Distributed Numerical Integration Algorithms and Application

计算积分的值是微积分及其应用的基本问题之一;数值积分解决了这个问题的复杂函数，不能解析处理。该项目将显著扩展ParInt 1.0系统，用于执行在先前NSF支持下开发的数值积分。它将增加一些技术，使系统能够处理具有各种困难特性（例如奇点，高维等）的集成问题。这包括开发用于计算大量积分（例如有限元问题）的分层过程结构，奇异问题的外推技术以及用于解决高维问题（例如计算金融）的准蒙特卡罗技术。相应的软件包的图形界面将允许跨学科的研究容易使用。特别是，可视化工具，以帮助用户看到为什么一个问题是困难的（并建议替代配方）和一个服务器，允许用户远程提交集成问题将被纳入。

Computing the values of integrals is one of the fundamental problems of calculus and its applications; numerical integration solves this problem for complex functions that cannot be handled analytically. This project will significantly extend the ParInt 1.0 system for performing numerical integration developed under previous NSF support. It will add techniques that enable the system to handle integration problems with a variety of difficult characteristics (e.g. singularities, high dimensions, etc.). This includes the development of a hierarchical process structure for the computation of large collections of integrals (e.g. finite element problems), extrapolation techniques for singular problems, and Quasi-Monte Carlo techniques for solving problems of high dimensions (e.g. computational finance). Corresponding additions to the package's graphical interface will allow for easy use across research disciplines. In particular, visualization tools to help the user see why a problem is difficult (and suggest alternative formulations) and a server allowing users to submit integration problems remotely will be incorporated.