Spherical harmonic transform with GPUs

We describe an algorithm for computing an inverse spherical harmonic transform suitable for graphic processing units (GPU). We use CUDA and base our implementation on a Fortran90 routine included in a publicly available parallel package, S2HAT. We focus our attention on the two major sequential steps involved in the transforms computation, retaining the efficient parallel framework of the original code. We detail optimization techniques used to enhance the performance of the CUDA-based code and contrast them with those implemented in the Fortran90 version. We also present performance comparisons of a single CPU plus GPU unit with the S2HAT code running on either a single or 4 processors. In particular we find that use of the latest generation of GPUs, such as NVIDIA GF100 (Fermi), can accelerate the spherical harmonic transforms by as much as 18 times with respect to S2HAT executed on one core, and by as much as 5.5 with respect to S2HAT on 4 cores, with the overall performance being limited by the Fast Fourier transforms. The work presented here has been performed in the context of the Cosmic Microwave Background simulations and analysis. However, we expect that the developed software will be of more general interest and applicability

Performance Analysis of a Novel GPU Computation-to-core Mapping Scheme for Robust Facet Image Modeling

Though the GPGPU concept is well-known in image processing, much more work remains to be done to fully exploit GPUs as an alternative computation engine. This paper investigates the computation-to-core mapping strategies to probe the efficiency and scalability of the robust facet image modeling algorithm on GPUs. Our fine-grained computation-to-core mapping scheme shows a significant performance gain over the standard pixel-wise mapping scheme. With in-depth performance comparisons across the two different mapping schemes, we analyze the impact of the level of parallelism on the GPU computation and suggest two principles for optimizing future image processing applications on the GPU platform

Accelerating moderately stiff chemical kinetics in reactive-flow simulations using GPUs

The chemical kinetics ODEs arising from operator-split reactive-flow simulations were solved on GPUs using explicit integration algorithms. Nonstiff chemical kinetics of a hydrogen oxidation mechanism (9 species and 38 irreversible reactions) were computed using the explicit fifth-order Runge-Kutta-Cash-Karp method, and the GPU-accelerated version performed faster than single- and six-core CPU versions by factors of 126 and 25, respectively, for 524,288 ODEs. Moderately stiff kinetics, represented with mechanisms for hydrogen/carbon-monoxide (13 species and 54 irreversible reactions) and methane (53 species and 634 irreversible reactions) oxidation, were computed using the stabilized explicit second-order Runge-Kutta-Chebyshev (RKC) algorithm. The GPU-based RKC implementation demonstrated an increase in performance of nearly 59 and 10 times, for problem sizes consisting of 262,144 ODEs and larger, than the single- and six-core CPU-based RKC algorithms using the hydrogen/carbon-monoxide mechanism. With the methane mechanism, RKC-GPU performed more than 65 and 11 times faster, for problem sizes consisting of 131,072 ODEs and larger, than the single- and six-core RKC-CPU versions, and up to 57 times faster than the six-core CPU-based implicit VODE algorithm on 65,536 ODEs. In the presence of more severe stiffness, such as ethylene oxidation (111 species and 1566 irreversible reactions), RKC-GPU performed more than 17 times faster than RKC-CPU on six cores for 32,768 ODEs and larger, and at best 4.5 times faster than VODE on six CPU cores for 65,536 ODEs. With a larger time step size, RKC-GPU performed at best 2.5 times slower than six-core VODE for 8192 ODEs and larger. Therefore, the need for developing new strategies for integrating stiff chemistry on GPUs was discussed.Comment: 27 pages, LaTeX; corrected typos in Appendix equations A.10 and A.1

On the Efficient Evaluation of the Exchange Correlation Potential on Graphics Processing Unit Clusters

The predominance of Kohn-Sham density functional theory (KS-DFT) for the theoretical treatment of large experimentally relevant systems in molecular chemistry and materials science relies primarily on the existence of efficient software implementations which are capable of leveraging the latest advances in modern high performance computing (HPC). With recent trends in HPC leading towards in increasing reliance on heterogeneous accelerator based architectures such as graphics processing units (GPU), existing code bases must embrace these architectural advances to maintain the high-levels of performance which have come to be expected for these methods. In this work, we purpose a three-level parallelism scheme for the distributed numerical integration of the exchange-correlation (XC) potential in the Gaussian basis set discretization of the Kohn-Sham equations on large computing clusters consisting of multiple GPUs per compute node. In addition, we purpose and demonstrate the efficacy of the use of batched kernels, including batched level-3 BLAS operations, in achieving high-levels of performance on the GPU. We demonstrate the performance and scalability of the implementation of the purposed method in the NWChemEx software package by comparing to the existing scalable CPU XC integration in NWChem.Comment: 26 pages, 9 figure

