Formal methods to generate parallel iterative codes for PDE-based applications

Developing parallel software is far more complex than traditional sequential software. An effective approach to deal with the complexity of parallel software is domain-specific programming in an abstraction higher than general-purpose programming languages. In this paper, we focus on the domain of the applications based on partial differential equations (PDE) and provide a formal framework and methods for PDE compilers to generate parallel iterative codes for the domain. We also provide a PDE compiler optimization to minimize the number of messages between parallel processors. Our framework and methods can be used to build PDE compilers to generate efficient parallel software for PDE-based applications automatically.