Efficient asynchronous executions of AMR computations and visualization on a GPU system

Adaptive Mesh Refinement is a method which dynamically varies the spatio-temporal resolution of localized mesh regions in numerical simulations, based on the strength of the solution features. In-situ visualization plays an important role for analyzing the time evolving characteristics of the domain structures. Continuous visualization of the output data for various timesteps results in a better study of the underlying domain and the model used for simulating the domain. In this paper, we develop strategies for continuous online visualization of time evolving data for AMR applications executed on GPUs. We reorder the meshes for computations on the GPU based on the users input related to the subdomain that he wants to visualize. This makes the data available for visualization at a faster rate. We then perform asynchronous executions of the visualization steps and fix-up operations on the CPUs while the GPU advances the solution. By performing experiments on Tesla S1070 and Fermi C2070 clusters, we found that our strategies result in 60% improvement in response time and 16% improvement in the rate of visualization of frames over the existing strategy of performing fix-ups and visualization at the end of the timesteps.

A Hybrid Parallel Algorithm for Computing and Tracking Level Set Topology

The contour tree is a topological abstraction of a scalar field that captures evolution in level set connectivity. It is an effective representation for visual exploration and analysis of scientific data. We describe a work-efficient, output sensitive, and scalable parallel algorithm for computing the contour tree of a scalar field defined on a domain that is represented using either an unstructured mesh or a structured grid. A hybrid implementation of the algorithm using the GPU and multi-core CPU can compute the contour tree of an input containing 16 million vertices in less than ten seconds with a speedup factor of upto 13. Experiments based on an implementation in a multi-core CPU environment show near-linear speedup for large data sets.

Automatic Data Allocation and Buffer Management for Multi-GPU Machines

Multi-GPU machines are being increasingly used in high-performance computing. Each GPU in such a machine has its own memory and does not share the address space either with the host CPU or other GPUs. Hence, applications utilizing multiple GPUs have to manually allocate and manage data on each GPU. Existing works that propose to automate data allocations for GPUs have limitations and inefficiencies in terms of allocation sizes, exploiting reuse, transfer costs, and scalability. We propose a scalable and fully automatic data allocation and buffer management scheme for affine loop nests on multi-GPU machines. We call it the Bounding-Box-based Memory Manager (BBMM). BBMM can perform at runtime, during standard set operations like union, intersection, and difference, finding subset and superset relations on hyperrectangular regions of array data (bounding boxes). It uses these operations along with some compiler assistance to identify, allocate, and manage data required by applications in terms of disjoint bounding boxes. This allows it to (1) allocate exactly or nearly as much data as is required by computations running on each GPU, (2) efficiently track buffer allocations and hence maximize data reuse across tiles and minimize data transfer overhead, and (3) and as a result, maximize utilization of the combined memory on multi-GPU machines. BBMM can work with any choice of parallelizing transformations, computation placement, and scheduling schemes, whether static or dynamic. Experiments run on a four-GPU machine with various scientific programs showed that BBMM reduces data allocations on each GPU by up to 75% compared to current allocation schemes, yields performance of at least 88% of manually written code, and allows excellent weak scaling.

3-D GPU Based Real Time Diffuse Optical Tomographic System

3-Dimensional Diffuse Optical Tomographic (3-D DOT) image reconstruction algorithm is computationally complex and requires excessive matrix computations and thus hampers reconstruction in real time. In this paper, we present near real time 3D DOT image reconstruction that is based on Broyden approach for updating Jacobian matrix. The Broyden method simplifies the algorithm by avoiding re-computation of the Jacobian matrix in each iteration. We have developed CPU and heterogeneous CPU/GPU code for 3D DOT image reconstruction in C and MatLab programming platform. We have used Compute Unified Device Architecture (CUDA) programming framework and CUDA linear algebra library (CULA) to utilize the massively parallel computational power of GPUs (NVIDIA Tesla K20c). The computation time achieved for C program based implementation for a CPU/GPU system for 3 planes measurement and FEM mesh size of 19172 tetrahedral elements is 806 milliseconds for an iteration.

Adaptive executions of hyperbolic block-structured AMR applications on GPU systems

A block-structured adaptive mesh refinement (AMR) technique has been used to obtain numerical solutions for many scientific applications. Some block-structured AMR approaches have focused on forming patches of non-uniform sizes where the size of a patch can be tuned to the geometry of a region of interest. In this paper, we develop strategies for adaptive execution of block-structured AMR applications on GPUs, for hyperbolic directionally split solvers. While effective hybrid execution strategies exist for applications with uniform patches, our work considers efficient execution of non-uniform patches with different workloads. Our techniques include bin-packing work units to load balance GPU computations, adaptive asynchronism between CPU and GPU executions using a knapsack formulation, and scheduling communications for multi-GPU executions. Our experiments with synthetic and real data, for single-GPU and multi-GPU executions, on Tesla S1070 and Fermi C2070 clusters, show that our strategies result in up to a 3.23 speedup in performance over existing strategies.

