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首页> 美国政府科技报告 >Multigrid Techniques for Nonlinear Eigenvalue Probems: Solutions of a NonlinearSchroedinger Eigenvalue Problem in 2D and 3D
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Multigrid Techniques for Nonlinear Eigenvalue Probems: Solutions of a NonlinearSchroedinger Eigenvalue Problem in 2D and 3D

机译：非线性特征值探针的多重网格技术：二维和三维非线性特格林格特征值问题的解

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摘要

This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems(EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

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