Productive Parallel Linear Algebra Programming with Unstructured Topology Adaption

Abstract

Sparse linear algebra is a key component of many scientific computations such as computational fluid dynamics, mechanical engineering or the design of new materials to mention only a few. The discretization of complex geometries in unstructured meshes leads to sparse matrices with irregular patterns. Their distribution in turn results in irregular communication patterns within parallel operations. In this paper, we show how sparse linear algebra can be implemented effortless on distributed memory architectures. We demonstrate how simple it is to incorporate advanced partitioning, network topology mapping, and data migration techniques into parallel HPC programs by establishing novel abstractions. For this purpose, we developed a linear algebra library - Parallel Matrix Template Library 4 - based on generic and meta-programming introducing a new paradigm: meta-tuning. The library establishes its own domain-specific language embedded in C++. The simplicity of software development is not paid by lower performance. Moreover, the incorporation of topology mapping demonstrated performance improvements up to 29%.