کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4642883 1341359 2007 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An efficient algorithm for the Schrödinger–Poisson eigenvalue problem
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
An efficient algorithm for the Schrödinger–Poisson eigenvalue problem
چکیده انگلیسی

We present a new implementation of the two-grid method for computing extremum eigenpairs of self-adjoint partial differential operators with periodic boundary conditions. A novel two-grid centered difference method is proposed for the numerical solutions of the nonlinear Schrödinger–Poisson (SP) eigenvalue problem.We solve the Poisson equation to obtain the nonlinear potential for the nonlinear Schrödinger eigenvalue problem, and use the block Lanczos method to compute the first k   eigenpairs of the Schrödinger eigenvalue problem until they converge on the coarse grid. Then we perform a few conjugate gradient iterations to solve each symmetric positive definite linear system for the approximate eigenvector on the fine grid. The Rayleigh quotient iteration is exploited to improve the accuracy of the eigenpairs on the fine grid. Our numerical results show how the first few eigenpairs of the Schrödinger eigenvalue problem are affected by the dopant in the Schrödinger–Poisson (SP) system. Moreover, the convergence rate of eigenvalue computations on the fine grid is O(h3)O(h3).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 205, Issue 1, 1 August 2007, Pages 509–532
نویسندگان
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