Multigrid Techniques for Nonlinear Eigenvalue Problems; Solutions of a Nonlinear Schroedinger Eigenvalue Problem in 2D and 3D.
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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This paper presents MG techniques for nonlinear 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 the 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 selfconsistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.
- Theoretical Mathematics