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math.NA2022
Virtual element method for modeling the deformation of multiphase composites
N. Sukumar, John E. Bolander
In this paper, we study applications of the virtual element method (VEM) for simulating the deformation of multiphase composites. The VEM is a Galerkin approach that is applicable…
math.NA2020
Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries
Eric B. Chin, N. Sukumar
This paper introduces the scaled boundary cubature (SBC) scheme for accurate and efficient integration of functions over polygons and two-dimensional regions bounded by parametric…
math.NA2019
A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition
R. Silva-Valenzuela, A. Ortiz-Bernardin, N. Sukumar +2
In this paper, we present a novel nodal integration scheme for meshfree Galerkin methods that draws on the mathematical framework of the virtual element method. We adopt linear max…