Computation and Visualisation in the NumLab Numerical Laboratory

A large range of software environments addresses numerical simulation, interactive visualisation and computational steering. Most such environments are designed to cover a limited application domain, such as Finite Elements, Finite Differences, or image processing. Their software structure rarely provides a simple and extendible mathematical model for the underlying mathematics. Assembling numerical simulations from computational and visualisation blocks, as well as building such blocks is a difficult task. The NumLab environment, a numerical laboratory for computational and visualisation applications, offers a basic, yet generic and efficient framework for a large class of computational applications, such as partial and ordinary differential equations, non-linear systems, matrix computations and image and signal processing. Building applications which combine interactive visualisation and computations is provided in an interactive visual manner. This paper focuses on the effcient implementation of one of the most complex NumLab components, the Finite Element assembler for systems of equations, such as Stokes or Navier-Stokes fluid-flow equations. It shows how the software framework as a whole has been targeted towards fast assemblers, and how a general purpose fast Finite Element assembler is embedded