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

On the acceleration of wavefront applications using distributed many-core architectures

In this paper we investigate the use of distributed graphics processing unit (GPU)-based architectures to accelerate pipelined wavefront applications—a ubiquitous class of parallel algorithms used for the solution of a number of scientific and engineering applications. Specifically, we employ a recently developed port of the LU solver (from the NAS Parallel Benchmark suite) to investigate the performance of these algorithms on high-performance computing solutions from NVIDIA (Tesla C1060 and C2050) as well as on traditional clusters (AMD/InfiniBand and IBM BlueGene/P). Benchmark results are presented for problem classes A to C and a recently developed performance model is used to provide projections for problem classes D and E, the latter of which represents a billion-cell problem. Our results demonstrate that while the theoretical performance of GPU solutions will far exceed those of many traditional technologies, the sustained application performance is currently comparable for scientific wavefront applications. Finally, a breakdown of the GPU solution is conducted, exposing PCIe overheads and decomposition constraints. A new k-blocking strategy is proposed to improve the future performance of this class of algorithm on GPU-based architectures

Distributed-Memory Breadth-First Search on Massive Graphs

This chapter studies the problem of traversing large graphs using the breadth-first search order on distributed-memory supercomputers. We consider both the traditional level-synchronous top-down algorithm as well as the recently discovered direction optimizing algorithm. We analyze the performance and scalability trade-offs in using different local data structures such as CSR and DCSC, enabling in-node multithreading, and graph decompositions such as 1D and 2D decomposition.Comment: arXiv admin note: text overlap with arXiv:1104.451

Exploring Computational Chemistry on Emerging Architectures

Emerging architectures, such as next generation microprocessors, graphics processing units, and Intel MIC cards, are being used with increased popularity in high performance computing. Each of these architectures has advantages over previous generations of architectures including performance, programmability, and power efficiency. With the ever-increasing performance of these architectures, scientific computing applications are able to attack larger, more complicated problems. However, since applications perform differently on each of the architectures, it is difficult to determine the best tool for the job. This dissertation makes the following contributions to computer engineering and computational science. First, this work implements the computational chemistry variational path integral application, QSATS, on various architectures, ranging from microprocessors to GPUs to Intel MICs. Second, this work explores the use of analytical performance modeling to predict the runtime and scalability of the application on the architectures. This allows for a comparison of the architectures when determining which to use for a set of program input parameters. The models presented in this dissertation are accurate within 6%. This work combines novel approaches to this algorithm and exploration of the various architectural features to develop the application to perform at its peak. In addition, this expands the understanding of computational science applications and their implementation on emerging architectures while providing insight into the performance, scalability, and programmer productivity

High-performance and hardware-aware computing: proceedings of the second International Workshop on New Frontiers in High-performance and Hardware-aware Computing (HipHaC\u2711), San Antonio, Texas, USA, February 2011 ; (in conjunction with HPCA-17)

High-performance system architectures are increasingly exploiting heterogeneity. The HipHaC workshop aims at combining new aspects of parallel, heterogeneous, and reconfigurable microprocessor technologies with concepts of high-performance computing and, particularly, numerical solution methods. Compute- and memory-intensive applications can only benefit from the full hardware potential if all features on all levels are taken into account in a holistic approach

High Lundquist Number Simulations of Parker\u27s Model of Coronal Heating: Scaling and Current Sheet Statistics Using Heterogeneous Computing Architectures

Parker\u27s model [Parker, Astrophys. J., 174, 499 (1972)] is one of the most discussed mechanisms for coronal heating and has generated much debate. We have recently obtained new scaling results for a 2D version of this problem suggesting that the heating rate becomes independent of resistivity in a statistical steady state [Ng and Bhattacharjee, Astrophys. J., 675, 899 (2008)]. Our numerical work has now been extended to 3D using high resolution MHD numerical simulations. Random photospheric footpoint motion is applied for a time much longer than the correlation time of the motion to obtain converged average coronal heating rates. Simulations are done for different values of the Lundquist number to determine scaling. In the high-Lundquist number limit (S \u3e 1000), the coronal heating rate obtained is consistent with a trend that is independent of the Lundquist number, as predicted by previous analysis and 2D simulations. We will present scaling analysis showing that when the dissipation time is comparable or larger than the correlation time of the random footpoint motion, the heating rate tends to become independent of Lundquist number, and that the magnetic energy production is also reduced significantly. We also present a comprehensive reprogramming of our simulation code to run on NVidia graphics processing units using the Compute Unified Device Architecture (CUDA) and report code performance on several large scale heterogenous machines