B-splines and NURBS based finite element methods for Kohn–Sham equations

Masud, Arif; Kannan, Raguraman

doi:10.1016/j.cma.2012.04.016

Cited by 31 publications

(22 citation statements)

References 38 publications

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“…In addition, due to the ease of constructing high order continuous basis functions, IGA has been used with great success in solving PDEs that incorporate fourth order (or higher) derivatives of the field variable such as the Hill-Cahnard equation [32], explicit gradient damage models [33] and gradient elasticity [34]. The high order NURBS basis has also found potential applications in the Kohn-Sham equation for electronic structure modeling of semiconducting materials [35].…”

Section: Introductionmentioning

confidence: 99%

Nitsche’s method for two and three dimensional NURBS patch coupling

et al. 2013

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A Nitche's method is presented to couple non-conforming two and three dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for elastic stress analyses under the static condition of two and three dimensional NURBS geometries. The contribution fills the gap in the literature and enlarges the applicability of NURBS-based isogeometric analysis.

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Section: Introductionmentioning

confidence: 99%

Nitsche’s method for two and three dimensional NURBS patch coupling

et al. 2013

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“…In addition, due to the ease of constructing high order continuous basis functions, IGA has been used with great success in solving PDEs that incorporate fourth order (or higher) derivatives of the field variable such as the Hill-Cahnard equation Gómez et al (2008), explicit gradient damage models Verhoosel et al (2011b) and gradient elasticity Fischer et al (2010). The high order NURBS basis have also found potential application in the Kohn-Sham equation for electronic structure modeling of semiconducting materials Masud and Kannan (2012).…”

Section: Introductionmentioning

confidence: 98%

Extended Isogeometric Analysis for Strong and Weak Discontinuities

Nguyen

Bordas

2015

Isogeometric Methods for Numerical Simulation

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Isogeometric analysis (IGA) is a fundamental step forward in computational mechanics that offers the possibility of integrating methods for analysis into Computer Aided Design (CAD) tools and vice versa. The benefits of such an approach are evident, since the time taken from design to analysis is greatly reduced leading to large savings in cost and time for industry. The tight coupling of CAD and analysis within IGA requires knowledge from both fields and it is one of the goals of the present paper to outline much of the commonly used notation. In this manuscript, through a clear and simple Matlab R implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implementation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several fracture examples in both two-dimensions and three-dimensions are given as illustration. The open source Matlab R code which accompanies the present paper can be applied to one, two and threedimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. It also implements the Bézier extraction concept that allows FE analysis to be performed on T-spline geometries. An attempt was also made to include a review of recent developments of IGA.G. Beer, S.Bordas (Eds.), Isogeometric Methods for Numerical Simulation,

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“…In addition, due to the ease of constructing high order continuous basis functions, IGA has been used with great success in solving PDEs that incorporate fourth order (or higher) derivatives of the field variable such as the Hill-Cahnard equation Gómez et al (2008), explicit gradient damage models and gradient elasticity Fischer et al (2010). The high order NURBS basis have also found potential application in the Kohn-Sham equation for electronic structure modeling of semiconducting materials Masud and Kannan (2012).…”

Section: Introductionmentioning

confidence: 99%

Isogeometric Methods for Numerical Simulation

Beer¹,

Bordas²

2015

CISM International Centre for Mechanical Sciences

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translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on micro lms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied speci cally for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

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B-splines and NURBS based finite element methods for Kohn–Sham equations

Cited by 31 publications

References 38 publications

Nitsche’s method for two and three dimensional NURBS patch coupling

Nitsche’s method for two and three dimensional NURBS patch coupling

Extended Isogeometric Analysis for Strong and Weak Discontinuities

Isogeometric Methods for Numerical Simulation

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