Integrated Modeling ⋅ Using the Parallel Processing in Solution of Large Scale Linear Equations Systems for the Project WAVES 67 Using the Parallel Processing in Solution of Large Scale Linear Equations Systems for the Project WAVES PEQUENO, MAURO C.; CARVALHO, KÍSSIA; OLIVEIRA, JEAN G. SOUZA; DONATO, ALINSON A.; SOUSA, AULER G.; NETO, CECÍLIO F. O.; RIBEIRO, RODRIGO FALCÃO and SANTOS, VITOR A. Departamento de Computação, Universidade Federal do Ceará, Campus do Pici, Caixa Postal 12.166, CEP 60.455-760 - Fortaleza,CE, Brazil e-mails: mauro@lia.ufc.br , karvalho@lia.ufc.br , jean@ufac.br , alinson@lia.ufc.br , auler@lia.ufc.br , cecilio@lia.ufc.br , drigo@lia.ufc.br , vitor@lia.ufc.br INTRODUCTION The Project WAVES aims at analyzing the interactions among readiness of water, natural resources and human activities with the purpose of predicting the impact of the variable readiness of water in natural and social systems. The end result of these studies can take to the development of models integrated regional that allow to understand the dynamics of the ecosystem and serve as a tool to evaluate and to propose strategies of maintainable rural development. The group of Integrated Modelling, coordinated by Prof. Dr. Mauro Pequeno, in 1999, developed four sub-projects, that obtained a good acting and it have been contributing to the improvement of human resources. • Subgroup I: Resolution of Large Scale Linear Equations Systems Using Parallel Processing; • Subgroup II: Modelling of the Practical Reasoning under Incomplete and Imprecise Knowledge in Situations of Climatical Changes; • Subgroup III: Digital Modelling of Lands Applied to the Problem of Lease; • Subgroup IV: Analysis of the Migration Using Symbolic Computation; RESOLUTION OF LARGE SCALE LINEAR EQUATIONS SYSTEMS USING PARALLEL PROCESSING This sub-project is very important for the project WAVES, once the problems approached involves meteorological and climatical studies, whose models can be described by Large Scale Linear Equations Systems (system whose number of equations and/or incognitoes can be up to thousands). The resolution of Linear Systems is one of the central problems of the computational mathematics and computer science, being the scientific processing the greatest responsible for the construction of computers of high performance. It’s hoped that if several processes are operating simultaneously, the time of processing is inversely proportional to the number of processes. Although it doesn't happen, due to other factors as the passage of parameters among the machines, the time of processing, in most of the cases, is reduced significantly, in way to compensate the utilization of parallel processing. Given a linear system with n equations and n variables, Ax = b, were A is the coefficient’s matrix (a ij ), x = ( x 1 ,..., x n ) and b=(b 1 ,..., b n ) are respectively the vectors of incognito and independent terms of the system. The matrix A, is no singular whose inverse it is denoted by A -1 . We wish to find h, that satisfies the system Ax = b, in the smallest time and obtaining the best possible accuracy. In fact, there is not a better method to solve systems of linear equations because each method depends on particularities presented by the linear system. In [Hest. 59], Hestenes and Stiefel supply properties to verify whether a numeric method it is a " good " method to solve linear systems: a) The method should be simple, composed of repetitions of routines elementary and requesting the minimum of storage space;