Advanced expression templates programming

Expression Templates (ET) are a powerful tool for development of user-friendly numerical libraries. By this concept and by operator overloading in C++, numerical algorithms can be implemented in a mathematical notation without decreasing the performance in comparison to optimized C or FORTRAN codes. In this paper, we present new Expression Template techniques. First, we explain the concept of “Easy Expression Templates”, which are easier to implement than classical ET. Then, we explain “Fast Expression Templates”. This concept leads to an optimal performance even on special architectures like vector machines. Furthermore, concepts for storing expressions and code optimizing are presented. In order to verify the usability of these programming techniques in real applications, we discuss a template library which calculates local stiffness matrices arising from Finite Element discretizations.