Introducing Finite Difference Schemes Synthesis in FAUST: A Cellular Automata Approach

In this paper we propose a technique for formalizing Finite Difference Schemes (FDSs) physical models in the Faust programming language. Faust libraries already allow for the implementation of several kinds of physical modeling techniques; however, to our knowledge, FDSs have never been integrated into this language. In fact, their implementation in imperative programming languages is typically achieved using data structures, which are not available in Faust. First, a method for coding FDSs in a functional programming way is introduced, starting from previous works on mass-interaction models. Then, we draw a connection between FDSs and cellular automata, and exploit it for building a library that eases the implementation of FDS synthesis in Faust.