Engineering topics

Dongarra, Jack J.

Publications and source records attributed to Dongarra, Jack J..

3 records

DOE OSTI2021

Advances in Mixed Precision Algorithms: 2021 Edition

Over the last year, the ECP xSDK-multiprecision effort has made tremendous progress in developing and deploying new mixed precision technology and customizing the algorithms for the hardware deployed in the ECP flagship supercomputers. The effort also has succeeded in creating a cross-laboratory community of scientists interested in mixed precision technology and now working together in deploying this technology for ECP applications. In this report, we highlight some of the most promising and impactful achievements of the last year. Among the highlights we present are: Mixed precision IR using a dense LU factorization and achieving a 1.8× speedup on Spock; results and strategies for mixed precision IR using a sparse LU factorization; a mixed precision eigenvalue solver; Mixed Precision GMRES-IR being deployed in Trilinos, and achieving a speedup of 1.4× over standard GMRES; compressed Basis (CB) GMRES being deployed in Ginkgo and achieving an average 1.4× speedup over standard GMRES; preparing hypre for mixed precision execution; mixed precision sparse approximate inverse preconditioners achieving an average speedup of 1.2×; and detailed description of the memory accessor separating the arithmetic precision from the memory precision, and enabling memory-bound low precision BLAS 1/2 operations to increase the accuracy by using high precision in the computations without degrading the performance. We emphasize that many of the highlights presented here have also been submitted to peer-reviewed journals or established conferences, and are under peer-review or have already been published.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Performance analysis and acceleration of explicit integration for large kinetic networks using batched GPU computations

Abstract—We demonstrate the systematic implementation of recently-developed fast explicit kinetic integration algorithms that solve efficiently N coupled ordinary differential equations (subject to initial conditions) on modern GPUs. We take representative test cases (Type Ia supernova explosions) and demonstrate two or more orders of magnitude increase in efficiency for solving such systems (of realistic thermonuclear networks coupled to fluid dynamics). This implies that important coupled, multiphysics problems in various scientific and technical disciplines that were intractable, or could be simulated only with highly schematic kinetic networks, are now computationally feasible. As examples of such applications we present the computational techniques developed for our ongoing deployment of these new methods on modern GPU accelerators. We show that similarly to many other scientific applications, ranging from national security to medical advances, the computation can be split into many independent computational tasks, each of relatively small-size. As the size of each individual task does not provide sufficient parallelism for the underlying hardware, especially for accelerators, these tasks must be computed concurrently as a single routine, that we call batched routine, in order to saturate the hardware with enough work.

Haidar Ahmad, Azzam↗

NASA NTRS1990

Automatic blocking of nested loops

Blocked algorithms have much better properties of data locality and therefore can be much more efficient than ordinary algorithms when a memory hierarchy is involved. On the other hand, they are very difficult to write and to tune for particular machines. The reorganization is considered of nested loops through the use of known program transformations in order to create blocked algorithms automatically. The program transformations used are strip mining, loop interchange, and a variant of loop skewing in which invertible linear transformations (with integer coordinates) of the loop indices are allowed. Some problems are solved concerning the optimal application of these transformations. It is shown, in a very general setting, how to choose a nearly optimal set of transformed indices. It is then shown, in one particular but rather frequently occurring situation, how to choose an optimal set of block sizes.

Schreiber, Robert↗