The Payne, Pólya and Weinberger Type Inequalities for the Dirichlet Eigenvalues

2017 ◽  
pp. 119-141
Keyword(s):  
Dirichlet Eigenvalues

scholarly journals Diamagnetic behavior of sums Dirichlet eigenvalues

2000 ◽  
Vol 50 (3) ◽  
pp. 891-907 ◽  
Author(s):  
László Erdös ◽  
Michael Loss ◽  
Vitali Vougalter
Keyword(s):  
Dirichlet Eigenvalues ◽  
Diamagnetic Behavior

scholarly journals Stable, high-order computation of impedance–impedance operators for three-dimensional layered medium simulations

2018 ◽  
Vol 474 (2212) ◽  
pp. 20170704 ◽  
Author(s):  
David P. Nicholls
Keyword(s):  
Applied Sciences ◽  
Numerical Simulations ◽  
Periodic Structure ◽  
Layered Medium ◽  
Three Dimensional ◽  
High Order ◽  
Surface Integral ◽  
Dirichlet Eigenvalues ◽  
Linear Waves ◽  
Spectral Algorithm

The faithful modelling of the propagation of linear waves in a layered, periodic structure is of paramount importance in many branches of the applied sciences. In this paper, we present a novel numerical algorithm for the simulation of such problems which is free of the artificial singularities present in related approaches. We advocate for a surface integral formulation which is phrased in terms of impedance–impedance operators that are immune to the Dirichlet eigenvalues which plague the Dirichlet–Neumann operators that appear in classical formulations. We demonstrate a high-order spectral algorithm to simulate these latter operators based upon a high-order perturbation of surfaces methodology which is rapid, robust and highly accurate. We demonstrate the validity and utility of our approach with a sequence of numerical simulations.

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