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.
There are several particle-based FMM implementations utilizing task-based programming available. The approach described in @cite_15 uses the Quark runtime environment @cite_21 , the implementation in @cite_10 @cite_42 uses StarPu @cite_30 , whilst @cite_11 uses OpenMP @cite_35 , and @cite_16 compares Cilk @cite_3 , HPX-5, and OpenMP tasks @cite_52 . Our choice of HPX for the task-based runtime system is motivated by the same findings as the above mentioned review and the need to implement specialized kernels for energy conservation that require coupling between different parts of the solver.
@cite_30 @cite_35 @cite_21 @cite_42 @cite_52 @cite_3 @cite_15 @cite_16 @cite_10 @cite_11
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Most high-performance, scientific libraries have adopted hybrid parallelization schemes - such as the popular MPI+OpenMP hybridization - to benefit from the capacities of modern distributed-memory machines. While these approaches have shown to achieve high performance, they require a lot of effort to design and maintain sophisticated synchronization communication strategies. On the other hand, task-based programming paradigms aim at delegating this burden to a runtime system for maximizing productivity. In this article, we assess the potential of task-based fast multipole methods (FMM) on clusters of multicore processors. We propose both a hybrid MPI+task FMM parallelization and a pure task-based parallelization where the MPI communications are implicitly handled by the runtime system. The latter approach yields a very compact code following a sequential task-based programming model. We show that task-based approaches can compete with a hybrid MPI+OpenMP highly optimized code and that furthermore the compact task-based scheme fully matches the performance of the sophisticated, hybrid MPI+task version, ensuring performance while maximizing productivity. We illustrate our discussion with the ScalFMM FMM library and the StarPU runtime system. In this paper, we explore data-driven execution of the adaptive fast multipole method by asynchronously scheduling available computational tasks using Cilk, C++11 standard thread and future libraries, the High Performance ParalleX (HPX-5) library, and OpenMP tasks. By comparing these implementations using various input data sets, this paper examines the runtime system's capability to spawn new task, the capacity of the tasks that can be managed, the performance impact between eager and lazy thread creation for new task, and the effectiveness of the task scheduler and its ability to recognize the critical path of the underlying algorithm. SUMMARY This paper presents a number of algorithms to run the fast multipole method (FMM) on NVIDIA CUDA-capable graphical processing units (GPUs) (Nvidia Corporation, Sta. Clara, CA, USA). The FMM is a class of methods to compute pairwise interactions between N particles for a given error tolerance and with computational cost of O(N). The methods described in the paper are applicable to any FMMs in which the multipole-to-local (M2L) operator is a dense matrix and the matrix is precomputed. This is the case for example in the black-box fast multipole method (bbFMM), which is a variant of the FMM that can handle large class of kernels. This example will be used in our benchmarks. In the FMM, two operators represent most of the computational cost, and an optimal implementation typically tries to balance those two operators. One is the nearby interaction calculation (direct sum calculation, line 29 in Listing 1), and the other is the M2L operation. We focus on the M2L. By combining multiple M2L operations and reordering the primitive loops of the M2L so that CUDA threads can reuse or share common data, these approaches reduce the movement of data in the GPU. Because memory bandwidth is the primary bottleneck of these methods, significant performance improvements are realized. Four M2L schemes are detailed and analyzed in the case of a uniform tree. The four schemes are tested and compared with an optimized, OpenMP parallelized, multi-core CPU code. We consider high and low precision calculations by varying the number of Chebyshev nodes used in the bbFMM. The accuracy of the GPU codes is found to be satisfactory and achieved performance over 200 Gflop s on one NVIDIA Tesla C1060 GPU (Nvidia Corporation, Sta. Clara, CA, USA). This was compared against two quad-core Intel Xeon E5345 processors (Intel Corporation, Sta. Clara, CA, USA) running at 2.33 GHz, for a combined peak performance of 149 Gflop s for single precision. For the low FMM accuracy case, the observed performance of the CPU code was 37 Gflop s, whereas for the high FMM accuracy case, the performance was about 8.5 Gflop s, most likely because of a higher frequency of cache misses. We also present benchmarks on an NVIDIA C2050 GPU (a Fermi processor)(Nvidia Corporation, Sta. Clara, CA, USA) in single and double precision. Copyright © 2011 John Wiley & Sons, Ltd. Task-based