An interpolation method for coupling non-conforming patches in isogeometric analysis of vibro-acoustic systems

Mi, Yongzhen; Zheng, Hui

doi:10.1016/j.cma.2018.07.002

Cited by 14 publications

(15 citation statements)

References 30 publications

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“…We start by underlying that the interpolation matrix P k defined in either (33)- (34) or (43)-(44) applies to the primal coefficients of the functions belonging to Y…”

Section: Transferring the Normal Derivativesmentioning

confidence: 99%

“…Remark 4.2 From now on, when the interfaces will be watertight we will implement INTERNODES by using the interpolation matrices (33) and (34), while in presence of non-watertight interfaces we will use (43) and (44). (2)…”

Section: (K)mentioning

confidence: 99%

“…In Sect. 8.1 we will show how to extend the definition of the interpolation matrices (33) and (34) when the interfaces are watertight. If two patches are non-watertight, we assume that the cardinality of the set A k,α associated with the corresponding interfaces is equal to one, thus the interpolation matrices are built as in (43) and (44).…”

Section: Internodes For Decompositions With M ≥ 2 Patchesmentioning

confidence: 99%

“…In the last years, the treatment of multipatch geometries has been investigated in several papers, far from be exhaustive we mention [10,11,26,37,41,47,8,7,34,30,27,43,6,32,15,29]. In this paper we propose to apply the INTERNODES method to solve elliptic problems within the IgA framework on non-overlapping and non-conforming multipatch configurations.…”

Section: Introductionmentioning

confidence: 99%

“…When instead the interfaces are non-watertight (as in Fig. 1 (a)) we overcome the difficulty to project the Greville abscissae from one face to the non-watertight corresponding one, by exploiting the Radial Basis Functions interpolation (see, e.g., [18,19] in the FEM context and [34] in the IgA context).…”

Section: Introductionmentioning

confidence: 99%

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The INTERNODES method for the treatment of non-conforming multipatch geometries in Isogeometric Analysis

Gervasio

Marini

2020

Computer Methods in Applied Mechanics and Engineering

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In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. IN-TERNODES is an interpolation-based method that, on each interface of the configuration, exploits two independent interpolation operators to enforce the continuity of the traces and of the normal derivatives. INTERNODES easily handles both parametric and geometric NURBS non-conformity. We specify how to set up the interpolation matrices on non-conforming interfaces, how to enforce the continuity of the normal derivatives and we give special attention to implementation aspects. The numerical results show that INTERNODES exhibits optimal convergence rate with respect to the mesh size of the NURBS spaces an that it is robust with respect to jumping coefficients.

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“…We start by underlying that the interpolation matrix P k defined in either (33)- (34) or (43)-(44) applies to the primal coefficients of the functions belonging to Y…”

Section: Transferring the Normal Derivativesmentioning

confidence: 99%