Parallel Environment with High Accuracy for Resolution of Numerical Problems

Abstract

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.