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POLYGONAL AND POLYHEDRAL FINITE ELEMENT METHODS

PHI PHI PHI
PHI PHI PHI

Polygonal and polyhedral elements: Shape functions and meshes

(Supported by NSF Grant CMMI-1334783, 09/2013–08/2017)


The development of Galerkin finite element methods on arbitrary polygonal and polyhedral elements to solve PDEs is pursued. The origins of this approach can be traced to Wachspress basis functions, which is a particular generalization of finite elements to planar convex polygons. Since then, many new shape functions on polygonal and polyhedral domains have emerged: mean value coordinates, metric coordinates, Laplace shape functions, maximum-entropy coordinates, harmonic coordinates, etc.

Current research focuses on contributions related to the virtual element method, a consistent and stable Galerkin method on arbitrary (polygonal and polyhedral) meshes with higher-order and smooth approximations; and on enabling fracture simulations on polygonal and polyhedral meshes. Coorganized minisymposium on Computational Fracture at SES 2014, SES 2015, USNCCM (2015, 2017) and WCCM XII and XIII (2016, 2018), as well as Polygonal and Polyhedral Discretizations in Computational Mechanics at USNCCM (2015, 2017, 2019) and WCCM XIII (2018).


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Disclaimer: Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation


© Copyright 2004–2018 N. Sukumar. All rights reserved.