Mathematical Sciences: Complementary Pivoting and Boundary Integral Methods

本研究关注的是 高效、通用且精确的算法， 微分方程的边界积分方法 三维空间 这些计划将基于最近 开发了有效逼近边界的技术 三维物体的线性近似 从互补的旋转方法。 新技术是 理想地适合于在数值近似中使用， 曲面上的积分和边界上固有的流形 积分法 内部和外部的问题， 拉普拉斯，热，波和双调和方程将被处理。 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.