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

很多项目都实现了元计算，其中最广为人知的是Globus。大型配置和实际应用的实验表明，广域网的延迟高得令人望而却步，而且很难获得实质性的带宽。我们最近对偏微分方程(PDE)元计算的高效算法的研究表明，在三维笛卡尔网格上设计用于非定常燃烧问题的元计算或椭圆型求解器的高效算法是可行的。这种算法的开发是(非常)困难的。对于泊松或亥姆霍兹算符，信息在空间域中的传播速度是无限的。然而，(1)根据格林函数的性质，以无限速度传播的信息在空间中可以相对较快地被衰减；(2)在实际计算中携带的90%以上的信息是噪声。我们正在设计一系列可以严格利用这两个因素的区域分解方法。

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.