Tiarajú Asmuz Diverio

An accurate and efficient selfverifying solver for systems with banded coefficient matrix

Publisher Summary This chapter discuss a self verifying solver for systems of linear equations Ax = b with banded matrices A and the future adaptation of the algorithms to cluster computers. An implementation of an algorithm to compute efficiently component-wise good enclosures for the solution of a sparse linear system on typical cluster computers are discussed. Implementation works with point, as well as interval data (data afflicted with tolerances). The algorithm is implemented using C-XSC library (a C++ class library for extended scientific computing). The chapter discusses software for validated numerics in high performance environments, using C-XSC in connection with the MPICH library. Actually, solver for linear system with banded matrices runs on two different clusters: ALICE 1 at the University of Wuppertal and LabTeC 2 at UFRGS. The preliminary tests with matrix-matrix multiplication show that the C-XSC library needs to be optimized in several ways to be efficient in a high performance environment (up to now the main goal of C-XSC was functionality and portability, not speed).

Processing Mesoscale Climatology in a Grid Environment

Enhancing the quality of weather and climate forecasts are central scientific research objectives worldwide. However, simulations of the atmosphere, usually demand high processing power and large storage resources. In this context, we present the GBRAMS project, that applies grid computing to speed up the generation of a regional model climatology for Brazil. A grid infrastructure was built to perform long-term integrations of a mesoscale numerical model (BRAMS), managing a queue of up to nine independent jobs submitted to three clusters spread over Brazil- Three distinct middlewares, Globus Toolkit, OurGrid and OAR/CIGRI, were compared in their ability to manage these jobs, and results on the usage of each node of the grid are provided. We analyze the impact of the resulted climatology in the accuracy of climate forecast, showing model bias removal which indicates correctness of the generated climatology. Our central contribution are how to use grid computing to speed-up climatology generation and the middleware impact on this enterprise.

Selfverifying Solvers for Linear Systems of Equations in C-XSC

In this paper we discuss the implementation of selfverifying solvers for systems of linear equations Ax = b with dense and banded matrices A and the future adaptation these solvers to high performance environments. The algorithms were implemented using C-XSC (a C++ class library for extended scientific computing). We discuss, too, the integration between C-XSC and MPI libraries on cluster computers. The main topics of our research are the development of software tools for Validated Numerics in High Performance Environments using C-XSC and MPI, the optimization of C-XSC and its use on cluster computers and the application these software tools to real life problems [5].

Automatic data-flow graph generation of MPI programs

The data-flow graph (DFG) of a parallel application is frequently used to take scheduling decisions, based on the information that it models (dependencies among the tasks and volume of exchanged data). In the case of MPI-based programs, the DFG may be built at run-time by overloading the data exchange primitives. This article presents a library that enables the generation of the DFG of a MPI program, and its use to analyze the network contention on a test-application: the Linpack benchmark. It is the first step towards automatic mapping of a MPI program on a distributed architecture.

Parallel computational model with dynamic load balancing in PC clusters

This work describes the use of dynamic load balancing in a PC cluster,applied to a multi–physics model that combines the parallel solution for three–dimensional(3D) PDEs of shallow water bodies flow and the parallel solution for the three–dimensional.PDEs of scalar transportation of substances.The dynamic load balancing is obtained via diffusion algorithms.Three approaches for dynamic load balancing were implemented and are described here.

Parallel Environment with High Accuracy for Resolution of Numerical Problems

In this paper we describe a high performance environment, like cluster computers, with high accuracy obtained by use of C-XSC library. The C-XSC library is a (free) C++ class library for scientific computing for the development of numerical algorithms delivering highly accurate and automatically verified results by use of the interval arithmetic. These calculus in high accuracy must be available for some basic arithmetic operations, mainly the operations that accomplish the summation and dot product. Because of these aspects, we wish to use the high performance through a cluster environment where we have several nodes executing tasks or calculus. The communication will be done by message passing using the MPI communication library. To obtain the high accuracy in this environment extensions or changes in the parallel programs had done to guarantee that the quality of final result done on cluster, where several nodes collaborate for the final result of the calculus, maintain the same result quality obtained in one sequential high accuracy environment. To validate the environment developed in this work we done basic tests about the dot product, the matrix multiplications, the implementation of interval solvers for banded and dense matrices and the implementation of some numeric methods to solve linear systems with the high accuracy characteristic (some of the methods implemented are used in real life applications like hydrodynamic, agriculture and power electric systems). With these tests we done analysis and comparisons about the performance and accuracy obtained with and without the use of C-XSC library in sequential and parallel programs. With the implementation of these routines and methods will be open a large research field about the study of real life applications that need during their resolution (or in part of their resolution) to calculate arithmetic operations with more accuracy than the accuracy obtained by the traditional computational tools. Our software run on labtec (UFRGS) and Colorado (UPF) clusters. Nowadays we are working in the implementation of parallel versions of programs to solve linear systems (without and with high accuracy) and the optimization of C-XSC library on cluster computers.

Dynamic load balancing in PC clusters: an application to a multiphysics model

We describe the use of dynamic load balancing in a PC cluster, applied to a multiphysics model that combines the parallel solution for three-dimensional (3D) PDEs of shallow water bodies flow and the parallel solution for the three-dimensional PDEs of scalar transportation of substances. The dynamic load balancing is obtained via diffusion algorithms. The numerical mesh is partitioned using RCB algorithm, in order to minimize communication and balance the load. Parallelism is obtained through Schwarzs additive domain decomposition method (DDM), so that the subproblems are solved concurrently. SPMD is the programming model used and the message passing between processes in the PC cluster is done with MPICH library.

Hyper-Automation System Applied to Geometry Demonstration Environment

This paper describes the conception and implementation of a learning system on Euclidean Geometry demonstrations and its knowledge base. We use the formalism of finite automata with output to represent and ordain the statements that constitute a geometric demonstration in the knowledge base. The system is built on the MOSCA learning protocol, based on learning with the assistance of examples and interaction among five agents (Mestre, Oraculo, Sonda, Cliente and Aprendiz) involved in the learning process. We briefly revise the Hyper-Automaton concept as a structural model for hypertext and its use as the basis for the central core of the agents in a learning system is analyzed.

Performance analysis of DECK collective communication service

Collective communication is very useful for parallel applications, especially those in which matrix and vector data structures need to be manipulated by a group of processes. We present a performance analysis of collective communication primitives designed for the DECK parallel programming environment, with the aid of different numerical methods used to solve hydrodynamics and mass transportation models.

Performance Evaluation Technique STU and libavi Library

In this paper we describe an analysis technique used for performance evaluation of mathematic libraries that manipulate arithmetic intervals. This work is the conclusion of the initial technique presented in SCAN’97 [14]. This Technique called Standard Time Unit (STU) has also been created to solve problems involved in the performance evaluation of libraries that could run in an heterogeneous environment.