The multiplication of a sparse matrix by a dense vector (SpMV) is a centerpiece of scientific computing applications: it is the essential kernel for the solution of sparse linear systems and sparse eigenvalue problems by iterative methods. The efficient implementation of the sparse matrixvector multiplication is therefore crucial and has been the subject of an immense amount of research, with interest renewed with every major new trend in high performance computing architectures. The introduction of General Purpose Graphics Processing Units (GPGPUs) is no exception, and many articles have been devoted to this problem.With this paper we provide a review of the techniques for implementing the SpMV kernel on GPGPUs that have appeared in the literature of the last few years. We discuss the issues and tradeoffs that have been encountered by the various researchers, and a list of solutions, organized in categories according to common features. We also provide a performance comparison across different GPGPU models and on a set of test matrices coming from various application domains.

In this article, a laser partially textured thrust bearing is theoretically and experimentally analyzed. An adiabatic model is developed in order to theoretically investigate the performances of the bearing. The bearing sample is partially textured both in radial and circumferential direction using the laser texturing process. The performance of the bearing (fluid film thickness and friction torque) is evaluated on a specially adapted test rig and the experimental results are compared with the theoretical model. A good agreement is found between the theoretical model and the experimental data. Also a comparison between a laser textured bearing and a bearing textured using the photolithographic method is presented.

We present a method for automatically selecting optimal implementations of sparse matrix-vector operations. Our software “AcCELS” (Accelerated Compress-storage Elements for Linear Solvers) involves a setup phase that probes machine characteristics, and a run-time phase where stored characteristics are combined with a measure of the actual sparse matrix to find the optimal kernel implementation. We present a performance model that is shown to be accurate over a large range of matrices.

Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are a popular ingredient of such linear solvers; this is the motivation for the present work where we examine some recent developments in a package of AMG preconditioners to improve efficiency, scalability and robustness on extreme scale problems. The main novelty is the design and implementation of a parallel coarsening algorithm based on aggregation of unknowns employing weighted graph matching techniques; this is a completely automated procedure, requiring no information from the user, and applicable to general symmetric positive definite (s.p.d.) matrices. The new coarsening algorithm improves in terms of numerical scalability at low operator complexity over decoupled aggregation algorithms available in previous releases of the package. The preconditioners package is built on the parallel software framework PSBLAS, which has also been updated to progress towards exascale. We present weak scalability results on one of the most powerful supercomputer in Europe for linear systems with sizes up to O(10 10 ) unknowns.

The efficiency of a sparse linear algebra operation heavily relies on the ability of the sparse matrix storage format to exploit the computing power of the underlying hardware. Since no format is universally better than the others across all possible kinds of operations and computers, sparse linear algebra software packages should provide facilities to easily implement and integrate new storage formats within a sparse linear algebra application without the need to modify it; it should also allow to dynamically change a storage format at run-time depending on the specific operations to be performed. Aiming at these important features, we present an Object Oriented design model for a sparse linear algebra package which relies on Design Patterns. We show that an implementation of our model can be efficiently achieved through some of the unique features of the Fortran 2003 language. Experimental results show that the proposed software infrastructure improves the modularity and ease of use of the code at no performance loss.