Quantum Monte Carlo for large chemical systems: Implementing efficient strategies for petascale platforms and beyond

Various strategies to implement efficiently QMC simulations for large chemical systems are presented. These include: i.) the introduction of an efficient algorithm to calculate the computationally expensive Slater matrices. This novel scheme is based on the use of the highly localized character of atomic Gaussian basis functions (not the molecular orbitals as usually done), ii.) the possibility of keeping the memory footprint minimal, iii.) the important enhancement of single-core performance when efficient optimization tools are employed, and iv.) the definition of a universal, dynamic, fault-tolerant, and load-balanced computational framework adapted to all kinds of computational platforms (massively parallel machines, clusters, or distributed grids). These strategies have been implemented in the QMC=Chem code developed at Toulouse and illustrated with numerical applications on small peptides of increasing sizes (158, 434, 1056 and 1731 electrons). Using 10k-80k computing cores of the Curie machine (GENCI-TGCC-CEA, France) QMC=Chem has been shown to be capable of running at the petascale level, thus demonstrating that for this machine a large part of the peak performance can be achieved. Implementation of large-scale QMC simulations for future exascale platforms with a comparable level of efficiency is expected to be feasible

GPU-Accelerated Algorithms for Compressed Signals Recovery with Application to Astronomical Imagery Deblurring

Compressive sensing promises to enable bandwidth-efficient on-board compression of astronomical data by lifting the encoding complexity from the source to the receiver. The signal is recovered off-line, exploiting GPUs parallel computation capabilities to speedup the reconstruction process. However, inherent GPU hardware constraints limit the size of the recoverable signal and the speedup practically achievable. In this work, we design parallel algorithms that exploit the properties of circulant matrices for efficient GPU-accelerated sparse signals recovery. Our approach reduces the memory requirements, allowing us to recover very large signals with limited memory. In addition, it achieves a tenfold signal recovery speedup thanks to ad-hoc parallelization of matrix-vector multiplications and matrix inversions. Finally, we practically demonstrate our algorithms in a typical application of circulant matrices: deblurring a sparse astronomical image in the compressed domain

On the parallelization of stellar evolution codes

Multidimensional nucleosynthesis studies with hundreds of nuclei linked through thousands of nuclear processes are still computationally prohibitive. To date, most nucleosynthesis studies rely either on hydrostatic/hydrodynamic simulations in spherical symmetry, or on post-processing simulations using temperature and density versus time profiles directly linked to huge nuclear reaction networks. Parallel computing has been regarded as the main permitting factor of computationally intensive simulations. This paper explores the different pros and cons in the parallelization of stellar codes, providing recommendations on when and how parallelization may help in improving the performance of a code for astrophysical applications. We report on different parallelization strategies succesfully applied to the spherically symmetric, Lagrangian, implicit hydrodynamic code SHIVA, extensively used in the modeling of classical novae and type I X-ray bursts. When only matrix build-up and inversion processes in the nucleosynthesis subroutines are parallelized (a suitable approach for post-processing calculations), the huge amount of time spent on communications between cores, together with the small problem size (limited by the number of isotopes of the nuclear network), result in a much worse performance of the parallel application than the 1-core, sequential version of the code. Parallelization of the matrix build-up and inversion processes in the nucleosynthesis subroutines is not recommended unless the number of isotopes adopted largely exceeds 10,000. In sharp contrast, speed-up factors of 26 and 35 have been obtained with a parallelized version of SHIVA, in a 200-shell simulation of a type I X-ray burstcarried out with two nuclear reaction networks: a reduced one, consisting of 324 isotopes and 1392 reactions, and a more extended network with 60 6 nuclides and 3551 nuclear interactions. Maximum speed-ups of ~41 (324-isotope network) and ~85 (606-isotope network), are also predicted for 200 cores, stressing that the number of shells of the computational domain constitutes an effective upper limit for the maximum number of cores that could be used in a parallel application.Peer ReviewedPostprint (published version

Rectangular Full Packed Format for Cholesky's Algorithm: Factorization, Solution and Inversion

We describe a new data format for storing triangular, symmetric, and Hermitian matrices called RFPF (Rectangular Full Packed Format). The standard two dimensional arrays of Fortran and C (also known as full format) that are used to represent triangular and symmetric matrices waste nearly half of the storage space but provide high performance via the use of Level 3 BLAS. Standard packed format arrays fully utilize storage (array space) but provide low performance as there is no Level 3 packed BLAS. We combine the good features of packed and full storage using RFPF to obtain high performance via using Level 3 BLAS as RFPF is a standard full format representation. Also, RFPF requires exactly the same minimal storage as packed format. Each LAPACK full and/or packed triangular, symmetric, and Hermitian routine becomes a single new RFPF routine based on eight possible data layouts of RFPF. This new RFPF routine usually consists of two calls to the corresponding LAPACK full format routine and two calls to Level 3 BLAS routines. This means {\it no} new software is required. As examples, we present LAPACK routines for Cholesky factorization, Cholesky solution and Cholesky inverse computation in RFPF to illustrate this new work and to describe its performance on several commonly used computer platforms. Performance of LAPACK full routines using RFPF versus LAPACK full routines using standard format for both serial and SMP parallel processing is about the same while using half the storage. Performance gains are roughly one to a factor of 43 for serial and one to a factor of 97 for SMP parallel times faster using vendor LAPACK full routines with RFPF than with using vendor and/or reference packed routines