programming models for shared memory—such as Cilk Plus and OpenMP 3—are well established and documented. However, with the increase in parallel, many-core, and heterogeneous systems, a number of research-driven projects have developed more diversified task-based support, employing various programming and runtime features. Unfortunately, despite the fact that dozens of different task-based systems exist today and are actively used for parallel and high-performance computing (HPC), no comprehensive overview or classification of task-based technologies for HPC exists. In this paper, we provide an initial task-focused taxonomy for HPC technologies, which covers both programming interfaces and runtime mechanisms. We demonstrate the usefulness of our taxonomy by classifying state-of-the-art task-based environments in use today. Computations with a sufficient amount of parallelism and workload size may take advantage of many-core coprocessors. In contrast, small-scale workloads usually suffer from a poor utilization of the coprocessor resources. For parallel applications with small but many computational kernels a concurrent processing on a shared coprocessor may be a viable solution. We evaluate the Xeon Phi offload models Intel LEO and OpenMP4 within multi-threaded and multi-process host applications with concurrent coprocessor offloading. Limitations of OpenMP4 regarding data persistence across function calls, e.g. when used within libraries, can slow down the application. We propose an offload-proxy approach for OpenMP4 to recover the performance in these cases. For concurrent kernel execution, we demonstrate the performance of the different offload models and our offload-proxy by using synthetic kernels and a parallel hybrid CPU Xeon Phi molecular simulation application. Fast multipole methods have O(N) complexity, are compute bound, and require very little synchronization, which makes them a favorable algorithm on next-generation supercomputers. Their most common application is to accelerate N-body problems, but they can also be used to solve boundary integral equations. When the particle distribution is irregular and the tree structure is adaptive, load-balancing becomes a non-trivial question. A common strategy for load-balancing FMMs is to use the work load from the previous step as weights to statically repartition the next step. The authors discuss in the paper another approach based on data-driven execution to efficiently tackle this challenging load-balancing problem. The core idea consists of breaking the most time-consuming stages of the FMMs into smaller tasks. The algorithm can then be represented as a Directed Acyclic Graph (DAG) where nodes represent tasks, and edges represent dependencies among them. The execution of the algorithm is performed by asynchronously scheduling the tasks using the QUARK runtime environment, in a way such that data dependencies are not violated for numerical correctness purposes. This asynchronous scheduling results in an out-of-order execution. The performance results of the data-driven FMM execution outperform the previous strategy and show linear speedup on a quad-socket quad-core Intel Xeon system. To fully tap into the potential of heterogeneous machines composed of multicore processors and multiple accelerators, simple offloading approaches in which the main trunk of the application runs on regular cores while only specific parts are offloaded on accelerators are not sufficient. The real challenge is to build systems where the application would permanently spread across the entire machine, that is, where parallel tasks would be dynamically scheduled over the full set of available processing units. To face this challenge, we previously proposed StarPU, a runtime system capable of scheduling tasks over multicore machines equipped with GPU accelerators. StarPU uses a software virtual shared memory (VSM) that provides a highlevel programming interface and automates data transfers between processing units so as to enable a dynamic scheduling of tasks. We now present how we have extended StarPU to minimize the cost of transfers between processing units in order to efficiently cope with multi-GPU hardware configurations. To this end, our runtime system implements data prefetching based on asynchronous data transfers, and uses data transfer cost prediction to influence the decisions taken by the task scheduler. We demonstrate the relevance of our approach by benchmarking two parallel numerical algorithms using our runtime system. We obtain significant speedups and high efficiency over multicore machines equipped with multiple accelerators. We also evaluate the behaviour of these applications over clusters featuring multiple GPUs per node, showing how our runtime system can combine with MPI. This paper presents the first in-depth models for compute and memory costs of the kernel-independent Fast Multipole Method (KIFMM). The Fast Multiple Method (FMM) has asymptotically linear time complexity with a guaranteed approximation