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

椭圆边值问题出现在许多学科中。在边界复杂、不规则的情况下，将这些问题转化为积分方程，用边界积分方程方法求解。这种技术需要线性系统的解。在许多实际问题中，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，矢量超级计算机已经扩大了可以用数值方法解决的问题范围，但仍有相当数量的问题超出了目前的能力。并行超级计算机和强大的迭代方法相结合，有望扩大可解问题的范围。这个SGER项目解决了这个组合的两个方面。最近在串行机和向量机上实现的O(N)算法将在并行架构上实现，并且将扩展现有的迭代方法库，以惟一地增强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.