Numerical integration in the virtual element method with the scaled boundary cubature scheme

Chin, Eric B.; Dassi, Franco; Manzini, Gianmarco; Sukumar, N.

doi:10.1002/nme.7549

Title: Numerical integration in the virtual element method with the scaled boundary cubature scheme

Journal Article · 04 July 2024 · International Journal for Numerical Methods in Engineering

DOI: https://doi.org/10.1002/nme.7549 · OSTI ID:2391042

Chin, Eric B. ^[1];

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Lawrence Livermore National Laboratory Livermore California USA
Dipartimento di Matematica e Applicazioni Università di Milano‐Bicocca Milan Italy
Theoretical Division Los Alamos National Laboratory Los Alamos New Mexico USA
Department of Civil and Environmental Engineering University of California Davis California USA

Abstract The virtual element method (VEM) is a stabilized Galerkin method on meshes that consist of arbitrary (convex and nonconvex) polygonal and polyhedral elements. A crucial ingredient in the implementation of low‐ and high‐order VEM is the numerical integration of monomials and nonpolynomial functions over such elements. In this article, we apply the recently proposed scaled boundary cubature (SBC) scheme to compute the weak form integrals in various virtual element formulations over polygonal and polyhedral meshes. In doing so, we demonstrate the flexibility of the approach and the accuracy that it delivers on a broad suite of boundary‐value problems in 2D and 3D over polytopes with affine faces as well as on elements with curved boundaries. In addition, the use of the SBC scheme is exemplified in an enriched Poisson formulation of the VEM in which weakly singular functions are required to be integrated. This study establishes the SBC method as a simple, accurate and efficient integration scheme for use in the VEM.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: 89233218CNA000001; AC52-07NA27344

OSTI ID:: 2391042

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering; ISSN 0029-5981

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

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