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

元计算被许多项目实现，其中GLOBUS是最广为人知的。具有大配置和真实的应用的实验已经表明，广域网的延迟高得令人望而却步，并且很难获得足够的带宽。我们最近对偏微分方程（PDE）元计算的有效算法的研究表明，在三维笛卡尔网格上设计非定常燃烧问题的元计算算法或椭圆型求解器是可行的。这种算法的开发是（非常）困难的。对于泊松或亥姆霍兹算子，信息在空间域中的传播速度是无限的。然而，（1）根据绿色函数的性质，以无限速度传播的信息可以在空间中相对较快地衰减;（2）实际计算中携带的信息中有90%以上是噪声。我们正在设计一系列的区域分解方法，可以严格利用这两个因素。

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.