A GPU-based hyperbolic SVD algorithm

A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue problem. Numerical testing demonstrates the gains in speed and accuracy over sequential and MPI-parallelized variants of similar Jacobi-type HSVD algorithms. Finally, possibilities of hybrid CPU--GPU parallelism are discussed.Comment: Accepted for publication in BIT Numerical Mathematic

A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

Highly-parallelized simulation of a pixelated LArTPC on a GPU

The rapid development of general-purpose computing on graphics processing units (GPGPU) is allowing the implementation of highly-parallelized Monte Carlo simulation chains for particle physics experiments. This technique is particularly suitable for the simulation of a pixelated charge readout for time projection chambers, given the large number of channels that this technology employs. Here we present the first implementation of a full microphysical simulator of a liquid argon time projection chamber (LArTPC) equipped with light readout and pixelated charge readout, developed for the DUNE Near Detector. The software is implemented with an end-to-end set of GPU-optimized algorithms. The algorithms have been written in Python and translated into CUDA kernels using Numba, a just-in-time compiler for a subset of Python and NumPy instructions. The GPU implementation achieves a speed up of four orders of magnitude compared with the equivalent CPU version. The simulation of the current induced on 10^3 pixels takes around 1 ms on the GPU, compared with approximately 10 s on the CPU. The results of the simulation are compared against data from a pixel-readout LArTPC prototype

A Checkpoint-on-Failure Protocol for Algorithm-Based Recovery in Standard MPI

Abstract. Most predictions of Exascale machines picture billion way parallelism, encompassing not only millions of cores, but also tens of thousands of nodes. Even considering extremely optimistic advances in hardware reliability, probabilistic amplification entails that failures will be unavoidable. Consequently, software fault tolerance is paramount to maintain future scientific productivity. Two major problems hinder ubiquitous adoption of fault tolerance techniques: 1) traditional checkpoint based approaches incur a steep overhead on failure free operations and 2) the dominant programming paradigm for parallel applications (the MPI standard) offers extremely limited support of software-level fault tolerance approaches. In this paper, we present an approach that relies exclusively on the features of a high quality implementation, as defined by the current MPI standard, to enable algorithmic based recovery, without incurring the overhead of customary periodic checkpointing. The validity and performance of this approach are evaluated on large scale systems, using the QR factorization as an example.