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Section: New Results

Application domain: data analysis in astrophysics

One of the application domain on which our algorithms are validated is data analysis in astrophysics. Estimation of the sky signal from sequences of time order data is one of the key steps in the Cosmic Microwave Background (CMB) data analysis, commonly referred to as the map-making problem. Some of the most popular and general methods proposed for this problem involve solving generalised least squares (GLS) equations with non-diagonal noise weights given by a block-diagonal matrix with Toeplitz blocks. In [14] we study new map-making solvers potentially suitable for applications to the largest, anticipated data sets. They are based on iterative conjugate gradient (CG) approaches enhanced with novel, parallel, two-level preconditioners (2lvl-PCG). We apply the proposed solvers to examples of simulated, non-polarised and polarised CMB observations and a set of idealised scanning strategies with a sky coverage ranging from nearly a full sky down to small sky patches. We discuss in detail their implementation for massively parallel computational platforms and their performance for a broad range of parameters characterising the simulated data sets. We find that our best new solver can outperform carefully optimised, standard solvers as used today, by as much as a factor of 5 in terms of the convergence rate and a factor of 4 in terms of the time to solution, and does so without increasing significantly the memory consumption or the volume of inter-processor communication. The performance of the new algorithms is also found to be more stable, robust and less dependent on specific characteristics of the analysed data set.We therefore conclude that the proposed approaches are well suited to address successfully challenges posed by new and forthcoming CMB data sets.

Spherical Harmonic Transforms (SHT) are at the heart of many scientific and practical applications ranging from climate modelling to cosmological observations. In many of these areas new, cutting-edge science goals have been recently proposed requiring simulations and analyses of experimental or observational data at very high resolutions and of unprecedented volumes. Both these aspects pose formidable challenge for the currently existing implementations of the transforms.

In [13] we describe parallel algorithms for computing SHT with two variants of intra-node parallelism appropriate for novel supercomputer architectures, multi-core processors and Graphic Processing Units (GPU). It also discusses their performance, alone and embedded within a top-level, MPI-based parallelisation layer ported from the S${}^2$HAT library, in terms of their accuracy, overall efficiency and scalability. We show that our inverse SHT run on GeForce 400 Series GPUs equipped with latest CUDA architecture ("Fermi") outperforms the state of the art implementation for a multi-core processor executed on a current Intel Core i7-2600K. Furthermore, we show that an MPI/CUDA version of the inverse transform run on a cluster of 128 Nvidia Tesla S1070 is as much as 3 times faster than the hybrid MPI/OpenMP version executed on the same number of quad-core processors Intel Nehalem for problem sizes motivated by our target applications. Performance of the direct transforms is however found to be at the best comparable in these cases. We discuss in detail the algorithmic solutions devised for the major steps involved in the transforms calculation, emphasising those with a major impact on their overall performance, and elucidates the sources of the dichotomy between the direct and the inverse operations.