Isogeometric analysis in electromagnetics: B-splines approximation

By Annalisa Buffa, Giancarlo Sangalli, Rafael Vázquez. 2010

396 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2eed8873b66449f009d104772e7940a74ca29918

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

A NURBS-based immersed methodology for fluid–structure interaction (2015, methodology): “IGA has been successfully applied to a large number of fields including body-fitted FSI problems [14, 38], fluid mechanics [39, 40], phase-filed models [26, 41, 42, 43, 44, 45], structural vibrations [46, 47], quasi-incompressible elasticity [48], shell modeling [49, 50], contact problems [51, 52, 5”
Isogeometric Shape Optimization of Vibrating Membranes (2011, neutral): “Since the mesh regularity aﬀects the accuracy of the numerical solution [8, 41], it is necessary to improve the parametrization of the reference conﬁguration as discussed in Section 3.4.”
Divergence-conforming discretization for Stokes problem on locally refined meshes using LR B-splines (2015, methodology): “[12], a characterization for the range of the div operator in the situations of interest for the Raviart-Thomas elements Vh × Qh which ensure the stability and divergence free conforming solutions were presented.”
Isogeometric discretizations of the Stokes problem: stability analysis by the macroelement technique (2013, background): “…a growing impact on several fields, from fluid dynamics (Bazilevs et al., 2007, 2008, 2010; Zhang et al., 2007; Gomez et al., 2010; Buffa et al., 2011) to structural mechanics (Cottrell et al., 2006; Auricchio et al., 2007; Lipton et al., 2010) and electromagnetics (Buffa et al., 2010, 2011).”
Mathematical analysis of variational isogeometric methods* (2014, methodology): “…of the previous references, de Rham-compatible edge and face elements, based on splines, have been used; they were developed and fully analysed in Buffa et al. (2010b) and Buffa, Rivas, Sangalli and Vázquez (2011b), again showing that smoothness is beneficial since it allows for the design of…”
Local refinement of analysis-suitable T-splines (2012, methodology): “Areas of application of NURBS-based isogeometric analysis include turbulence [5–8], fluid–structure interaction [9–12], incompressibility [13–15], structural analysis [16,3], plates and shells [17–21], phase-field analysis [22,23], large deformation with mesh distortion [24], shape optimization [25–”
Isogeometric collocation methods for the Reissner–Mindlin plate problem (2015, positive): “The isogeometric compatible spaces described below were introduced in [30,31] for electromagnetic problems, and first used in [32] for Reissner–Mindlin plates with Galerkin IGA.”
A large deformation frictional contact formulation using NURBS‐based isogeometric analysis (2011, background): “In the last few years this new computational mechanics technology has been successfully applied to a variety of problems [2–7].”
IsoGeometric Analysis: Stable elements for the 2D Stokes equation (2011, background): “The condition is that d d , d =1,2, [2, 21].”
ISOGEOMETRIC DIVERGENCE-CONFORMING B-SPLINES FOR THE STEADY NAVIER–STOKES EQUATIONS (2013, methodology): “These spaces are motivated by the recent theory of isogeometric discrete differential forms [9, 10] and may be interpreted as smooth generalizations of Raviart-Thomas elements [32].”
Isogeometric boundary element analysis using unstructured T-splines (2013, methodology): “A small sampling includes fluids and turbulence [5, 6, 7, 8], fluid-structure interaction [9, 10, 11, 12], incompressibility [13, 14, 15], structural and vibration analysis [16, 3], plates and shells [17, 18, 19, 20, 21], phase-field analysis [22, 23, 24], large deformation structural analysis with ”
A hierarchical approach to adaptive local refinement in isogeometric analysis (2011, methodology): “Isogeometric analysis has been applied to a wide range of problems from fluid-structure interaction [3], shape optimization [4], shell analysis [5] to electromagnetics [6], just to name a few.”