ALGORITHMS: Efficient Algorithms for Metacomputing of Partial Differential Equations (PDEs)

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Meta-computing was implemented by many projects among which GLOBUS is the most widely known. Experiments with large configurations and real applications have shown that the latency of wide area networks is prohibitively high and that substantial bandwidth can hardly be achieved. Our recent research on efficient algorithms for the meta-computing of Partial Differential Equations (PDEs) has shown that it is feasible to design efficient algorithm for meta-computing of unsteady combustion problems or elliptic solvers on three dimensional Cartesian grids. The development of such algorithms is (very)difficult. For Poisson or Helmholtz operators, the speed of propagation of information in the spatial domain is infinite. However, (1) information that propagates at infinite speed can be damped in space relatively quickly according to Green function properties and (2) more than 90 per cent of the information carried in a practical computation is noise. We are designing a family of domain decomposition methods that can rigorously take advantage of both factors.