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

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

Optimised hybrid parallelisation of a CFD code on Many Core architectures

COSA is a novel CFD system based on the compressible Navier-Stokes model for unsteady aerodynamics and aeroelasticity of fixed structures, rotary wings and turbomachinery blades. It includes a steady, time domain, and harmonic balance flow solver. COSA has primarily been parallelised using MPI, but there is also a hybrid parallelisation that adds OpenMP functionality to the MPI parallelisation to enable larger number of cores to be utilised for a given simulation as the MPI parallelisation is limited to the number of geometric partitions (or blocks) in the simulation, or to exploit multi-threaded hardware where appropriate. This paper outlines the work undertaken to optimise these two parallelisation strategies, improving the efficiency of both and therefore reducing the computational time required to compute simulations. We also analyse the power consumption of the code on a range of leading HPC systems to further understand the performance of the code.Comment: Submitted to the SC13 conference, 10 pages with 8 figure

PPF - A Parallel Particle Filtering Library

We present the parallel particle filtering (PPF) software library, which enables hybrid shared-memory/distributed-memory parallelization of particle filtering (PF) algorithms combining the Message Passing Interface (MPI) with multithreading for multi-level parallelism. The library is implemented in Java and relies on OpenMPI's Java bindings for inter-process communication. It includes dynamic load balancing, multi-thread balancing, and several algorithmic improvements for PF, such as input-space domain decomposition. The PPF library hides the difficulties of efficient parallel programming of PF algorithms and provides application developers with the necessary tools for parallel implementation of PF methods. We demonstrate the capabilities of the PPF library using two distributed PF algorithms in two scenarios with different numbers of particles. The PPF library runs a 38 million particle problem, corresponding to more than 1.86 GB of particle data, on 192 cores with 67% parallel efficiency. To the best of our knowledge, the PPF library is the first open-source software that offers a parallel framework for PF applications.Comment: 8 pages, 8 figures; will appear in the proceedings of the IET Data Fusion & Target Tracking Conference 201

Analytical modelling for the performance prediction and optimisation of near-neighbour structured grid hydrodynamics

The advent of modern High Performance Computing (HPC) has facilitated the use of powerful supercomputing machines that have become the backbone of data analysis and simulation. With such a variety of software and hardware available today, understanding how well such machines can perform is key for both efficient use and future planning. With significant costs and multi-year turn-around times, procurement of a new HPC architecture can be a significant undertaking. In this work, we introduce one such measure to capture the performance of such machines – analytical performance models. These models provide a mathematical representation of the behaviour of an application in the context of how its various components perform for an architecture. By parameterising its workload in such a way that the time taken to compute can be described in relation to one or more benchmarkable statistics, this allows for a reusable representation of an application that can be applied to multiple architectures. This work goes on to introduce one such benchmark of interest, Hydra. Hydra is a benchmark 3D Eulerian structured mesh hydrocode implemented in Fortran, with which the explosive compression of materials, shock waves, and the behaviour of materials at the interface between components can be investigated. We assess its scaling behaviour and use this knowledge to construct a performance model that accurately predicts the runtime to within 15% across three separate machines, each with its own distinct characteristics. Further, this work goes on to explore various optimisation techniques, some of which see a marked speedup in the overall walltime of the application. Finally, another software application of interest with similar behaviour patterns, PETSc, is examined to demonstrate how different applications can exhibit similar modellable patterns

Chaotic multigrid methods for the solution of elliptic equations

Supercomputer power has been doubling approximately every 14 months for several decades, increasing the capabilities of scientific modelling at a similar rate. However, to utilize these machines effectively for applications such as computational fluid dynamics, improvements to strong scalability are required. Here, the particular focus is on semi-implicit, viscous-flow CFD, where the largest bottleneck to strong scalability is the parallel solution of the linear pressure-correction equation — an elliptic Poisson equation. State-of-the-art linear solvers, such as Krylov subspace or multigrid methods, provide excellent numerical performance for elliptic equations, but do not scale efficiently due to frequent synchronization between processes. Complete desynchronization is possible for basic, Jacobi-like solvers using the theory of ‘chaotic relaxations’. These non-deterministic, chaotic solvers scale superbly, as demonstrated herein, but lack the numerical performance to converge elliptic equations — even with the relatively lax convergence requirements of the example CFD application. However, these chaotic principles can also be applied to multigrid solvers. In this paper, a ‘chaotic-cycle’ algebraic multigrid method is described and implemented as an open-source library. It is tested on a model Poisson equation, and also within the context of CFD. Two CFD test cases are used: the canonical lid-driven cavity flow and the flow simulation of a ship (KVLCC2). The chaotic-cycle multigrid shows good scalability and numerical performance compared to classical V-, W- and F-cycles. On 2048 cores the chaotic-cycle multigrid solver performs up to faster than Flexible-GMRES and faster than classical V-cycle multigrid. Further improvements to chaotic-cycle multigrid can be made, relating to coarse-grid communications and desynchronized residual computations. It is expected that the chaotic-cycle multigrid could be applied to other scientific fields, wherever a scalable elliptic-equation solver is required