Scalable Partitioning for Parallel Position Based Dynamics

April 13th, 2015


We introduce a practical partitioning technique designed for parallelizing Position Based Dynamics, and exploiting the ubiquitous multi-core processors present in current commodity GPUs. The input is a set of particles whose dynamics is influenced by spatial constraints. In the initialization phase, we build a graph in which each node corresponds to a constraint and two constraints are connected by an edge if they influence at least one common particle. We introduce a novel greedy algorithm for inserting additional constraints (phantoms) in the graph such that the resulting topology is qˆ-colourable, where qˆ ≥ 2 is an arbitrary number. We color the graph, and the constraints with the same color are assigned to the same partition. Then, the set of constraints belonging to each partition is solved in parallel during the animation phase. We demonstrate this by using our partitioning technique; the performance hit caused by the GPU kernel calls is significantly decreased, leaving unaffected the visual quality, robustness and speed of serial position based dynamics.

(Fratarcangeli M and Pellacini F, Scalable Partitioning for Parallel Position Based Dynamics, Computer Graphics Forum (Special Issue of Eurographics 2015 Conference). Vol. 34(2) 2015)

PARALUTION Release 1.0

April 13th, 2015

PARALUTION is a library for sparse iterative methods which can be performed on various parallel devices, including multi-core CPU, GPU (CUDA and OpenCL) and Intel Xeon Phi.

The 1.0 version of the PARALUTION Library supports multi-node and multi-GPU configuration via MPI. All iterative solvers support global operations (i.e. distributed matrices and vectors) and all preconditioners can be used in a block-Jacobi fashion locally on each node/GPU. In addition, the software provides a global (fully distributed) Pair-Wise AMG solver. Read the rest of this entry »

PARALUTION v0.8.0 released

November 14th, 2014

PARALUTION is a library for sparse iterative methods which can be performed on various parallel devices, including multi-core CPU, GPU (CUDA and OpenCL) and Intel Xeon Phi. The new 0.8.0 release provides the following extra features:

  • Complex support
  • TNS, Variable preconditioner
  • BiCGStab(l), QMRCGStab, FCG solvers
  • RS and PairWise AMG
  • SIRA eigenvalue solver
  • Replace/Extract column/row functions
  • Stencil computation

For details, visit

PARALUTION 0.7.0 released

May 27th, 2014

PARALUTION is a library for sparse iterative methods which can be performed on various parallel devices, including multi-core CPU, GPU (CUDA and OpenCL) and Intel Xeon Phi. The new 0.7.0 version provides the following new features:

  • Windows support – full windows support for all backends (CUDA, OpenCL, OpenMP)
  • Assembling function – new OpenMP parallel assembling function for sparse matrices (includes an update function for time-dependent problems)
  • Direct (dense) solvers (for very small problems)
  • (Restricted) Additive Schwarz preconditioners
  • MATLAB/Octave plug-in

To avoid OpenMP overhead for small sized problems, the library will compute in serial if the size of the matrix/vector is below a pre-defined threshold. Internally, the OpenCL backend has been modified for simplified cross platform compilation.

VexCL 1.0.0 released with CUDA support

November 20th, 2013

VexCL is a modern C++ library created for ease of GPGPU development with C++. VexCL strives to reduce the amount of boilerplate code needed to develop GPGPU applications. The library provides a convenient and intuitive notation for vector arithmetic, reduction, sparse matrix-vector multiplication, etc. The source code is available under the permissive MIT license. As of v1.0.0, VexCL provides two backends: OpenCL and CUDA. Users may choose either of those at compile time with a preprocessor macro definition. More information is available at the GitHub project page and release notes page.

Performance benchmarks on CPU/GPU/Xeon Phi

October 19th, 2013

PARALUTION is a library for sparse iterative methods which can be performed on various parallel devices, including multi-core CPU and GPU. In the new 0.4.0 version, the library provides also a backend for Xeon Phi (MIC). With this new version, various performance benchmarks based on vector-vector routines, sparse matrix-vector multiplication and CG method on different backends have been released: OpenMP/CUDA/OpenCL- NVIDIA GPU, AMD GPU, CPU and Xeon Phi. More information:

A unified sparse matrix data format for modern processors with wide SIMD units

September 4th, 2013


Sparse matrix-vector multiplication (spMVM) is the most time-consuming kernel in many numerical algorithms and has been studied extensively on all modern processor and accelerator architectures. However, the optimal sparse matrix data storage format is highly hardware-specific, which could become an obstacle when using heterogeneous systems. Also, it is as yet unclear how the wide single instruction multiple data (SIMD) units in current multi- and many-core processors should be used most efficiently if there is no structure in the sparsity pattern of the matrix. We suggest SELL-C-sigma, a variant of Sliced ELLPACK, as a SIMD-friendly data format which combines long-standing ideas from General Purpose Graphics Processing Units (GPGPUs) and vector computer programming. We discuss the advantages of SELL-C-sigma compared to established formats like Compressed Row Storage (CRS) and ELLPACK, and show its suitability on a variety of hardware platforms (Intel Sandy Bridge, Intel Xeon Phi and Nvidia Tesla K20) for a wide range of test matrices from different application areas. Using appropriate performance models we develop deep insight into the data transfer properties of the SELL-C-sigma spMVM kernel. SELL-C-sigma comes with two tuning parameters whose performance impact across the range of test matrices is studied and for which reasonable choices are proposed. This leads to a hardware-independent (“catch-all”) sparse matrix format, which achieves very high efficiency for all test matrices across all hardware platforms.

(M. Kreutzer, G. Hager, G. Wellein, H. Fehske, and A. R. Bishop: “A unified sparse matrix data format for modern processors with wide SIMD units.” Submitted, July 2013 [preprint])

Communication-Avoiding Krylov Techniques on Graphic Processing Units

May 11th, 2013


Communicating data within the graphic processing unit (GPU) memory system and between the CPU and GPU are major bottlenecks in accelerating Krylov solvers on GPUs. Communication-avoiding techniques reduce the communication cost of Krylov subspace methods by computing several vectors of a Krylov subspace “at once,” using a kernel called “matrix powers.” The matrix powers kernel is implemented on a recent generation of NVIDIA GPUs and speedups of up to 5.7 times are reported for the communication-avoiding matrix powers kernel compared to the standards prase matrix vector multiplication (SpMV) implementation.

(M. Mehri Dehnavi, Y. El-Kurdi, J. Demmel and D. Giannacopoulos: “Communication-Avoiding Krylov Techniques on Graphic Processing Units”, IEEE Transactions on Magnetics 49(5):1749-1752, May 2013. [DOI])

PARALUTION – A fast, user-friendly library for sparse iterative methods on CPUs and GPUs

February 25th, 2013

PARALUTION is a library for sparse iterative methods with special focus on multi-core and accelerator technology such as GPUs. In particular, it incorporates fine-grained parallel preconditioners designed to expolit modern multi-/many-core devices. Based on C++, it provides a generic and flexible design and interface which allow seamless integration with other scientific software packages. The library is open source and released under GPL. Key features are:

  • OpenMP, CUDA and OpenCL support
  • No special hardware/library requirement
  • Portable code and results across all hardware
  • Many sparse matrix formats
  • Various iterative solvers/preconditioners
  • Generic and robust design
  • Plug-in for the finite element package Deal.II
  • Documentation: user manual (pdf), reports, doxygen

More information, including documentation and case studies, is available at

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])

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