Multiscale Scienti c Computation : Six Year Research

The Gauss Center research on multiscale computational methods is reported, emphasizing main ideas and interrelations between various elds, and listing the relevant bibliography. The reported areas include: top-eeciency multigrid methods in uid dynamics; atmospheric ows and data assimilation; feedback optimal control; PDE solvers on unbounded domains; wave/ray methods for highly indeenite equations; rigorous quantitative analysis of multigrid; many-eigenfunction problems and ab-initio quantum chemistry; fast evaluation of integral transforms on adaptive grids; multigrid Dirac solvers; fast inverse-matrix and determinant updates; multiscale Monte-Carlo methods in statistical physics; molecular mechanics (including fast force summation, fast macromolecular energy minimization, Monte-Carlo methods at equilibrium, both for macromolecules and for large ensembles of small molecules, and the combination of small-scale equilibrium with large-scale dynamics); image processing (edge detection and seg-mentation); and tomography (medical imaging and radar reconstruction).