Hierarchichal Representation and Computation of Approximate Solutions in Scientiic Simulations

In many applications involving large scale scientiic computing a massive amount of data is generated in a typical simulation. Such simulations generally require the numerical solution of systems of diierential equations where the results are often generated remotely using special high-performance software and computer systems and then examined and investigated interactively using visualization tools. The visualization packages are usually run on local workstations and make use of colour, lighting, texture, sound and animation to highlight and reveal interesting characteristics or features of the approximate solution. Thisìnteractive' viewing of the data is thèrendering' stage of the modeling process and it can be very selective and local in the sense that only a subset of the variables are rendered and then only in regions where something interesting is happening. The result is that, in many simulations, large amounts of data must be stored and shared in a distributed environment while only a very small fraction of this data will ever be viewed by anyone. In this paper we propose an approach, using a hierarchichal representation of the approximate solution, which will avoid the generation and storage of data that is not required.