalar fields, tensors, and the like, but these 211u001ealgebraic structures are hardly recognizable in actual PDE solvers. The general 211u001eaim of the Sophus programming style is to bridge the gap between theory and 211u001epractice in the domain of PDE solvers. Its main ingredients are a library of 211u001eabstract datatypes corresponding to the algebraic structures used in the 211u001emathematical theory and an algebraic expression style similar to the expression 211u001estyle used in the mathematical theory. Because of its emphasis on abstract 211u001edatatypes, Sophus is most naturally combined with object-oriented languages or 211u001eother languages supporting abstract datatypes. The resulting source code patterns 211u001eare beyond the scope of current compiler optimizations, but are sufficiently 211u001especific for a dedicated source-to-source optimizer. The limited, domain-211u001especific, character of Sophus is the key to success here. This kind of 211u001eoptimization has been tested on computationally intensive Sophus style code with 211u001epromising results. The general approach may be useful for other styles and in 211u001eother application domains as well.