Mathematical Sciences: Complementary Pivoting and Boundary Integral Methods

这项研究致力于发展高效、通用和精确的算法来求解三维空间中的偏微分方程组。这些方案将基于最近开发的技术，使用由互补旋转方法产生的线性近似来有效地逼近三维体的边界。这些新技术非常适合于边界积分法所固有的曲面和流形上积分的数值逼近。本课程将讨论拉普拉斯方程、热方程、波动方程和双调和方程的内部和外部问题。时间相关和时间无关的问题将被研究。

This research is concerned with the development of efficient, versatile, and accurate algorithms to solve partial differential equations using the boundary integral method in three space dimensions. These schemes will be based on recently developed techniques for efficiently approximating the boundaries of three-dimensional bodies using linear approximants arising from complementary pivoting methods. The new techniques are ideally suited for use in the numerical approximation of integrals over surfaces and manifolds inherent in the boundary integral method. Both interior and exterior problems for the Laplace, heat, wave, and biharmonic equations will be treated. Time dependent and time independent problems will be studied.