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1.1 Introduction

The MODULEF library contains numerous solution modules for linear systems  which respond to different needs encountered in the solution of partial differential equations by the finite element method. They correspond to, either direct methods  , that give the solution of a linear system in a finite number of operations which can be calculated in advance, or iterative methods , for which the computational cost is proportional to the number of iterations, a priori unknown, and depends on several parameters whose influence is often difficult to measure: conditioning of the system, precision of convergence test, ...

These two families of methods also offer several possibilities for storing the matrix of the linear system to be solved, in order to best use the memory space available in the computer. In particular, we need to note that if machines offers bigger and bigger memory capacity, the users' needs tend to saturate them rapidly. The course pursued, computational time/memory space, is therefore far from being completed, and algorithms using secondary memory are still current.

This guide is essentially dedicated to the description of solution programs for linear systems in the MODULEF library, and includes operating instructions for these modules. However, the reader who is interested in a theoretical presentation of the algorithms, or modifications to be done in order to use these models on vectorial and/or parallel computers, should consult [1].