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

High Performance Transaction Processing on Non-Uniform Hardware Topologies

Transaction processing is a mission critical enterprise application that runs on high-end servers. Traditionally, transaction processing systems have been designed for uniform core-to-core communication latencies. In the past decade, with the emergence of multisocket multicores, for the first time we have Islands, i.e., groups of cores that communicate fast among themselves and slower with other groups. In current mainstream servers, each multicore processor corresponds to an Island. As the number of cores on a chip increases, however, we expect that multiple Islands will form within a single processor in the nearby future. In addition, the access latencies to the local memory and to the memory of another server over fast interconnect are converging, thus creating a hierarchy of Islands within a group of servers. Non-uniform hardware topologies pose a significant challenge to the scalability and the predictability of performance of transaction processing systems. Distributed transaction processing systems can alleviate this problem; however, no single deployment configuration is optimal for all workloads and hardware topologies. In order to fully utilize the available processing power, a transaction processing system needs to adapt to the underlying hardware topology and tune its configuration to the current workload. More specifically, the system should be able to detect any changes to the workload and hardware topology, and adapt accordingly without disrupting the processing. In this thesis, we first systematically quantify the impact of hardware Islands on deployment configurations of distributed transaction processing systems. We show that none of these configurations is optimal for all workloads, and the choice of the optimal configuration depends on the combination of the workload and hardware topology. In the cluster setting, on the other hand, the choice of optimal configuration additionally depends on the properties of the communication channel between the servers. We address this challenge by designing a dynamic shared-everything system that adapts its data structures automatically to hardware Islands. To ensure good performance in the presence of shifting workload patterns, we use a lightweight partitioning and placement mechanism to balance the load and minimize the synchronization overheads across Islands. Overall, we show that masking the non-uniformity of inter-core communication is critical for achieving predictably high performance for latency-sensitive applications, such as transaction processing. With clusters of a handful of multicore chips with large main memories replacing high-end many-socket servers, the deployment rules of thumb identified in our analysis have a potential to significantly reduce the synchronization and communication costs of transaction processing. As workloads become more dynamic and diverse, while still running on partitioned infrastructure, the lightweight monitoring and adaptive repartitioning mechanisms proposed in this thesis will be applicable to a wide range of designs for which traditional offline schemes are impractical