Convergence Analysis of Planewave Expansion Methods for 2D Schrödinger Operators with Discontinuous Periodic Potentials

DOI10.1137/090756545zbMath1218.65124OpenAlexW2050225490MaRDI QIDQ3069075

Richard A. Norton, Robert Scheichl

Publication date: 24 January 2011

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://opus.bath.ac.uk/19094/1/SIAMJNumAnalysis47(6)p4356.pdf

zbMATH Keywords

computational complexityconvergencesmoothingeigenvaluesdiscontinuous coefficientsnumerical experimentsSchrödinger operatorfast Fourier transformerror analysiseigenfunctionsspectral approximationFourier methodsoptimal preconditionersPDE eigenproblems

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Estimates of eigenvalues in context of PDEs (35P15) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) PDEs with low regular coefficients and/or low regular data (35R05) Schrödinger operator, Schrödinger equation (35J10) Numerical methods for discrete and fast Fourier transforms (65T50) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Complexity and performance of numerical algorithms (65Y20)

Related Items

Analysis of the Feshbach–Schur method for the Fourier spectral discretizations of Schrödinger operators, CONVERGENT ADAPTIVE FINITE ELEMENT METHODS FOR PHOTONIC CRYSTAL APPLICATIONS, Numerical realization of Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides, Finite element calculation of photonic band structures for frequency dependent materials, Adaptive finite element methods for computing band gaps in photonic crystals, An a posteriori error estimator for \(hp\)-adaptive discontinuous Galerkin methods for computing band gaps in photonic crystals, An a posteriori error estimator for \(hp\)-adaptive continuous Galerkin methods for photonic crystal applications, Regularity for Maxwell eigenproblems in photonic crystal fibre modelling

Uses Software

• ARPACK