Three-dimensional shapelets and an automated classification scheme for dark matter haloes

We extend the two-dimensional Cartesian shapelet formalism to d-dimensions. Concentrating on the three-dimensional case, we derive shapelet-based equations for the mass, centroid, root-mean-square radius, and components of the quadrupole moment and moment of inertia tensors. Using cosmological N-body simulations as an application domain, we show that three-dimensional shapelets can be used to replicate the complex sub-structure of dark matter halos and demonstrate the basis of an automated classification scheme for halo shapes. We investigate the shapelet decomposition process from an algorithmic viewpoint, and consider opportunities for accelerating the computation of shapelet-based representations using graphics processing units (GPUs).Comment: 19 pages, 11 figures, accepted for publication in MNRA

Distributed Memory, GPU Accelerated Fock Construction for Hybrid, Gaussian Basis Density Functional Theory

With the growing reliance of modern supercomputers on accelerator-based architectures such a GPUs, the development and optimization of electronic structure methods to exploit these massively parallel resources has become a recent priority. While significant strides have been made in the development of GPU accelerated, distributed memory algorithms for many-body (e.g. coupled-cluster) and spectral single-body (e.g. planewave, real-space and finite-element density functional theory [DFT]), the vast majority of GPU-accelerated Gaussian atomic orbital methods have focused on shared memory systems with only a handful of examples pursuing massive parallelism on distributed memory GPU architectures. In the present work, we present a set of distributed memory algorithms for the evaluation of the Coulomb and exact-exchange matrices for hybrid Kohn-Sham DFT with Gaussian basis sets via direct density-fitted (DF-J-Engine) and seminumerical (sn-K) methods, respectively. The absolute performance and strong scalability of the developed methods are demonstrated on systems ranging from a few hundred to over one thousand atoms using up to 128 NVIDIA A100 GPUs on the Perlmutter supercomputer.Comment: 45 pages, 9 figure

QTM: computational package using MPI protocol for quantum trajectories method

The Quantum Trajectories Method (QTM) is one of {the} frequently used methods for studying open quantum systems. { The main idea of this method is {the} evolution of wave functions which {describe the system (as functions of time). Then,} so-called quantum jumps are applied at {a} randomly selected point in time. {The} obtained system state is called as a trajectory. After averaging many single trajectories{,} we obtain the approximation of the behavior of {a} quantum system.} {This fact also allows} us to use parallel computation methods. In the article{,} we discuss the QTM package which is supported by the MPI technology. Using MPI allowed {utilizing} the parallel computing for calculating the trajectories and averaging them -- as the effect of these actions{,} the time {taken by} calculations is shorter. In spite of using the C++ programming language, the presented solution is easy to utilize and does not need any advanced programming techniques. At the same time{,} it offers a higher performance than other packages realizing the QTM. It is especially important in the case of harder computational tasks{,} and the use of MPI allows {improving the} performance of particular problems which can be solved in the field of open quantum systems.Comment: 28 pages, 9 figure

Parallelization of dynamic programming recurrences in computational biology

The rapid growth of biosequence databases over the last decade has led to a performance bottleneck in the applications analyzing them. In particular, over the last five years DNA sequencing capacity of next-generation sequencers has been doubling every six months as costs have plummeted. The data produced by these sequencers is overwhelming traditional compute systems. We believe that in the future compute performance, not sequencing, will become the bottleneck in advancing genome science. In this work, we investigate novel computing platforms to accelerate dynamic programming algorithms, which are popular in bioinformatics workloads. We study algorithm-specific hardware architectures that exploit fine-grained parallelism in dynamic programming kernels using field-programmable gate arrays: FPGAs). We advocate a high-level synthesis approach, using the recurrence equation abstraction to represent dynamic programming and polyhedral analysis to exploit parallelism. We suggest a novel technique within the polyhedral model to optimize for throughput by pipelining independent computations on an array. This design technique improves on the state of the art, which builds latency-optimal arrays. We also suggest a method to dynamically switch between a family of designs using FPGA reconfiguration to achieve a significant performance boost. We have used polyhedral methods to parallelize the Nussinov RNA folding algorithm to build a family of accelerators that can trade resources for parallelism and are between 15-130x faster than a modern dual core CPU implementation. A Zuker RNA folding accelerator we built on a single workstation with four Xilinx Virtex 4 FPGAs outperforms 198 3 GHz Intel Core 2 Duo processors. Furthermore, our design running on a single FPGA is an order of magnitude faster than competing implementations on similar-generation FPGAs and graphics processors. Our work is a step toward the goal of automated synthesis of hardware accelerators for dynamic programming algorithms