A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces

Coox, Laurens; Greco, Francesco; Atak, Onur; Vandepitte, Dirk; Desmet, Wim

doi:10.1016/j.cma.2016.06.022

Cited by 59 publications

(48 citation statements)

References 40 publications

(61 reference statements)

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“…Moreover, in [36] the restrictions are enforced by means of a penalty method, whereas the coupling technique presented here employs static condensation. The proposed procedure is explained below; a more detailed study of it can be found in [37].…”

Section: Enforcing Continuity Across Non-conforming Nurbs Patchesmentioning

confidence: 99%

An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains

Coox

Atak

Vandepitte

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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This work introduces an indirect Boundary Element Method (BEM) within a NURBSbased isogeometric framework for solving three-dimensional acoustic problems in the frequency domain. Developments of isogeometric boundary elements so far have focused on the direct BEM. Yet, a multitude of common problems in acoustics involves openboundary surfaces, which require a more involved, indirect, boundary element formulation. The current work presents an indirect variational BEM which makes use of NURBS shape functions. Additionally, a novel technique for coupling (strongly) non-conforming patches is introduced to allow the analysis of more complex geometries. The proposed isogeometric indirect boundary element method is verified against analytical solutions and benchmarked against the conventional polynomial-based indirect BEM. Also two open-boundary problems are studied, including analyses over wider frequency ranges, and one industrial-type, complex geometry containing multiple non-conforming patches. The proposed method is found to be not only significantly more efficient than its polynomialbased counterpart, but also very robust against strong non-conformities in the NURBS descriptions.

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Section: Enforcing Continuity Across Non-conforming Nurbs Patchesmentioning

confidence: 99%

An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains

Coox

Atak

Vandepitte

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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“…γ 1,1 is the sole interface of Ω (1) and it has non-null intersection with just one interface of each one of the other subdomains. Ω (2) has two interfaces: γ 2,1 (that adjacent to Ω (1) ) and γ 2,2 (the top one adjacent to both Ω (3) and Ω (4) ); Ω (3) has three interfaces: γ 3,1 (that adjacent to Ω (4) ), γ 3,2 (that adjacent to Ω (1) ) and γ 3,3 (that adjacent to Ω (2) ); Ω (4) has three interfaces: γ 4,1 (that adjacent to Ω (3) ), γ 4,2 (that adjacent to Ω (1) ) and γ 4,3 (that adjacent to Ω (2) ) In the patch Ω (k) we define a NURBS space N (k) h k as defined in (20) and the corresponding finite dimensional spaces V (k) h k (see (8)) that are totally independent of the discretizations inside the adjacent patches. For each face γ k,α ⊂ Γ k we define the trace space…”

Section: Remark 81mentioning

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%

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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“…Different approaches are considered, e.g., Nitsche's method [6,7], penalty based methods [8] and mortar methods [9,10], and there is a recent interest in higher-order couplings, see, e.g. [11,12]. A recent practical review, which includes the related issue of trimming, is given in [13].…”

Section: Introductionmentioning

confidence: 99%

Biorthogonal splines for optimal weak patch-coupling in isogeometric analysis with applications to finite deformation elasticity

Wunderlich

Seitz

Alaydin

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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A new construction of biorthogonal splines for isogeometric mortar methods is proposed. The biorthogonal basis has a local support and, at the same time, optimal approximation properties, which yield optimal results with mortar methods. We first present the univariate construction, which has an inherent crosspoint modification. The multivariate construction is then based on a tensor product for weighted integrals, whereby the important properties are inherited from the univariate case. Numerical results including large deformations confirm the optimality of the newly constructed biorthogonal basis.

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A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces

Abstract: A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces

Cited by 59 publications

References 40 publications

An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains

An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains

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

Biorthogonal splines for optimal weak patch-coupling in isogeometric analysis with applications to finite deformation elasticity

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