Computer generated hologram with geometric occlusion using GPU-accelerated depth buffer rasterization for three-dimensional display

We present a method of rapidly producing computer-generated holograms that exhibit geometric occlusion in the reconstructed image. Conceptually, a bundle of rays is shot from every hologram sample into the object volume.We use z buffering to find the nearest intersecting object point for every ray and add its complex field contribution to the corresponding hologram sample. Each hologram sample belongs to an independent operation, allowing us to exploit the parallel computing capability of modern programmable graphics processing units (GPUs). Unlike algorithms that use points or planar segments as the basis for constructing the hologram, our algorithm's complexity is dependent on fixed system parameters, such as the number of ray-casting operations, and can therefore handle complicated models more efficiently. The finite number of hologram pixels is, in effect, a windowing function, and from analyzing the Wigner distribution function of windowed free-space transfer function we find an upper limit on the cone angle of the ray bundle. Experimentally, we found that an angular sampling distance of 0:01' for a 2:66' cone angle produces acceptable reconstruction quality. © 2009 Optical Society of America.

GPU-accelerated optimization of fuel treatments for mitigating wildfire hazard

Fuel treatment is considered a suitable way to mitigate the hazard related to potential wildfires on a landscape. However, designing an optimal spatial layout of treatment units represents a difficult optimization problem. In fact, budget constraints, the probabilistic nature of fire spread and interactions among the different area units composing the whole treatment, give rise to challenging search spaces on typical landscapes. In this paper we formulate such optimization problem with the objective of minimizing the extension of land characterized by high fire hazard. Then, we propose a computational approach that leads to a spatially-optimized treatment layout exploiting Tabu Search and General-Purpose computing on Graphics Processing Units (GPGPU). Using an application example, we also show that the proposed methodology can provide high-quality design solutions in low computing time. © 2013 The Authors. Published by Elsevier B.V.

Understanding GPU programming for statistical computation: Studies in massively parallel massive mixtures

This article describes advances in statistical computation for large-scale data analysis in structured Bayesian mixture models via graphics processing unit (GPU) programming. The developments are partly motivated by computational challenges arising in fitting models of increasing heterogeneity to increasingly large datasets. An example context concerns common biological studies using high-throughput technologies generating many, very large datasets and requiring increasingly high-dimensional mixture models with large numbers of mixture components.We outline important strategies and processes for GPU computation in Bayesian simulation and optimization approaches, give examples of the benefits of GPU implementations in terms of processing speed and scale-up in ability to analyze large datasets, and provide a detailed, tutorial-style exposition that will benefit readers interested in developing GPU-based approaches in other statistical models. Novel, GPU-oriented approaches to modifying existing algorithms software design can lead to vast speed-up and, critically, enable statistical analyses that presently will not be performed due to compute time limitations in traditional computational environments. Supplementalmaterials are provided with all source code, example data, and details that will enable readers to implement and explore the GPU approach in this mixture modeling context. © 2010 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

Comparing the implementation of two-dimensional numerical quadrature on GPU, FPGA and ClearSpeed systems to study electron scattering by atoms

The use of accelerators, with compute architectures different and distinct from the CPU, has become a new research frontier in high-performance computing over the past ?ve years. This paper is a case study on how the instruction-level parallelism offered by three accelerator technologies, FPGA, GPU and ClearSpeed, can be exploited in atomic physics. The algorithm studied is the evaluation of two electron integrals, using direct numerical quadrature, a task that arises in the study of intermediate energy electron scattering by hydrogen atoms. The results of our ‘productivity’ study show that while each accelerator is viable, there are considerable differences in the implementation strategies that must be followed on each.

cudaMap: a GPU accelerated program for gene expression connectivity mapping

Background: Modern cancer research often involves large datasets and the use of sophisticated statistical techniques. Together these add a heavy computational load to the analysis, which is often coupled with issues surrounding data accessibility. Connectivity mapping is an advanced bioinformatic and computational technique dedicated to therapeutics discovery and drug re-purposing around differential gene expression analysis. On a normal desktop PC, it is common for the connectivity mapping task with a single gene signature to take >2h to complete using sscMap, a popular Java application that runs on standard CPUs (Central Processing Units). Here, we describe new software, cudaMap, which has been implemented using CUDA C/C++ to harness the computational power of NVIDIA GPUs (Graphics Processing Units) to greatly reduce processing times for connectivity mapping.

