Stabilized Finite Element Methods for the Schrödinger Wave Equation-Reference-Cited by-同舟云学术

Stabilized Finite Element Methods for the Schrödinger Wave Equation

Published:2009-01-14 Issue:2 Volume:76 Page:
ISSN:0021-8936
Container-title:Journal of Applied Mechanics
language:en
Short-container-title:

Author:

Kannan Raguraman¹,Masud Arif²

Affiliation:

1. Department of Civil and Materials Engineering, University of Illinois at Chicago, Chicago, IL 60607

2. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

Abstract

This paper presents two stabilized formulations for the Schrödinger wave equation. First formulation is based on the Galerkin/least-squares (GLS) method, and it sets the stage for exploring variational multiscale ideas for developing the second stabilized formulation. These formulations provide improved accuracy on cruder meshes as compared with the standard Galerkin formulation. Based on the proposed formulations a family of tetrahedral and hexahedral elements is developed. Numerical convergence studies are presented to demonstrate the accuracy and convergence properties of the two methods for a model electronic potential for which analytical results are available.

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Link

http://asmedigitalcollection.asme.org/appliedmechanics/article-pdf/doi/10.1115/1.3059564/5478100/021203_1.pdf

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