Newton-Based Methods for Finding the Positive Ground State of Gross-Pitaevskii Equations

The discretization of Gross-Pitaevskii equations (GPE) leads to a nonlinear eigenvalue problem with eigenvector nonlinearity (NEPv). We use two Newton-based methods to compute the positive ground state of GPE. The first method comes from the Newton-Noda iteration for saturable nonlinear Schrödinger...

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Bibliographic Details
Published in:Journal of scientific computing 2022, Vol.90 (1), p.49, Article 49
Main Authors: Huang, Pengfei, Yang, Qingzhi
Format: Article
Language:English
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Eigenvalues
Eigenvectors
Fourier transforms
Ground state
Iterative methods
Linear algebra
Linear systems
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Newton methods
Nonlinearity
Schrodinger equation
Theoretical
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Summary:The discretization of Gross-Pitaevskii equations (GPE) leads to a nonlinear eigenvalue problem with eigenvector nonlinearity (NEPv). We use two Newton-based methods to compute the positive ground state of GPE. The first method comes from the Newton-Noda iteration for saturable nonlinear Schrödinger equations proposed by Ching-Sung Liu, which can be transferred to GPE naturally. The second method combines the idea of the root-finding methods and the idea of Newton method, in which, each subproblem involving block tridiagonal linear systems can be solved easily. We give an explicit convergence and computational complexity analysis for it. Numerical experiments are provided to support the theoretical results.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-021-01711-9