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The Virtual Element Decomposition: A New Paradigm for Developing Nodal Integration Schemes for Meshfree Galerkin Methods

A talk given by A. Ortiz-Bernardin at WONAPDE 2019, January 22, 2019, Concepción, Chile. THE VIRTUAL ELEMENT DECOMPOSITION: A NEW PARADIGM FOR DEVELOPING NODAL INTEGRATION SCHEMES FOR MESHFREE GALERKIN METHODS R. SILVA-VALENZUELA a, A. ORTIZ-BERNARDIN a, N. SUKUMAR b AND E. ARTIOLI c Abstract. In meshfree Galerkin methods to solve partial differential equations, a cloud of nodes…

Accepted Paper: Veamy: an extensible object-oriented C++ library for the virtual element method

Paper Accepted for Publication in Numerical Algorithms Aleandro Ortiz-Bernardin, Catalina Alvarez, Nancy Hitschfeld-Kahler, Alessandro Russo, Rodrigo Silva-Valenzuela, Edgardo Olate-Sanzana, “Veamy: an extensible object-oriented C++ library for the virtual element method” ABSTRACT This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is…


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Veamy: an extensible object-oriented C++ library for the virtual element method

Numerical Algorithms In press. Alejandro Ortiz-Bernardin, Catalina Alvarez, Nancy Hitschfeld-Kahler, Alessandro Russo, Rodrigo Silva-Valenzuela, Edgardo Olate-Sanzana. Abstract This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is focused on its extensibility. The linear elastostatic and Poisson problems in two dimensions have…

On the behaviour of spherical inclusions in a cylinder under tension loads

Ingenius Vol. 19, 2018, pp. 69-78 S. Montero, R. Bustamante, A. Ortiz-Bernardin Abstract In the present paper the behaviour of a hyperelastic body is studied, considering the presence of one, two and more spherical inclusions, under the effect of an external tension load. The inclusions are modelled as nonlinear elastic bodies that undergo small strains….

A volume-averaged nodal projection method for the Reissner-Mindlin plate model

Computer Methods in Applied Mechanics and Engineering Volume 341, Issue 1, 2018, Pages 827-850 A. Ortiz-Bernardin, Philip Köbrich, Jack S. Hale, Edgardo Olate-Sanzana, Stéphane P. A. Bordas, Sundararajan Natarajan. Abstract We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e.,…