Analysis of the Feshbach-Schur method for the planewave discretizations of Schrödinger operators

08/25/2020
by   Genevieve Dusson, et al.
0

In this article, we propose a new numerical method and its analysis to solve eigen-value problems for self-adjoint Schrödinger operators, by combining the Feshbach-Schur perturbation theory with planewave discretization. In order to analyze the method, we establish an abstract framework of Feshbach-Schur perturbation theory with minimal regularity assumptions on the potential that is then applied to the setting of the new planewave discretization method. Finally, we present some numerical results that underline the theoretical findings.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/14/2021

Unified Analysis for Variational Time Discretizations of Higher Order and Higher Regularity Applied to Non-stiff ODEs

We present a unified analysis for a family of variational time discretiz...
research
08/30/2019

Numerical analysis of a semilinear fractional diffusion equation

This paper considers the numerical analysis of a semilinear fractional d...
research
12/13/2022

Analysis of a fully-discrete, non-conforming approximation of evolution equations and applications

In this paper, we consider a fully-discrete approximation of an abstract...
research
06/06/2022

Perturbation formulae for quenched random dynamics with applications to open systems and extreme value theory

We consider quasi-compact linear operator cocycles ℒ^n_ω:=ℒ_σ^n-1ω∘⋯∘ℒ_σ...
research
09/30/2018

Convergence and perturbation theory for an infinite-dimensional Metropolis-Hastings algorithm with self-decomposable priors

We study a Metropolis-Hastings algorithm for target measures that are ab...
research
04/16/2020

Convergence of Eigenvector Continuation

Eigenvector continuation is a computational method that finds the extrem...
research
11/20/2020

A mixed parameter formulation with applications to linear viscoelasticity

In this work we propose and analyze an abstract parameter dependent mode...

Please sign up or login with your details

Forgot password? Click here to reset