Implementation of an O(N) BIEM for the Solution of Laplace'sEquation on a Parallel Machine

椭圆型边值问题存在于许多学科中。在边界复杂和不规则的情况下，这些问题被转化为积分方程组，并用边界积分方程法求解。这项技术需要线性系统的解。在许多实际感兴趣的问题中，这些系统足够大，以至于解决它们所需的计算工作量是令人望而却步的。近年来，向量超级计算机扩大了可以用数值方法解决的问题的范围，但仍然有大量的问题超出了当前的能力范围。并行超级计算机和强大的迭代方法的结合有望扩大可解问题的领域。该SGER项目解决了这一组合的两个方面。最近在串行机和向量机上实现的O(N)算法将在并行结构上实现，并将扩展现有的迭代方法指令库，以唯一地增强O(N)算法的能力。

Elliptic boundary value problems occur in many disciplines. In cases where the boundaries are complex and irregular, these problems are recast as integral equations and solved by boundary integral equation methods. This technique requires the solution of a linear system. In many problems of practical interest these systems are large enough that the computational effort required for their solution is prohibitive. In recent years, vector supercomputers have expanded the range of problems which may be solved numerically but there remains a significant number of problems which lie beyond current capabilities. The combination of parallel supercomputers and powerful iterative methods holds the promise of expanding the territory of solvable problems. This SGER project addresses both aspects of this combination. An O(N) algorithm which was recently implemented on serial and vector machines will be implemented on a parallel architecture, and the existing repertoire of iterative methods will be expanded to uniquely augment the power of the O(N) algorithm.