ROW (Researh Planning Grant): Research on Multigrid Algorithms

多重网格法是用于解决各种问题的有效算法。PI之前对多重网格软件的开发是相当具体的。在这个项目中，将使用更广泛的方法和设计。PI将实现一个通用的面向对象的多重网格工具栏，具有以下特点：通用和快速访问的数据结构；面向对象和识字的编程思想；微分方程和变分不等式公式；图形用户界面；并将解决一些非标准的目标问题。该工具箱将用于以下非标准问题的多重网格法的发展：小波长(不定系统)Helmholtz方程：变分不等式和本征值问题。从多重网格的角度来看，这些问题很难解决。PI将为新方法和可能出现的其他问题设计并行算法。

Multigrid Methods are efficient algorithms used for solving a variety of problems. Previous development of multigrid software by the PI was rather specific. In this project a broader approach and design will be used. The PI will implement a general object-oriented multigrid toolbar with the following features: Versatile and fast access data structure; OOP and literate programming philosophy; differential equation and variational inequality formulations; graphical user interface; and will solve some non-standard target problems. The toolbox will be used for the development of multigrid methods for the following non-standard problems: Small wavelength-(indefinite system) Helmholtz equations: variational inequalities and eigenvalue problems. These problems are hard from the multigrid point of view. The PI will design parallel algorithms for the new methods and for other problems which may rise.