The fast multipole method at exascale

This thesis presents a top to bottom analysis on designing and implementing fast algorithms for current and future systems. We present new analysis, algorithmic techniques, and implementations of the Fast Multipole Method (FMM) for solving N- body problems. We target the FMM because it is broadly applicable to a variety of scientific particle simulations used to study electromagnetic, fluid, and gravitational phenomena, among others. Importantly, the FMM has asymptotically optimal time complexity with guaranteed approximation accuracy. As such, it is among the most attractive solutions for scalable particle simulation on future extreme scale systems. We specifically address two key challenges. The first challenge is how to engineer fast code for today’s platforms. We present the first in-depth study of multicore op- timizations and tuning for FMM, along with a systematic approach for transforming a conventionally-parallelized FMM into a highly-tuned one. We introduce novel opti- mizations that significantly improve the within-node scalability of the FMM, thereby enabling high-performance in the face of multicore and manycore systems. The second challenge is how to understand scalability on future systems. We present a new algorithmic complexity analysis of the FMM that considers both intra- and inter- node communication costs. Using these models, we present results for choosing the optimal algorithmic tuning parameter. This analysis also yields the surprising prediction that although the FMM is largely compute-bound today, and therefore highly scalable on current systems, the trajectory of processor architecture designs, if there are no significant changes could cause it to become communication-bound as early as the year 2015. This prediction suggests the utility of our analysis approach, which directly relates algorithmic and architectural characteristics, for enabling a new kind of highlevel algorithm-architecture co-design. To demonstrate the scientific significance of FMM, we present two applications namely, direct simulation of blood which is a multi-scale multi-physics problem and large-scale biomolecular electrostatics. MoBo (Moving Boundaries) is the infrastruc- ture for the direct numerical simulation of blood. It comprises of two key algorithmic components of which FMM is one. We were able to simulate blood flow using Stoke- sian dynamics on 200,000 cores of Jaguar, a peta-flop system and achieve a sustained performance of 0.7 Petaflop/s. The second application we propose as future work in this thesis is biomolecular electrostatics where we solve for the electrical potential using the boundary-integral formulation discretized with boundary element methods (BEM). The computational kernel in solving the large linear system is dense matrix vector multiply which we propose can be calculated using our scalable FMM. We propose to begin with the two dielectric problem where the electrostatic field is cal- culated using two continuum dielectric medium, the solvent and the molecule. This is only a first step to solving biologically challenging problems which have more than two dielectric medium, ion-exclusion layers, and solvent filled cavities. Finally, given the difficulty in producing high-performance scalable code, productivity is a key concern. Recently, numerical algorithms are being redesigned to take advantage of the architectural features of emerging multicore processors. These new classes of algorithms express fine-grained asynchronous parallelism and hence reduce the cost of synchronization. We performed the first extensive performance study of a recently proposed parallel programming model, called Concurrent Collections (CnC). In CnC, the programmer expresses her computation in terms of application-specific operations, partially-ordered by semantic scheduling constraints. The CnC model is well-suited to expressing asynchronous-parallel algorithms, so we evaluate CnC using two dense linear algebra algorithms in this style for execution on state-of-the-art mul- ticore systems. Our implementations in CnC was able to match and in some cases even exceed competing vendor-tuned and domain specific library codes. We combine these two distinct research efforts by expressing FMM in CnC, our approach tries to marry performance with productivity that will be critical on future systems. Looking forward, we would like to extend this to distributed memory machines, specifically implement FMM in the new distributed CnC, distCnC to express fine-grained paral- lelism which would require significant effort in alternative models.Ph.D

Collaborative Heterogeneity-Aware OS Scheduler for Asymmetric Multicore Processors

