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

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1994
Accession Number
ADA289506

Entities

People

  • Shlomo Ta'asan
  • Sorin Costiner

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Applied Mathematics
  • Computational Complexity
  • Computations
  • Computer Science
  • Computers
  • Eigenvalues
  • Eigenvectors
  • Engineering
  • Equations
  • Interpolation
  • Iterations
  • Mathematics
  • Sequences
  • Three Dimensional
  • Two Dimensional

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Materials Science and Engineering.