accuracy, making it an attractive candidate for a wide variety of particle system simulations on future exascale systems. This paper reports on three key advances. First, we present lower bounds on cache complexity for key phases of the FMM and use these bounds to derive analytical performance models. Secondly, using these models, we present results for choosing the optimal algorithmic tuning parameter. Lastly, we use these performance models to make predictions about FMM's scalability on possible exascale system configurations, based on current technology trends. Looking forward to exascale, we suggest that the FMM, though highly compute-bound on today's systems, could in fact become memory-bound by 2020. We present new scalable algorithms and a new implementation of our kernel-independent fast multipole method ( ACM IEEE SC '03), in which we employ both distributed memory parallelism (via MPI) and shared memory streaming parallelism (via GPU acceleration) to rapidly evaluate two-body non-oscillatory potentials. On traditional CPU-only systems, our implementation scales well up to 30 billion unknowns on 65K cores (AMD CRAY-based Kraken system at NSF NICS) for highly non-uniform point distributions. On GPU-enabled systems, we achieve 30x speedup for problems of up to 256 million points on 256 GPUs (Lincoln at NSF NCSA) over a comparable CPU-only based implementations. We achieve scalability to such extreme core counts by adopting a new approach to scalable MPI-based tree construction and partitioning, and a new reduction algorithm for the evaluation phase. For the sub-components of the evaluation phase (the direct- and approximate-interactions, the target evaluation, and the source-to-multipole translations), we use NVIDIA's CUDA framework for GPU acceleration to achieve excellent performance. To do so requires carefully constructed data structure transformations, which we describe in the paper and whose cost we show is minor. Taken together, these components show promise for ultrascalable FMM in the petascale era and beyond. Fast multipole methods FMMs have ON complexity, are compute bound, and require very little synchronization, which makes them a favorable algorithm on next-generation supercomputers. Their most common application is to accelerate N-body problems, but they can also be used to solve boundary integral equations. When the particle distribution is irregular and the tree structure is adaptive, load balancing becomes a non-trivial question. A common strategy for load balancing FMMs is to use the work load from the previous step as weights to statically repartition the next step. The authors discuss in the paper another approach based on data-driven execution to efficiently tackle this challenging load balancing problem. The core idea consists of breaking the most time-consuming stages of the FMMs into smaller tasks. The algorithm can then be represented as a directed acyclic graph where nodes represent tasks and edges represent dependencies among them. The execution of the algorithm is performed by asynchronously scheduling the tasks using the queueing and runtime for kernels runtime environment, in a way such that data dependencies are not violated for numerical correctness purposes. This asynchronous scheduling results in an out-of-order execution. The performance results of the data-driven FMM execution outperform the previous strategy and show linear speedup on a quad-socket quad-core Intel Xeon system.Copyright © 2013 John Wiley & Sons, Ltd. We fundamentally reconsider implementation of the Fast Multipole Method (FMM) on a computing node with a heterogeneous CPU-GPU architecture with multicore CPU(s) and one or more GPU accelerators, as well as on an interconnected cluster of such nodes. The FMM is a divide-and-conquer algorithm that performs a fast N-body sum using a spatial decomposition and is often used in a time-stepping or iterative loop. Using the observation that the local summation and the analysis-based translation parts of the FMM are independent, we map these respectively to the GPUs and CPUs. Careful analysis of the FMM is performed to distribute work optimally between the multicore CPUs and the GPU accelerators. We first develop a single node version where the CPU part is parallelized using OpenMP and the GPU version via CUDA. New parallel algorithms for creating FMM data structures are presented together with load balancing strategies for the single node and distributed multiple-node versions. Our implementation can perform the N-body sum for 128M particles on 16 nodes in 4.23 seconds, a performance not achieved by others in the literature on such clusters. High performance fast multipole method is crucial for the numerical simulation of many physical problems. In a previous study, we have shown that task-based fast multipole method provides the flexibility required to process a wide spectrum of particle distributions efficiently on multicore architectures. In this paper, we now show how such an approach can be extended to fully exploit