Devito: Towards a generic Finite Difference DSL using Symbolic Python

Domain specific languages (DSL) have been used in a variety of fields to express complex scientific problems in a concise manner and provide automated performance optimization for a range of computational architectures. As such DSLs provide a powerful mechanism to speed up scientific Python computation that goes beyond traditional vectorization and pre-compilation approaches, while allowing domain scientists to build applications within the comforts of the Python software ecosystem. In this paper we present Devito, a new finite difference DSL that provides optimized stencil computation from high-level problem specifications based on symbolic Python expressions. We demonstrate Devito's symbolic API and performance advantages over traditional Python acceleration methods before highlighting its use in the scientific context of seismic inversion problems.Comment: pyHPC 2016 conference submissio

Efficient Mesh Management in Firedrake Using PETSc DMPlex

The use of composable abstractions allows the application of new and established algorithms to a wide range of problems, while automatically inheriting the benefits of well-known performance optimizations. This work highlights the composition of the PETSc DMPlex domain topology abstraction with the Firedrake automated finite element system to create a PDE solving environment that combines expressiveness, flexibility, and high performance. We describe how Firedrake utilizes DMPlex to provide the indirection maps required for finite element assembly, while supporting various mesh input formats and runtime domain decomposition. In particular, we describe how DMPlex and its accompanying data structures allow the generic creation of user-defined discretizations, while utilizing data layout optimizations that improve cache coherency and ensure overlapped communication during assembly computation