PYI: Computational Issues in the Solution of Partial Differential Equations

偏微分方程的数值解法是 最困难的计算任务，所以只有 可以使用最有效的算法。 的实际数字 算法中使用的公式是相当好理解的， 但是几何问题带来的计算问题 就没那么好了 其中一项研究旨在确定正确的处理方法 偏微分方程的网格。 求解技术 例如有限元方法需要细分 几何域分解为小的多边形元素。 本研究 将建立最好的方式来执行这一细分， 特别是当畴具有复杂形状时。 它将 确定正确的方法来划分域， 并行计算机的处理器。 边界元技术显示出很大的前景处理 复杂的几何形状 他们最近受到关注 因为它们与小波的新发现联系 转变 这项研究寻求新的算法， 加快边界元计算。

Numerical solution of partial differential equations is one of the most computationally difficult tasks in existence, so only the most efficient algorithms can be used. The actual numerical formulas used in the algorithms are fairly well understood by now, but the computational issues arising from geometrical issues are less so. One line of research is intended to determine the proper handling of grids for partial differential equations. Solution techniques such as finite element methods require the subdivision of the geometric domain into small polygonal elements. This research will establish the best ways to carry out this subdivision, especially when the domain has a complicated shape. It will determine the proper method to partition the domain among processors of a parallel computer. Boundary element techniques show great promise for handling complicated geometries. They are receiving recent attention because of their newly-discovered links to wavelet transformations. The research seeks new algorithms that will speed up boundary element calculations.