heterogeneous platforms. For that, we design highly tuned graphics processing unit GPU versions of the two dominant operators P2P and M2L as well as a scheduling strategy that dynamically decides which proportion of subsequent tasks is processed on regular CPU cores and on GPU accelerators. We assess our method with the StarPU runtime system for executing the resulting task flow on an Intel X5650 Nehalem multicore processor possibly enhanced with one, two, or three Nvidia Fermi M2070 or M2090 GPUs Santa Clara, CA, USA. A detailed experimental study on two 30 million particle distributions a cube and an ellipsoid shows that the resulting software consistently achieves high performance across architectures. Copyright © 2015 John Wiley & Sons, Ltd. Abstract This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop s on gpu hardware using single precision. The simulations use a vortex particle method to solve the Navier–Stokes equations, with a highly parallel fast multipole method ( fmm ) as numerical engine, and match the current record in mesh size for this application, a cube of 4096 3 computational points solved with a spectral method. The standard numerical approach used in this field is the pseudo-spectral method, relying on the fft algorithm as the numerical engine. The particle-based simulations presented in this paper quantitatively match the kinetic energy spectrum obtained with a pseudo-spectral method, using a trusted code. In terms of parallel performance, weak scaling results show the fmm -based vortex method achieving 74 parallel efficiency on 4096 processes (one gpu per mpi process, 3 gpu s per node of the tsubame -2.0 system). The fft -based spectral method is able to achieve just 14 parallel efficiency on the same number of mpi processes (using only cpu cores), due to the all-to-all communication pattern of the fft algorithm. The calculation time for one time step was 108 s for the vortex method and 154 s for the spectral method, under these conditions. Computing with 69 billion particles, this work exceeds by an order of magnitude the largest vortex-method calculations to date. This paper presents a new technique for reducing the energy consumption of a multi-task system by sharing its scratchpad memory (SPM) space among the tasks. With this technique, tasks can interfere by using common areas of the SPM. However, this requires to update these areas during context switches, which involves considerable overheads. Hence, an integer linear programming formulation is used at compile time for finding the best assignment of memory objects to the SPM and their respective locations inside it. Experiments show that the technique achieves up to 85 energy reduction with 8Kb of SPM and surpasses other sharing approaches. As high-end computer systems present users with rapidly increasing numbers of processors, possibly also incorporating attached co-processors, programmers are increasingly challenged to express the necessary levels of concurrency with the dominant parallel programming model, Fortran+MPI+OpenMP (or minor variations). In this paper, we examine the languages developed under the DARPA High-Productivity Computing Systems (HPCS) program (Chapel, Fortress, and XIO) as representatives of a different parallel programming model which might be more effective on emerging high-performance systems. The application used in this study is the Hartree-Fock method from quantum chemistry, which combines access to distributed data with a task-parallel algorithm and is characterized by significant irregularity in the computational tasks. We present several different implementation strategies for load balancing of the task-parallel computation, as well as distributed array operations, in each of the three languages. We conclude that the HPCS languages provide a wide variety of mechanisms for expressing parallelism, which can be combined at multiple levels, making them quite expressive for this problem. As the complexity of software for Cyber-Physical Systems (CPS) rapidly increases, multi-core processors and parallel programming models such as OpenMP become appealing to CPS developers for guaranteeing timeliness. Hence, a parallel task on multi-core processors is expected to become a vital component in CPS such as a self-driving car, where tasks must be scheduled in real-time. In this paper, we extend the fork-join parallel task model to be scheduled in real-time, where the number of parallel threads can vary depending on the physical attributes of the system. To efficiently schedule the proposed task model, we develop the task stretch transform. Using this transform for global Deadline Monotonic scheduling for fork-join real-time tasks, we achieve a resource augmentation bound of 3.73. In other words, any task set that is feasible on m unit-speed processors can be scheduled by the proposed algorithm on m processors that are 3.73 times faster. The proposed scheme is implemented on Linux RK as a proof of concept, and ported to Boss, the self-driving vehicle that won the 2007 DARPA