Elements of finite element programming

Abstract

In this chapter we focus more deeply on a number of aspects relating to the translation of the finite-element method into computer code. This implementation process can hide some pitfalls. Beyond the syntactic requirements of a given programming language, the need for a high computational efficiency leads to an implementation that is generally not the immediate translation of what has been seen during the theoretical presentation. Efficiency depends on many factors, including the language used and the architecture on which one works. Personal experience can play a role as fundamental as learning from a textbook. Moreover, although spending time searching for a bug in the code or for a more efficient data structure can sometimes appear to be a waste of time, it (almost) never is. For this reason, we wish to propose the present chapter as a sort of “guideline“ for trials that the reader can perform on his own, rather than a chapter to be studied in the traditional sense.

Currently, engineering applications involving scientific computing are running on parallel architectures with hundreds or thousands of Central Processor Units (CPUs) or Graphical Processor Units (GPUs), and this requires specific coding techniques. This topic is beyond the scope of the present book.