A Newton‐type method for two‐dimensional eigenvalue problems

2021 ◽  
Author(s):  
Tianyi Lu ◽  
Yangfeng Su
Keyword(s):  
Eigenvalue Problems ◽  
Two Dimensional ◽  
Type Method

scholarly journals Perturbation of eigenvalues due to gaps in two-dimensional boundaries

2006 ◽  
Vol 463 (2079) ◽  
pp. 759-786 ◽  
Author(s):  
Anthony M.J Davis ◽  
Stefan G Llewellyn Smith
Keyword(s):  
Eigenvalue Problems ◽  
Numerical Solutions ◽  
Neumann Boundary ◽  
Diffusion Problem ◽  
Length Scale ◽  
Two Dimensional ◽  
Constructive Approach ◽  
Term Outcome ◽  
Long Term Outcome

Motivated by problems involving diffusion through small gaps, we revisit two-dimensional eigenvalue problems with localized perturbations to Neumann boundary conditions. We recover the known result that the gravest eigenvalue is O (|ln  ϵ | −1 ), where ϵ is the ratio of the size of the hole to the length-scale of the domain, and provide a simple and constructive approach for summing the inverse logarithm terms and obtaining further corrections. Comparisons with numerical solutions obtained for special geometries, both for the Dirichlet ‘patch problem’ where the perturbation to the boundary consists of a different boundary condition and for the gap problem, confirm that this approach is a simple way of obtaining an accurate value for the gravest eigenvalue and hence the long-term outcome of the underlying diffusion problem.

A Two-Dimensional Nonorthogonal WLP-FDTD Method for Eigenvalue Problems

2013 ◽  
Vol 23 (10) ◽  
pp. 515-517
Author(s):  
Wei-Jun Chen ◽  
Wei Shao ◽  
Jia-Lin Li ◽  
Bing-Zhong Wang
Keyword(s):  
Eigenvalue Problems ◽  
Fdtd Method ◽  
Two Dimensional
Sign in / Sign up

Export Citation Format

Share Document