Urban Challenge. We evaluate our scheme on Boss by showing its driving quality, i.e., curvature and velocity profiles of the vehicle. The OpenMP standard was conceived to parallelize dense array-based applications, and it has achieved much success with that. Recently, a novel tasking proposal to handle unstructured parallelism in OpenMP has been submitted to the OpenMP 3.0 Language Committee. We tested its expressiveness and flexibility, using it to parallelize a number of examples from a variety of different application areas. Furthermore, we checked whether the model can be implemented efficiently, evaluating the performance of an experimental implementation of the tasking proposal on an SGI Altix 4700, and comparing it to the performance achieved with Intel's Workqueueing model and other worksharing alternatives currently available in OpenMP 2.5. We conclude that the new OpenMP tasks allow the expression of parallelism for a broad range of applications and that they will not hamper application performance. This paper describes our OpenACC porting efforts for a code that we have developed that solves the isothermal incompressible Navier Stokes equation via the lattice Boltzmann method (LBM). Implemented initially as a hybrid MPI OpenMP parallel program, we ported our code to use OpenACC in order to obtain the benefit of accelerators in a high performance computing (HPC) environment. We describe the elements of parallelism inherent in the LBM algorithm and the way in which that parallelism can be expressed using OpenACC directives. By setting compile-time flags during the build process, the program alternatively can be compiled for, and continue to run without the benefit of, accelerators. Through this porting process we were able to accelerate our code in an incremental fashion without extensive code transformation. We point out some additional efforts that were required to expose C++ class data members to the OpenACC compiler and describe difficulties encountered in this process. We show an instance where similar code segments decorated with the same OpenACC directives can result in different compiler outputs with significantly different performance properties. The result of the code porting process, which occurred primarily during OpenACC EuroHack, a 5-day intensive computing workshop, was a 5.5x speedup over the non-accelerated version of the code. We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of search-based performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to a lattice Boltzmann application (LBMHD) that historically has made poor use of scalar microprocessors due to its complex data structures and memory access patterns. We explore one of the broadest sets of multicore architectures in the high-performance computing (HPC) literature, including the Intel Xeon E5345 (Clovertown), AMD Opteron 2214 (Santa Rosa), AMD Opteron 2356 (Barcelona), Sun T5140 T2+ (Victoria Falls), as well as a QS20 IBM Cell Blade. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us to identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our auto-tuned LBMHD application achieves up to a 15 times improvement compared with the original code at a given concurrency. Additionally, we present a detailed analysis of each optimization, which reveals surprising hardware bottlenecks and software challenges for future multicore systems and applications. Many scientific applications are programmed using hybrid programming models that use both message passing and shared memory, due to the increasing prevalence of large-scale systems with multicore, multisocket nodes. Previous work has shown that energy efficiency can be improved using software-controlled execution schemes that consider both the programming model and the power-aware execution capabilities of the system. However, such approaches have focused on identifying optimal resource utilization for one programming model, either shared memory or message passing, in isolation. The potential solution space, thus the challenge, increases substantially when optimizing hybrid models since the possible resource configurations increase exponentially. Nonetheless, with the accelerating adoption of hybrid programming models, we increasingly need improved energy efficiency in hybrid parallel applications on large-scale systems. In this work, we present new software-controlled execution schemes that consider the effects of dynamic concurrency throttling (DCT) and dynamic voltage and frequency scaling (DVFS) in the context of hybrid programming models. Specifically, we present predictive models and novel algorithms based on statistical analysis that anticipate application power and time requirements under different concurrency and frequency configurations. We apply our models and methods to the NPB MZ benchmarks and selected applications from the ASC Sequoia codes. Overall, we achieve substantial energy savings (8.74 percent on average and up to 13.8 percent) with some performance gain (up to 7.5 percent) or negligible performance loss.