Funding: This work is supported in part by the China Postdoctoral Science Foundation (Grant No. 2020TQ0169), the ShuiMu Tsinghua Scholar fellowship (2019SM131), National Key R&D Program of China (2020AAA0105200), National Natural Science Foundation of China (U20A20226), Beijing Natural Science Foundation (4202031), Beijing Academy of Artificial Intelligence BAAI), the UK EPSRC grants Discovery: Pattern Discovery and Program Shaping for Manycore Systems (EP/P020631/1). This work is also supported by the Royal Academy of Engineering under the Research Fellowship scheme.Asymmetric multicore processors (AMP) offer multiple types of cores under the same programming interface. Extracting the full potential of AMPs requires intelligent scheduling decisions, matching each thread with the right kind of core, the core that will maximize performance or minimize wasted energy for this thread. Existing OS schedulers are not up to this task. While they may handle certain aspects of asymmetry in the system, none can handle all runtime factors affecting AMPs for the general case of multi-threaded multi-programmed workloads. We address this problem by introducing COLAB, a general purpose asymmetry-aware scheduler targeting multi-threaded multi-programmed workloads. It estimates the performance and power of each thread on each type of core and identifies communication patterns and bottleneck threads. With this information, the scheduler makes coordinated core assignment and thread selection decisions that still provide each application its fair share of the processor’s time. We evaluate our approach using both the GEM5 simulator on four distinct big.LITTLE configurations and a development board with ARM Cortex-A73/A53 processors and mixed workloads composed of PARSEC and SPLASH2 benchmarks. Compared to the state-of-the art Linux CFS and AMP-aware schedulers, we demonstrate performance gains of up to 25% and 5% to 15% on average,together with an average 5% energy saving depending on the hardware setup.PostprintPeer reviewe

Heterogeneity-aware scheduling and data partitioning for system performance acceleration

Over the past decade, heterogeneous processors and accelerators have become increasingly prevalent in modern computing systems. Compared with previous homogeneous parallel machines, the hardware heterogeneity in modern systems provides new opportunities and challenges for performance acceleration. Classic operating systems optimisation problems such as task scheduling, and application-specific optimisation techniques such as the adaptive data partitioning of parallel algorithms, are both required to work together to address hardware heterogeneity. Significant effort has been invested in this problem, but either focuses on a specific type of heterogeneous systems or algorithm, or a high-level framework without insight into the difference in heterogeneity between different types of system. A general software framework is required, which can not only be adapted to multiple types of systems and workloads, but is also equipped with the techniques to address a variety of hardware heterogeneity. This thesis presents approaches to design general heterogeneity-aware software frameworks for system performance acceleration. It covers a wide variety of systems, including an OS scheduler targeting on-chip asymmetric multi-core processors (AMPs) on mobile devices, a hierarchical many-core supercomputer and multi-FPGA systems for high performance computing (HPC) centers. Considering heterogeneity from on-chip AMPs, such as thread criticality, core sensitivity, and relative fairness, it suggests a collaborative based approach to co-design the task selector and core allocator on OS scheduler. Considering the typical sources of heterogeneity in HPC systems, such as the memory hierarchy, bandwidth limitations and asymmetric physical connection, it proposes an application-specific automatic data partitioning method for a modern supercomputer, and a topological-ranking heuristic based schedule for a multi-FPGA based reconfigurable cluster. Experiments on both a full system simulator (GEM5) and real systems (Sunway Taihulight Supercomputer and Xilinx Multi-FPGA based clusters) demonstrate the significant advantages of the suggested approaches compared against the state-of-the-art on variety of workloads."This work is supported by St Leonards 7th Century Scholarship and Computer Science PhD funding from University of St Andrews; by UK EPSRC grant Discovery: Pattern Discovery and Program Shaping for Manycore Systems (EP/P020631/1)." -- Acknowledgement

From Piz Daint to the Stars: Simulation of Stellar Mergers using High-Level Abstractions

We study the simulation of stellar mergers, which requires complex simulations with high computational demands. We have developed Octo-Tiger, a finite volume grid-based hydrodynamics simulation code with Adaptive Mesh Refinement which is unique in conserving both linear and angular momentum to machine precision. To face the challenge of increasingly complex, diverse, and heterogeneous HPC systems, Octo-Tiger relies on high-level programming abstractions. We use HPX with its futurization capabilities to ensure scalability both between nodes and within, and present first results replacing MPI with libfabric achieving up to a 2.8x speedup. We extend Octo-Tiger to heterogeneous GPU-accelerated supercomputers, demonstrating node-level performance and portability. We show scalability up to full system runs on Piz Daint. For the scenario's maximum resolution, the compute-critical parts (hydrodynamics and gravity) achieve 68.1% parallel efficiency at 2048 nodes.Comment: Accepted at SC1