Symbolic Integration At Compile Time In Finite Element Methods

In most existing software packages for the finite element method it is not possible to supply the weak formulation of the problem of interest in a compact form, which was in the early days of programming due to the low abstrac-tion capabilities of available programming languages. With the advent of pure object-oriented programming, abstrac-tion was long said to be achievable only in trade-off with run time efficiency. In this work we show that it is possible to obtain both a high level of abstraction and good run time efficiency by the use of template metaprogramming in C++. We focus on a mathematical expressions engine, by which element matrices are computed during compile time and by which the weak formulation can be specified in a single line of code. A comparison of system matrix assembly times of existing finite element software shows that the template metaprogramming approach is up to an order of magnitude faster than traditional software designs