Stabilized finite element methods for the schrödinger wave equation

Raguraman Kannan, Arif Masud

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1-7
Number of pages7
JournalJournal of Applied Mechanics, Transactions ASME
Volume76
Issue number2
DOIs
StatePublished - Dec 1 2009

Keywords

  • Finite elements
  • Quantum mechanics
  • Schrödinger wave equation
  • Stabilized formulations

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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