Finite element method to solve the spectral problem for arbitrary self-adjoint extensions of the Laplace-Beltrami operator on manifolds with a boundary

JOURNAL OF COMPUTATIONAL PHYSICS

卷:347

Article

Lopez-Yela, A.¹  Perez-Pardo, J. M.^2,3 

[1] Univ Carlos III Madrid, Dept Teoria Senal & Telecomun, Avda Univ 30, Madrid 28911, Spain

[2] Complesso Univ Monte S Angelo, Sez Napoli, INFN, Via Cintia, I-80126 Naples, Italy

[3] Univ Carlos III Madrid, Dept Matemat, Avda Univ 30, Madrid 28911, Spain

关键词: Self-adjoint extensions;    Spectral problem;    Laplace;    Higher dimension;    Boundary conditions;    Finite element method;   

DOI  :  10.1016/j.jcp.2017.06.043

来源: Elsevier

【 摘 要 】

A numerical scheme to compute the spectrum of a large class of self-adjoint extensions of the Laplace-Beltrami operator on manifolds with boundary in any dimension is presented. The algorithm is based on the characterisation of a large class of self-adjoint extensions of Laplace-Beltrami operators in terms of their associated quadratic forms. The convergence of the scheme is proved. A two-dimensional version of the algorithm is implemented effectively and several numerical examples are computed showing that the algorithm treats in a unified way a wide variety of boundary conditions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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