Generation of large finite-element matrices on multiple graphics processors

February 7th, 2013


The paper presents techniques for generating very large finite-element matrices on a multicore workstation equipped with several graphics processing units (GPUs). To overcome the low memory size limitation of the GPUs, and at the same time to accelerate the generation process, we propose to generate the large sparse linear systems arising in finite-element analysis in an iterative manner on several GPUs and to use the graphics accelerators concurrently with CPUs performing collection and addition of the matrix fragments using a fast multithreaded procedure. The scheduling of the threads is organized in such a way that the CPU operations do not affect the performance of the process, and the GPUs are idle only when data are being transferred from GPU to CPU. This approach is verified on two workstations: the first consists of two 6-core Intel Xeon X5690 processors with two Fermi GPUs: each GPU is a GeForce GTX 590 with two graphics processors and 1.5 GB of fast RAM; the second workstation is equipped with two Tesla C2075 boards carrying 6 GB of RAM each and two 12-core Opteron 6174s. For the latter setup, we demonstrate the fast generation of sparse finite-element matrices as large as 10 million unknowns, with over 1 billion nonzero entries. Comparing with the single-threaded and multithreaded CPU implementations, the GPU-based version of the algorithm based on the ideas presented in this paper reduces the finite-element matrix-generation time in double precision by factors of 100 and 30, respectively.

(Dziekonski, A., Sypek, P., Lamecki, A. and Mrozowski, M.: “Generation of large finite-element matrices on multiple graphics processors”. International Journal on Numerical Methoths in Engineering, 2012, in press. [DOI])

A scalable, numerically stable, high-performance tridiagonal solver using GPUs

January 29th, 2013


In this paper, we present a scalable, numerically stable, high-performance tridiagonal solver. The solver is based on the SPIKE algorithm for partitioning a large matrix into small independent matrices, which can be solved in parallel. For each small matrix, our solver applies a general 1-by-1 or 2-by-2 diagonal pivoting algorithm, which is also known to be numerically stable. Our paper makes two major contributions. First, our solver is the first numerically stable tridiagonal solver for GPUs. Our solver provides comparable quality of stable solutions to Intel MKL and Matlab, at speed comparable to the GPU tridiagonal solvers in existing packages like CUSPARSE. It is also scalable to multiple GPUs and CPUs. Second, we present and analyze two key optimization strategies for our solver: a high-throughput data layout transformation for memory efficiency, and a dynamic tiling approach for reducing the memory access footprint caused by branch divergence.

(Chang, Li-Wen and Stratton, John A. and Kim, Hee-Seok and Hwu, Wen-mei W.: “A scalable, numerically stable, high-performance tridiagonal solver using GPUs”, Supercomputing 2012. [WWW])

Parallel Computing Training Dates from AccelerEyes

January 29th, 2013

AccelerEyes has released dates for their upcoming CUDA and OpenCL training courses.



More information can be found on the courses’ webpages.

Acceleware parallel programming courses

January 25th, 2013

Acceleware has recently announced four courses on parallel programming:

More information is available on the courses’ webpages.

A Multi-GPU Programming Library for Real-Time Applications

January 11th, 2013


We present MGPU, a C++ programming library targeted at single-node multi-GPU systems. Such systems combine disproportionate floating point performance with high data locality and are thus well suited to implement real-time algorithms. We describe the library design, programming interface and implementation details in light of this specific problem domain. The core concepts of this work are a novel kind of container abstraction and MPI-like communication methods for intra-system communication. We further demonstrate how MGPU is used as a framework for porting existing GPU libraries to multi-device architectures. Putting our library to the test, we accelerate an iterative non-linear image reconstruction algorithm for real-time magnetic resonance imaging using multiple GPUs. We achieve a speed-up of about 1.7 using 2 GPUs and reach a final speed-up of 2.1 with 4 GPUs. These promising results lead us to conclude that multi-GPU systems are a viable solution for real-time MRI reconstruction as well as signal-processing applications in general.

