The project ``Advanced Algorithms for Scientific Computing'' is devoted to the search for algorithms for numerical libraries. The goal of the work is to obtain parallel algorithms which are also numerically reliable. In linear algebra, the methods studied cater to sparse matrices. Of special concern are the projection methods which approximate the solution in subspaces of reduced dimension. New parallel schemes are designed for integrating ordinary differential equations. Their study includes a full characterization of their stability as well as their behaviour on algebraic differential equations. Most of our procedures are tested within large numerical simulations as for example Computational Fluid Dynamics or Electronic Device Simulation. The project is also concerned with programming environments for scientific computing. In this direction, new tools have been designed which should help the user assess the numerical reliability of a code (eg. Aquarels toolbox).
Scientific Context