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C0-IPM with Generalised Periodicity and Application to Flexoelectricity-Based 2D Metamaterials

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Abstract

We propose a methodology to solve high-order PDE boundary value problems with generalised periodicity, in the framework of the \(\mathcal {C}^0\) interior penalty method. The method is developed for the analysis of flexoelectricity-based metamaterial unit cells, formalising the corresponding problem statement and weak form, and giving details on the implementation of the local and macro conditions for generalised periodicity. Numerical examples demonstrate the high-order convergence of the method and its applicability in realistic problem settings.

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Data sharing is not applicable to this article as no datasets were generated or analysed during the current study. The information to reproduce the numerical results is included in the paper.

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Funding

This work was supported by the European Research Council (StG-679451 to Irene Arias), Agencia Estatal de Investigación (RTI2018-101662-B-I00),Ministerio de Economía y Competitividad (CEX2018-000797-S) and Generalitat de Catalunya (2017-SGR-1278).

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Authors and Affiliations

  1. Laboratori de Càlcul Numèric, Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain

    Oscar Balcells-Quintana & Sonia Fernández-Méndez

  2. Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, Spain

    David Codony

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  1. Oscar Balcells-Quintana
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  2. David Codony
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  3. Sonia Fernández-Méndez
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Correspondence to Sonia Fernández-Méndez.

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Beyond the received support stated in the funding declaration, the authors have no further competing interests to declare that are relevant to the content of this article.

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Balcells-Quintana, O., Codony, D. & Fernández-Méndez, S. C0-IPM with Generalised Periodicity and Application to Flexoelectricity-Based 2D Metamaterials. J Sci Comput 92, 5 (2022). https://doi.org/10.1007/s10915-022-01848-1

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  • DOI: https://doi.org/10.1007/s10915-022-01848-1

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