Computational modes and grid imprinting on five quasi-uniform spherical C-grids

Currently, most operational forecasting models use latitude-longitude grids, whose convergence of meridians towards the poles limits parallel scaling. Quasi-uniform grids might avoid this limitation. Thuburn et al, JCP, 2009 and Ringler et al, JCP, 2010 have developed a method for arbitrarily-structured, orthogonal C-grids (TRiSK), which has many of the desirable properties of the C-grid on latitude-longitude grids but which works on a variety of quasi-uniform grids. Here, five quasi-uniform, orthogonal grids of the sphere are investigated using TRiSK to solve the shallow-water equations. We demonstrate some of the advantages and disadvantages of the hexagonal and triangular icosahedra, a Voronoi-ised cubed sphere, a Voronoi-ised skipped latitude-longitude grid and a grid of kites in comparison to a full latitude-longitude grid. We will show that the hexagonal-icosahedron gives the most accurate results (for least computational cost). All of the grids suffer from spurious computational modes; this is especially true of the kite grid, despite it having exactly twice as many velocity degrees of freedom as height degrees of freedom. However, the computational modes are easiest to control on the hexagonal icosahedron since they consist of vorticity oscillations on the dual grid which can be controlled using a diffusive advection scheme for potential vorticity

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected with measurement errors on discretized grids. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo. Compared to the standard Bayesian inference that suffers serious computational burden and unstableness for analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results as the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids where the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes.Comment: Under revie

Parallel memetic algorithms for independent job scheduling in computational grids

In this chapter we present parallel implementations of Memetic Algorithms (MAs) for the problem of scheduling independent jobs in computational grids. The problem of scheduling in computational grids is known for its high demanding computational time. In this work we exploit the intrinsic parallel nature of MAs as well as the fact that computational grids offer large amount of resources, a part of which could be used to compute the efficient allocation of jobs to grid resources. The parallel models exploited in this work for MAs include both fine-grained and coarse-grained parallelization and their hybridization. The resulting schedulers have been tested through different grid scenarios generated by a grid simulator to match different possible configurations of computational grids in terms of size (number of jobs and resources) and computational characteristics of resources. All in all, the result of this work showed that Parallel MAs are very good alternatives in order to match different performance requirement on fast scheduling of jobs to grid resources.Peer ReviewedPostprint (author's final draft

Comparison between nested grids and unstructured grids for a high-resolution wave forecasting system in the western Mediterranean sea

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Operational Oceanography on 2017, available online at: http://www.tandfonline.com/10.1080/1755876X.2016.1260389Traditionally wave modelling uses a downscaling process by means of successive nested grids to obtain high-resolution wave fields near the coast. This supposes an uncertain error due to internal boundary conditions and a long computational time. Unstructured grids avoid multiple meshes and thus the problem of internal boundary conditions. In the present study high resolution wave simulations are analysed for a full year where high-resolution meteorological models were available in the Catalan coast. This coastal case presents sharp gradients in bathymetry and orography and therefore correspondingly sharp variations in the wind and wave fields. Simulations with SWAN v.4091A using a traditional nested sequence and a regional unstructured grid have been compared. Also a local unstructured grid nested in an operational forecast system is included in the analysis. The obtained simulations are compared to wave observations from buoys near the coast; almost no differences are found between the unstructured grids and the regular grids. Simultaneously, tests have been carried out in order to analyse the computational time required for each of the alternatives, showing a decrease to less than half the time when working with regional unstructured grids and maintaining the forecast accuracy and coastal resolution with respect to the downscaling system.Peer ReviewedPostprint (author's final draft

Adaptive structured parallelism for computational grids

Algorithmic skeletons abstract commonly-used patterns of parallel computation, communication, and interaction. They provide top-down design composition and control inheritance throughout the whole structure. Parallel programs are expressed by interweaving parameterised skeletons analogously to the way sequential structured programs are constructed. This design paradigm, known as structured parallelism, provides a high-level parallel programming method which allows the abstract description of programs and fosters portability. That is to say, structured parallelism requires the description of the algorithm rather than its implementation, providing a clear and consistent meaning across platforms while their associated structure depends on the particular implementation. By decoupling the structure from the meaning of a parallel program, it benefits entirely from any performance improvements in the systems infrastructure