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Sample of two-dimensional nodal cells used in nodal integration

Accepted Paper: A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition

  • December 18, 2019
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Paper Accepted for Publication in International Journal for Numerical Methods in Engineering R. Silva-Valenzuela, A. Ortiz-Bernardin, N. Sukumar, E. Artioli,  N. Hitschfeld-Kahler, “A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition” ABSTRACT In this paper, we present a novel nodal integration scheme for meshfree Galerkin methods that draws on the mathematical

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Sample of two-dimensional nodal cells used in nodal integration

A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition

  • December 18, 2019
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International Journal for Numerical Methods in Engineering Vol. 121, No. 10, pp. 2174-2205, 2020 R. Silva-Valenzuela, A. Ortiz-Bernardin, N. Sukumar, E. Artioli,  N. Hitschfeld-Kahler Abstract 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 maximum-entropy basis

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Accepted Paper: Consistent and stable meshfree Galerkin methods using the virtual element decomposition

  • January 24, 2017
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Paper Accepted for Publication in the International Journal for Numerical Methods in Engineering A. Ortiz-Bernardin, A. Russo, N. Sukumar, “Consistent and stable meshfree Galerkin methods using the virtual element decomposition.” ABSTRACT Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to

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Consistent and stable meshfree Galerkin methods using the virtual element decomposition

  • January 24, 2017
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International Journal for Numerical Methods in Engineering Vol. 112, No. 7, pp 655-684, 2017 A. Ortiz-Bernardin, A. Russo, N. Sukumar Abstract Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to finite elements, the basis functions in meshfree methods are smooth

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Paper Submitted: Consistent and stable meshfree Galerkin methods using the virtual element decomposition

  • November 7, 2016
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A. Ortiz-Bernardin, A. Russo, N. Sukumar, “Consistent and stable meshfree Galerkin methods using the virtual element decomposition,” submitted. ABSTRACT Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to finite elements, the basis functions in meshfree method are smooth (nonpolynomial functions),

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Paper Accepted: Linear smoothed polygonal and polyhedral finite elements

  • June 1, 2016
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Paper Accepted for Publication in International Journal for Numerical Methods in Engineering A. Francis, A. Ortiz-Bernardin, SPA. Bordas, S. Natarajan, “Linear smoothed polygonal and polyhedral finite elements.” ABSTRACT It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as

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