Luis F. Romero

Data distributions for sparse matrix vector multiplication

Sparse matrix vector multiplication (SpMxV) is often one of the core components of many scientific applications. Many authors have proposed methods for its data distribution in distributed memory multiprocessors. We can classify these into four groups: Scatter, D-Way Strip, Recursive and Miscellaneous. In this work we propose a new method (Multiple Recursive Decomposition (MRD)), which partitions the data using the prime factors of the dimensions of a multiprocessor network with mesh topology. Furthermore, we introduce a new storage scheme, storage-by-row-of-blocks, that significantly increases the efficiency of the Scatter method. We will name Block Row Scatter (BRS) method this new variant. The MRD and BRS methods achieve results that improve those obtained by other analyzed methods, being their implementation easier. In fact, the data distributions resulting from the MRD and BRS methods are a generalization of the Block and Cyclic distributions used in dense matrices.

Simultaneous computation of total viewshed on large high resolution grids

The knowledge of visibility information on a terrain is essential for a large number of current applications. There exist several algorithms in the literature for building visibility maps (VMs) but only for one single viewpoint or at most for a very small number of observers. This limitation is due to the high computational complexity of the used methods (which is greater than O , where N is the number of the terrain points) and also due to the fact that single-point algorithms cannot efficiently be scaled to all points. We present a novel fast algorithm able to compute the complete VM, also called total viewshed, where, given a terrain T represented by its regular digital elevation model (DEM), our method simultaneously produces a continuous VM for all the points of T. In particular, the proposed algorithm combines two algorithms, (i) a visible heights algorithm that divides the terrain into sectors and calculates the end of all the visible ring sectors and (ii) an algorithm that finds out the start of those visible ring sectors using a low-cost calculation. Theoretical and experimental comparisons were performed considering the VM of one single observer, because the most used GIS tools compute the viewshed by point. The results demonstrate that our algorithm is faster by many orders of magnitude than the widely used GIS visibility tools showing similar accuracy.

Parallel scheduling of the PCG method for banded matrices rising from FDM/FEM

An implicit time-linearized finite difference discretization of partial differential equations on regular/structured meshes results in an n-diagonal block system of algebraic equations, which is usually solved by means of the Preconditioned Conjugate Gradient (PCG) method. In this paper, an analysis of the parallel implementation of this method on several computer architectures and for several programming paradigms is presented. For three-dimensional regular/structured meshes, a new implementation of the PCG method with Jacobi preconditioner is proposed. For the computer architectures and number of processors employed in this study, it has been found that this implementation is more efficient than the standard one, and can be applied to narrow-band matrices and other preconditioners, such as, for example, polynomial ones.

Sparse Block and Cyclic Data Distributions for Matrix Computations

A significant part of scientific codes consist of sparse matrix computations. In this work we propose two new pseudoregular data distributions for sparse matrices. The Multiple Recursive Decomposition (MRD) partitions the data using the prime factors of the dimensions of a multiprocessor network with mesh topology. Furthermore, we introduce a new storage scheme, storage-by-row-of-blocks, that significantly increases the efficiency of the Scatter distribution. We will name Block Row Scatter (BRS) distribution this new variant. The MRD and BRS methods achieve results that improve those obtained by other analyzed methods, being their implementation easier. In fact, the data distributions resulting from the MRD and BRS methods are a generalization of the Block and Cyclic distributions used in dense matrices.

High-performance three-horizon composition algorithm for large-scale terrains

This work presents a high-performance algorithm to compute the horizon in very large high-resolution DEMs. We used Stewarts algorithm as the core of our implementation and considered that the horizon has three components: the ground, near, and far horizons. To eliminate the edge-effect, we introduced a multi-resolution halo method. Moreover, we used a new data partition approach, to substantially increase the parallelism in the algorithm. In addition, several optimizations have been applied to considerably reduce the number of arithmetical operations in the core of the algorithm. The experimental results have demonstrated that by applying the above-described contributions, the proposed algorithm is more than twice faster than Stewarts algorithm while maintaining the same accuracy.

