Firedrake is a new tool for automating the numerical solution of partial differential equations. Firedrake adopts the domain-specific language for the finite element method of the FEniCS project, but with a pure Python runtime-only implementation centered on the composition of several existing and new abstractions for particular aspects of scientific computing. The result is a more complete separation of concerns that eases the incorporation of separate contributions from computer scientists, numerical analysts, and application specialists. These contributions may add functionality or improve performance. Firedrake benefits from automatically applying new optimizations. This includes factorizing mixed function spaces, transforming and vectorizing inner loops, and intrinsically supporting block matrix operations. Importantly, Firedrake presents a simple public API for escaping the UFL abstraction. This allows users to implement common operations that fall outside of pure variational formulations, such as flux limiters.
We present a performance analysis and benchmarking study of the OP2 "active" library, which provides an abstraction framework for the solution of parallel unstructured mesh applications. OP2 aims to decouple the scientific specification of the application from its parallel implementation, achieving code longevity and near-optimal performance through re-targeting the back-end to different hardware.Runtime performance results are presented for a representative unstructured mesh application written using OP2 on a variety of many-core processor systems, including the traditional X86 architectures from Intel (Xeon based on the older Penryn and current Nehalem micro-architectures) and GPU offerings from NVIDIA (GTX260, Tesla C2050). Our analysis demonstrates the contrasting performance between the use of CPU (OpenMP) and GPU (CUDA) parallel implementations for the solution on an industrial sized unstructured mesh consisting of about 1.5 million edges.Results show the significance of choosing the correct partition and thread-block configuration, the factors limiting the GPU performance and insights into optimizations for improved performance.
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