Multigrid Techniques for Nonlinear Eigenvalue Problems; Solutions of a NonlinearSchroedinger Eigenvalue Problem in 2D and 3D

摘要

This paper presents MG techniques for nonlinear EP and emphasizes an MG algorithmfor 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.