(Sebastian Schaetz and Martin Uecker: “A Multi-GPU Programming Library for Real-Time Applications”,  Algorithms and Architectures for Parallel Processing (2012): 114-128. [DOI] [ARXIV])

Finite Element Matrix Generation on a GPU

January 6th, 2013


This paper presents an efficient technique for fast generation of sparse systems of linear equations arising in computational electromagnetics in a finite element method using higher order elements. The proposed approach employs a graphics processing unit (GPU) for both numerical integration and matrix assembly. The performance results obtained on a test platform consisting of a Fermi GPU (1x Tesla C2075) and a CPU (2x twelve-core Opterons), indicate that the GPU implementation of the matrix generation allows one to achieve speedups by a factor of 81 and 19 over the optimized single-and multi-threaded CPU-only implementations, respectively.

(Adam Dziekonski et al., “Finite Element Matrix Generation on a GPU”, Progress In Electromagnetics Research 128:249-265, 2012. [PDF])

Lattice microbes: High-performance stochastic simulation method for the reaction-diffusion master equation

January 6th, 2013


Spatial stochastic simulation is a valuable technique for studying reactions in biological systems. With the availability of high-performance computing (HPC), the method is poised to allow integration of data from structural, single-molecule and biochemical studies into coherent computational models of cells. Here, we introduce the Lattice Microbes software package for simulating such cell models on HPC systems. The software performs either well-stirred or spatially resolved stochastic simulations with approximated cytoplasmic crowding in a fast and efficient manner. Our new algorithm efficiently samples the reaction-diffusion master equation using NVIDIA graphics processing units and is shown to be two orders of magnitude faster than exact sampling for large systems while maintaining an accuracy of ∼0.1%. Display of cell models and animation of reaction trajectories involving millions of molecules is facilitated using a plug-in to the popular VMD visualization platform. The Lattice Microbes software is open source and available for download at

(Elijah Roberts, John E. Stone and Zaida Luthey-Schulten: “Lattice Microbes: High-Performance Stochastic Simulation Method for the Reaction-Diffusion Master Equation”, Journal of Computational Chemistry, 34:245-255, 2013. [DOI])

amgcl: an accelerated algebraic multigrid for C++

December 21st, 2012

amgcl is a simple and generic algebraic multigrid (AMG) hierarchy builder. Supported coarsening methods are classical Ruge-Stuben coarsening, and either plain or smoothed aggregation. The constructed hierarchy is stored and used with help of one of the supported backends including VexCL, ViennaCL, and CUSPARSE/Thrust.

With help of amgcl, solution of a large sparse system of linear equations may be easily accelerated through OpenCL, CUDA, or OpenMP technologies. Source code of the library is publicly available under MIT license at

rCUDA 4.0 released

December 18th, 2012

rCUDA (remote CUDA) v4.0 has just been released. It provides full binary compatibility with CUDA applications (no need to modify the application source code or recompile your program), native InfiniBand support, enhanced data transfers, and CUDA 5.0 API support (excluding graphics interoperability). This new release of rCUDA allows to execute existing GPU-accelerated applications by leveraging remote GPUs within a cluster (both via sharing and/or aggregating GPUs) with a negligible overhead. The new version is available free of charge ar, along with examples, manuals and additional information.

Alea.cuBase – GPU computing in .NET

December 17th, 2012

Alea.cuBase allows to create GPU accelerated applications at all levels of sophistication, from simple GPU kernels up to complex GPU algorithms using textures, shared memory and other advanced GPU programming techniques, fully integrated into .NET. The GPU kernels are developed in functional language F# and are callable from any other .NET language. No additional wrappers or assembly translation processes are required. Alea.cuBase allows dynamic creation of GPU code at run time, thereby opening completely new dimensions for GPU accelerated applications. Trial versions are available at

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