Results: cudaMap can identify candidate therapeutics from the same signature in just over thirty seconds when using an NVIDIA Tesla C2050 GPU. Results from the analysis of multiple gene signatures, which would previously have taken several days, can now be obtained in as little as 10 minutes, greatly facilitating candidate therapeutics discovery with high throughput. We are able to demonstrate dramatic speed differentials between GPU assisted performance and CPU executions as the computational load increases for high accuracy evaluation of statistical significance.

Conclusion: Emerging 'omics' technologies are constantly increasing the volume of data and information to be processed in all areas of biomedical research. Embracing the multicore functionality of GPUs represents a major avenue of local accelerated computing. cudaMap will make a strong contribution in the discovery of candidate therapeutics by enabling speedy execution of heavy duty connectivity mapping tasks, which are increasingly required in modern cancer research. cudaMap is open source and can be freely downloaded from http://purl.oclc.org/NET/cudaMap.

Autonomic scheduling of tasks from data parallel patterns to CPU/GPU core mixes

We propose a methodology for optimizing the execution of data parallel (sub-)tasks on CPU and GPU cores of the same heterogeneous architecture. The methodology is based on two main components: i) an analytical performance model for scheduling tasks among CPU and GPU cores, such that the global execution time of the overall data parallel pattern is optimized; and ii) an autonomic module which uses the analytical performance model to implement the data parallel computations in a completely autonomic way, requiring no programmer intervention to optimize the computation across CPU and GPU cores. The analytical performance model uses a small set of simple parameters to devise a partitioning-between CPU and GPU cores-of the tasks derived from structured data parallel patterns/algorithmic skeletons. The model takes into account both hardware related and application dependent parameters. It computes the percentage of tasks to be executed on CPU and GPU cores such that both kinds of cores are exploited and performance figures are optimized. The autonomic module, implemented in FastFlow, executes a generic map (reduce) data parallel pattern scheduling part of the tasks to the GPU and part to CPU cores so as to achieve optimal execution time. Experimental results on state-of-the-art CPU/GPU architectures are shown that assess both performance model properties and autonomic module effectiveness. © 2013 IEEE.

GPU Acceleration of Partial Differential Equation Solvers

Differential equations are often directly solvable by analytical means only in their one dimensional version. Partial differential equations are generally not solvable by analytical means in two and three dimensions, with the exception of few special cases. In all other cases, numerical approximation methods need to be utilized. One of the most popular methods is the finite element method. The main areas of focus, here, are the Poisson heat equation and the plate bending equation. The purpose of this paper is to provide a quick walkthrough of the various approaches that the authors followed in pursuit of creating optimal solvers, accelerated with the use of graphical processing units, and comparing them in terms of accuracy and time efficiency with existing or self-made non-accelerated solvers.

Enhancing design space exploration by extending CPU/GPU specifications onto FPGAs

The design cycle for complex special-purpose computing systems is extremely costly and time-consuming. It involves a multiparametric design space exploration for optimization, followed by design verification. Designers of special purpose VLSI implementations often need to explore parameters, such as optimal bitwidth and data representation, through time-consuming Monte Carlo simulations. A prominent example of this simulation-based exploration process is the design of decoders for error correcting systems, such as the Low-Density Parity-Check (LDPC) codes adopted by modern communication standards, which involves thousands of Monte Carlo runs for each design point. Currently, high-performance computing offers a wide set of acceleration options that range from multicore CPUs to Graphics Processing Units (GPUs) and Field Programmable Gate Arrays (FPGAs). The exploitation of diverse target architectures is typically associated with developing multiple code versions, often using distinct programming paradigms. In this context, we evaluate the concept of retargeting a single OpenCL program to multiple platforms, thereby significantly reducing design time. A single OpenCL-based parallel kernel is used without modifications or code tuning on multicore CPUs, GPUs, and FPGAs. We use SOpenCL (Silicon to OpenCL), a tool that automatically converts OpenCL kernels to RTL in order to introduce FPGAs as a potential platform to efficiently execute simulations coded in OpenCL. We use LDPC decoding simulations as a case study. Experimental results were obtained by testing a variety of regular and irregular LDPC codes that range from short/medium (e.g., 8,000 bit) to long length (e.g., 64,800 bit) DVB-S2 codes. We observe that, depending on the design parameters to be simulated, on the dimension and phase of the design, the GPU or FPGA may suit different purposes more conveniently, thus providing different acceleration factors over conventional multicore CPUs.

Calcul en n-dimensions sur GPU

Le code source de la libraire développée accompagne ce dépôt dans l'état où il était à ce moment. Il est possible de trouver une version plus à jour sur github (http://github.com/abergeron).