GRADIENT FLOW FINITE ELEMENT DISCRETISATIONS WITH ENERGY-BASED ADAPTIVITY FOR EXCITED STATES OF SCHRÖDINGER'S EQUATION  

作　　者：Pascal Heid 

机构地区：[1]Mathematical Institute,University of Oxford,Woodstock Road,Oxford OX26GG,UK

出　　处：《Journal of Computational Mathematics》2023年第5期933-955,共23页计算数学（英文）

基　　金：the financial support of the Swiss National Science Foundation(SNSF),Project No.P2BEP2_191760.

摘　　要：The purpose of this paper is to verify that the computational scheme from[Heid et al.,Gradient flow finite element discretizations with energy-based adaptivity for the Gross–Pitaevskii equation,J.Comput.Phys.436(2021)]for the numerical approximation of the ground state of the Gross–Pitaevskii equation can equally be applied for the effective approximation of excited states of Schr¨odinger’s equation.That procedure employs an adaptive interplay of a Sobolev gradient flow iteration and a novel local mesh refinement strategy,and yields a guaranteed energy decay in each step of the algorithm.The computational tests in the present work highlight that this strategy is indeed able to approximate excited states,with(almost)optimal convergence rate with respect to the number of degrees of freedom.

关 键 词：Schrodinger’s equation Excited states Gradient flows Adaptive finite element methods 

分 类 号：O24[理学—计算数学]