MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision based on multiresolution analysis and separated representations. Underpinning the numerical capabilities is a powerful petascale parallel programming environment that aims to increase both programmer productivity and code scalability. This paper describes the features and capabilities of MADNESS and briefly discusses some current applications in chemistry and several areas of physics

Granite: A scientific database model and implementation

The principal goal of this research was to develop a formal comprehensive model for representing highly complex scientific data. An effective model should provide a conceptually uniform way to represent data and it should serve as a framework for the implementation of an efficient and easy-to-use software environment that implements the model. The dissertation work presented here describes such a model and its contributions to the field of scientific databases. In particular, the Granite model encompasses a wide variety of datatypes used across many disciplines of science and engineering today. It is unique in that it defines dataset geometry and topology as separate conceptual components of a scientific dataset. We provide a novel classification of geometries and topologies that has important practical implications for a scientific database implementation. The Granite model also offers integrated support for multiresolution and adaptive resolution data. Many of these ideas have been addressed by others, but no one has tried to bring them all together in a single comprehensive model. The datasource portion of the Granite model offers several further contributions. In addition to providing a convenient conceptual view of rectilinear data, it also supports multisource data. Data can be taken from various sources and combined into a unified view. The rod storage model is an abstraction for file storage that has proven an effective platform upon which to develop efficient access to storage. Our spatial prefetching technique is built upon the rod storage model, and demonstrates very significant improvement in access to scientific datasets, and also allows machines to access data that is far too large to fit in main memory. These improvements bring the extremely large datasets now being generated in many scientific fields into the realm of tractability for the ordinary researcher. We validated the feasibility and viability of the model by implementing a significant portion of it in the Granite system. Extensive performance evaluations of the implementation indicate that the features of the model can be provided in a user-friendly manner with an efficiency that is competitive with more ad hoc systems and more specialized application specific solutions

A proximal iteration for deconvolving Poisson noisy images using sparse representations

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key contributions are: First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a {\it non-linear} degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minimization of a convex functional with a data-fidelity term reflecting the noise properties, and a non-smooth sparsity-promoting penalties over the image representation coefficients (e.g. $\ell_1$-norm). Third, a fast iterative backward-forward splitting algorithm is proposed to solve the minimization problem. We derive existence and uniqueness conditions of the solution, and establish convergence of the iterative algorithm. Finally, a GCV-based model selection procedure is proposed to objectively select the regularization parameter. Experimental results are carried out to show the striking benefits gained from taking into account the Poisson statistics of the noise. These results also suggest that using sparse-domain regularization may be tractable in many deconvolution applications with Poisson noise such as astronomy and microscopy

A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems

Classical iterative methods for tomographic reconstruction include the class of Algebraic Reconstruction Techniques (ART). Convergence of these stationary linear iterative methods is however notably slow. In this paper we propose the use of Krylov solvers for tomographic linear inversion problems. These advanced iterative methods feature fast convergence at the expense of a higher computational cost per iteration, causing them to be generally uncompetitive without the inclusion of a suitable preconditioner. Combining elements from standard multigrid (MG) solvers and the theory of wavelets, a novel wavelet-based multi-level (WMG) preconditioner is introduced, which is shown to significantly speed-up Krylov convergence. The performance of the WMG-preconditioned Krylov method is analyzed through a spectral analysis, and the approach is compared to existing methods like the classical Simultaneous Iterative Reconstruction Technique (SIRT) and unpreconditioned Krylov methods on a 2D tomographic benchmark problem. Numerical experiments are promising, showing the method to be competitive with the classical Algebraic Reconstruction Techniques in terms of convergence speed and overall performance (CPU time) as well as precision of the reconstruction.Comment: Journal of Computational and Applied Mathematics (2014), 26 pages, 13 figures, 3 table

Survey of semi-regular multiresolution models for interactive terrain rendering

Rendering high quality digital terrains at interactive rates requires carefully crafted algorithms and data structures able to balance the competing requirements of realism and frame rates, while taking into account the memory and speed limitations of the underlying graphics platform. In this survey, we analyze multiresolution approaches that exploit a certain semi-regularity of the data. These approaches have produced some of the most efficient systems to date. After providing a short background and motivation for the methods, we focus on illustrating models based on tiled blocks and nested regular grids, quadtrees and triangle bin-trees triangulations, as well as cluster-based approaches. We then discuss LOD error metrics and system-level data management aspects of interactive terrain visualization, including dynamic scene management, out-of-core data organization and compression, as well as numerical accurac

LOCALIS: Locally-adaptive Line Simplification for GPU-based Geographic Vector Data Visualization

Visualization of large vector line data is a core task in geographic and cartographic systems. Vector maps are often displayed at different cartographic generalization levels, traditionally by using several discrete levels-of-detail (LODs). This limits the generalization levels to a fixed and predefined set of LODs, and generally does not support smooth LOD transitions. However, fast GPUs and novel line rendering techniques can be exploited to integrate dynamic vector map LOD management into GPU-based algorithms for locally-adaptive line simplification and real-time rendering. We propose a new technique that interactively visualizes large line vector datasets at variable LODs. It is based on the Douglas-Peucker line simplification principle, generating an exhaustive set of line segments whose specific subsets represent the lines at any variable LOD. At run time, an appropriate and view-dependent error metric supports screen-space adaptive LOD levels and the display of the correct subset of line segments accordingly. Our implementation shows that we can simplify and display large line datasets interactively. We can successfully apply line style patterns, dynamic LOD selection lenses, and anti-aliasing techniques to our line rendering