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    Stabilized Finite Element Methods for the Schrödinger Wave Equation

    Source: Journal of Applied Mechanics:;2009:;volume( 076 ):;issue: 002::page 21203
    Author:
    Raguraman Kannan
    ,
    Arif Masud
    DOI: 10.1115/1.3059564
    Publisher: The American Society of Mechanical Engineers (ASME)
    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.
    keyword(s): Schrödinger equation , Eigenvalues , Functions , Finite element methods AND Bricks ,
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      Stabilized Finite Element Methods for the Schrödinger Wave Equation

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    http://yetl.yabesh.ir/yetl1/handle/yetl/139762
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    contributor authorRaguraman Kannan
    contributor authorArif Masud
    date accessioned2017-05-09T00:31:19Z
    date available2017-05-09T00:31:19Z
    date copyrightMarch, 2009
    date issued2009
    identifier issn0021-8936
    identifier otherJAMCAV-26744#021203_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/139762
    description abstractThis 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.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleStabilized Finite Element Methods for the Schrödinger Wave Equation
    typeJournal Paper
    journal volume76
    journal issue2
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.3059564
    journal fristpage21203
    identifier eissn1528-9036
    keywordsSchrödinger equation
    keywordsEigenvalues
    keywordsFunctions
    keywordsFinite element methods AND Bricks
    treeJournal of Applied Mechanics:;2009:;volume( 076 ):;issue: 002
    contenttypeFulltext
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