Fast clear-sky solar irradiation computation for very large digital elevation models

This paper presents a fast algorithm to compute the global clear-sky irradiation, appropriate for extended high-resolution Digital Elevation Models (DEMs). The latest equations published in the European Solar Radiation Atlas (ESRA) have been used as a starting point for the proposed model and solved using a numerical method. A new calculation reordering has been performed to (1) substantially diminish the computational requirements, and (2) to reduce dependence on both, the DEM size and the simulated period, i.e., the period during which the irradiation is calculated. All relevant parameters related to shadowing, atmospheric, and climatological factors have been considered. The computational results demonstrate that the obtained implementation is faster by many orders of magnitude than all existing advanced irradiation models while maintaining accuracy. Although this paper focuses on the clear-sky irradiation, the developed software also computes the global irradiation applying a filter that considers the clear-sky index.

Fast Cloth Simulation with Parallel Computers

The computational requirements of cloth and other non-rigid solid simulations are high and often the running time is far from real time. In this paper, an efficient solution of the problem on parallel computer is presented. An application, which combines data parallelism with task parallelism has been developed, achieving a good load balancing and minimizing the communication cost. The execution time obtained for a typical problem size, its super-linear speed-up, and the iso-scalability shown by the model, will allow to reach real-time simulations in sceneries of growing complexity, using the most powerful multiprocessors.

Parallel techniques in irregular codes: cloth simulation as case of study

When parallelizing irregular applications on ccNUMA machines several issues should be taken into account in order to achieve high code performance. These factors include locality exploitation and parallelism, as well as careful use of memory resources (memory overhead). An important number of numerical simulation codes are clear examples of irregular applications. Frequently these kinds of codes include reduction operations in their core, so that an important fraction of the computational time is spent on such operations. Specifically, cloth simulation belongs to this class of applications, being a topic of increasing interest in diverse areas, like in the multimedia industry. Moreover, when real time simulation is the aim, its parallelization becomes an important option. This paper discusses and compares different irregular reduction parallelization techniques on ccNUMA share memory machines. Broadly speaking, we may classify them into two groups: privatization-based and data partitioning-based methods. In this paper we describe a framework, based on data affinity, that permits to develop various algorithms inside the group of the data partitioning-based techniques. All these techniques and approaches are analyzed and adapted to the computational structure of a real, physically based, cloth simulator.

Efficient Data Structure and Highly Scalable Algorithm for Total-Viewshed Computation

This paper presents an efficient and highly scalable algorithm, designed from scratch, to calculate total-viewshed in large high-resolution digital elevation models (DEMs) without restrictions as to whether or not the observer is linked to the ground. The keys to the high efficiency of the proposed method are: 1) the selection of a reliable sampling to represent the subareas of study; 2) the use of a compact and stable data structure to store the calculated data; and 3) the high reutilization of data and calculation between the large number of viewpoints. The obtained results demonstrate that the proposed algorithm is the fastest over the most commonly used GIS-software showing very similar numerical accuracy.

A Fast GIS-tool to Compute the Maximum Solar Energy on Very Large Terrains

This study presents a new functionality of Geographic Information Systems (GIS) to assess solar energy input on vast high resolution Digital Elevation Models (DEMs). This tool is able to find out 1) the maximum solar energy that can be captured on a surface situated at a determined hight on each point of the DEM and 2) the optimal angles (i.e., slope and orientation) that allow capturing this maximum energy. Insolator: the open source high performance solar radiation model, we developed in a previous work, is used as baseline for this tool. Contrarily to most existent GIS tools, the proposed algorithm doesn’t suffer memory limitations and is specially suitable for GPU-CPU heterogeneous systems. The experimental results show that the proposed algorithm is able to compute the maximum irradiation and optimal angles maps on large DEMs with high accuracy in very short times and showing a high scalability.