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The reduced basis method in all-electron calculations with finite elements

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Abstract

The reduced basis method successfully diminishes the required amount of degrees of freedom in the solution of a parameter dependent differential equation, and is applied in this work to the determination of the electronic structure with the Kohn-Sham equations in combination with the finite element method. It is thereby demonstrated, how the basis sizes in all-electron calculations can be essentially reduced, yielding new opportunities in the modeling of the electronic structure. In this context, a generalization of the reduced basis set construction is proposed and shown to increase the flexibility of the method.

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Authors and Affiliations

  1. Institute of Applied Mechanics (CE) Chair I, Stuttgart University, 70550, Stuttgart, Germany

    Volker Schauer

  2. Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, 94305, USA

    Christian Linder

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  1. Volker Schauer
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  2. Christian Linder
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Correspondence to Christian Linder.

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Communicated by: Editors of Special Issue on MoRePas

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Schauer, V., Linder, C. The reduced basis method in all-electron calculations with finite elements. Adv Comput Math 41, 1035–1047 (2015). https://doi.org/10.1007/s10444-014-9374-z

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  • DOI: https://doi.org/10.1007/s10444-014-9374-z

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