ROW (Researh Planning Grant): Research on Multigrid Algorithms

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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.