Alinea: An Advanced Linear Algebra Library for Massively Parallel Computations on Graphics Processing Units

Abstract

Direct and iterative methods are often used to solve linear systems in engineering. The matrices involved can be large, which leads to heavy computations on the central processing unit. A graphics processing unit can be used to accelerate these computations. In this paper, we propose a new library, named Alinea, for advanced linear algebra. This library is implemented in C++, CUDA and OpenCL. It includes several linear algebra operations and numerous algorithms for solving linear systems. For both central processing unit and graphic processing unit devices, there are different matrix storage formats, and real and complex arithmetics in single- and double-precision. The CUDA version includes a self-tuning of the grid, i.e. threading distribution, depending upon the hardware configuration and the size of the problems. Numerical experiments and comparison with existing libraries illustrates the efficiency, accuracy and robustness of the proposed library.

Synchronous and asynchronous optimized Schwarz methods for one‐way subdivision of bounded domains

“…To solve the resulting linear system, the synchronous and asynchronous optimized Schwarz methods with zeroth-order optimized interface conditions were implemented in the recently developed C++ library Alinea. 26 The parallel implementation of the asynchronous optimized Schwarz methods is quite similar to the synchronous implementation we have described in the work of Magoulès et al, 27 except that the asynchronous iterations and asynchronous communications are managed by a new additional layer. This new additional layer, JACK, 28 a recently developed C++ library, is defined on top of the MPI library; the version of the MPI library used in the experiments is MPICH2.…”

Green computing on graphics processing units

“…Figures (a) and (b), respectively, show graphical presentation of data of execution time in seconds and energy consumption in Joule, given in Table . Here, the kernel is performed by both Alinea and Cusp. The energy consumption in Joule is calculated by the multiplication of energy and time of the operation plus the fundamental energy consumption by the GPU.…”

On Extensions of Limited Memory Steepest Descent Method

“…We implement these algorithms by a linear algebra programming library [8]. QR factorization combining with (4) is used for computing the Ritz values.…”