Achieving Efficient Strong Scaling with PETSc using Hybrid MPI/OpenMP Optimisation

The increasing number of processing elements and decreas- ing memory to core ratio in modern high-performance platforms makes efficient strong scaling a key requirement for numerical algorithms. In order to achieve efficient scalability on massively parallel systems scientific software must evolve across the entire stack to exploit the multiple levels of parallelism exposed in modern architectures. In this paper we demonstrate the use of hybrid MPI/OpenMP parallelisation to optimise parallel sparse matrix-vector multiplication in PETSc, a widely used scientific library for the scalable solution of partial differential equations. Using large matrices generated by Fluidity, an open source CFD application code which uses PETSc as its linear solver engine, we evaluate the effect of explicit communication overlap using task-based parallelism and show how to further improve performance by explicitly load balancing threads within MPI processes. We demonstrate a significant speedup over the pure-MPI mode and efficient strong scaling of sparse matrix-vector multiplication on Fujitsu PRIMEHPC FX10 and Cray XE6 systems

Optimizing sparse matrix-vector multiplication in NEC SX-Aurora vector engine

Sparse Matrix-Vector multiplication (SpMV) is an essential piece of code used in many High Performance Computing (HPC) applications. As previous literature shows, achieving efficient vectorization and performance in modern multi-core systems is nothing straightforward. It is important then to revisit the current stateof-the-art matrix formats and optimizations to be able to deliver deliver high performance in long vector architectures. In this tech-report, we describe how to develop an efficient implementation that achieves high throughput in the NEC Vector Engine: a 256 element-long vector architecture. Combining several pre-processing and kernel optimizations we obtain an average 12% improvement over a base SELLC-s implementation on a heterogeneous set of 24 matrices.Preprin

Benchmarking mixed-mode PETSc performance on high-performance architectures

The trend towards highly parallel multi-processing is ubiquitous in all modern computer architectures, ranging from handheld devices to large-scale HPC systems; yet many applications are struggling to fully utilise the multiple levels of parallelism exposed in modern high-performance platforms. In order to realise the full potential of recent hardware advances, a mixed-mode between shared-memory programming techniques and inter-node message passing can be adopted which provides high-levels of parallelism with minimal overheads. For scientific applications this entails that not only the simulation code itself, but the whole software stack needs to evolve. In this paper, we evaluate the mixed-mode performance of PETSc, a widely used scientific library for the scalable solution of partial differential equations. We describe the addition of OpenMP threaded functionality to the library, focusing on sparse matrix-vector multiplication. We highlight key challenges in achieving good parallel performance, such as explicit communication overlap using task-based parallelism, and show how to further improve performance by explicitly load balancing threads within MPI processes. Using a set of matrices extracted from Fluidity, a CFD application code which uses the library as its linear solver engine, we then benchmark the parallel performance of mixed-mode PETSc across multiple nodes on several modern HPC architectures. We evaluate the parallel scalability on Uniform Memory Access (UMA) systems, such as the Fujitsu PRIMEHPC FX10 and IBM BlueGene/Q, as well as a Non-Uniform Memory Access (NUMA) Cray XE6 platform. A detailed comparison is performed which highlights the characteristics of each particular architecture, before demonstrating efficient strong scalability of sparse matrix-vector multiplication with significant speedups over the pure-MPI mode

GHOST: Building blocks for high performance sparse linear algebra on heterogeneous systems

While many of the architectural details of future exascale-class high performance computer systems are still a matter of intense research, there appears to be a general consensus that they will be strongly heterogeneous, featuring "standard" as well as "accelerated" resources. Today, such resources are available as multicore processors, graphics processing units (GPUs), and other accelerators such as the Intel Xeon Phi. Any software infrastructure that claims usefulness for such environments must be able to meet their inherent challenges: massive multi-level parallelism, topology, asynchronicity, and abstraction. The "General, Hybrid, and Optimized Sparse Toolkit" (GHOST) is a collection of building blocks that targets algorithms dealing with sparse matrix representations on current and future large-scale systems. It implements the "MPI+X" paradigm, has a pure C interface, and provides hybrid-parallel numerical kernels, intelligent resource management, and truly heterogeneous parallelism for multicore CPUs, Nvidia GPUs, and the Intel Xeon Phi. We describe the details of its design with respect to the challenges posed by modern heterogeneous supercomputers and recent algorithmic developments. Implementation details which are indispensable for achieving high efficiency are pointed out and their necessity is justified by performance measurements or predictions based on performance models. The library code and several applications are available as open source. We also provide instructions on how to make use of GHOST in existing software packages, together with a case study which demonstrates the applicability and performance of GHOST as a component within a larger software stack.Comment: 32 pages, 11 figure