The applications are pursued in co-operation with workers from other disciplines, from academia and industry. Computational fluid dynamics is a classical interdisciplinary application area which has great industrial potential, and collaboration with the department of Aeronautics strengthens our efforts in this area. High Reynold's number flows, such as encountered in aero- and hydrodynamics, exhibit extreme variation in scales and require both new algorithmic ideas and large computational effort. Recently also models for non-Newtonian flow have attracted attention. The problems with large spans of scales are computationally challenging, since brute force approaches are intractable.
Similar comments apply to the solution of continuous field problems by boundary integral methods.
Recently the wavelet bases have attracted attention and have been shown to yield very efficient algorithms for signal and picture processing. Applications to solutions of PDEs have yet to prove themselves against more established tecchniques, but there is well-founded hope that wavelet bases will contribute to the development of fast algorithms for multiscale problems. As an example, constant coefficient evolution operator equations can be solved approximately in logarithmic time by truncating the matrix representation of the time step operator. The Numerical algorithms devised for various classes of problems must be adapted to high performance computers. Many important PDE problems have a parallel structure and are therefore wellsuited to modern high performance distributed computers.