Isogeometric Bézier dual mortaring: Refineable higher-order spline dual bases and weakly continuous geometry

Zou, Z.; Scott, Michael A.; Borden, Michael J.; Thomas, Derek C.; Dornisch, Wolfgang; Brivadis, Ericka

doi:10.1016/j.cma.2018.01.023

Cited by 35 publications

(25 citation statements)

References 35 publications

(69 reference statements)

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“…In the second case ( Figure 6b) the same subdomains are considered, but with a different parametrization, such that the parametrizations along the interface do no longer match. We note, that this is a situation, where the construction of [31] is not exact, but requires additional steps of refinement. In the third case (Figure 6c), the subdomains are coupled across a curved interface.…”

Section: Numerical Resultsmentioning

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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Section: Numerical Resultsmentioning

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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“…The linear system (16) is a saddle point problem, implying that the approximation spaces of the Lagrange multipliers should be carefully chosen in order to satisfy the inf-sup condition. Recent works present optimal approximation spaces for Mortar coupling in isogeometric analysis [23,27,29,30]. In particular, Schuß et al [30] deal with the G 1 coupling of non-matching Kirchhoff-Love shells.…”

Section: Approximation Spacesmentioning

confidence: 99%

“…The coupling can be addressed by different techniques, and in the specific case of arbitrary non-conforming interfaces, one may resort to weak coupling approaches. There exist three principal classes of methods, namely penalty coupling [20][21][22], Mortar coupling [23][24][25][26][27][28][29][30], and Nitsche coupling [31][32][33][34][35]. We focus in this work on shell analysis and especially on the case of isogeometric Kirchhoff-Love shell formulations.…”

Section: Introductionmentioning

confidence: 99%

A dual domain decomposition algorithm for the analysis of non-conforming isogeometric Kirchhoff–Love shells

Hirschler

Bouclier

Dureisseix

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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Originally, Isogeometric Analysis aimed at using geometric models for the structural analysis. The actual realization of this objective to complex real-world structures requires a special treatment of the non-conformities between the patches generated during the geometric modeling. Different advanced numerical tools now enable to analyze elaborated multipatch models, especially regarding the imposition of the interface coupling conditions. However, in order to push forward the isogeometric concept, a closer look at the algorithm of resolution for multipatch geometries seems crucial. Hence, we present a dual Domain Decomposition algorithm for accurately analyzing non-conforming multipatch Kirchhoff-Love shells. The starting point is the use of a Mortar method for imposing the coupling conditions between the shells. The additional degrees of freedom coming from the Lagrange multiplier field enable to formulate an interface problem, known as the one-level FETI problem. The interface problem is solved using an iterative solver where, at each iteration, only local quantities defined at the patch level (i.e. per sub-domain) are involved which makes the overall algorithm naturally parallelizable. We study the preconditioning step in order to get an algorithm which is numerically scalable. Several examples ranging from simple benchmark cases to semi-industrial problems highlight the great potential of the method.

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“…Another possibility to determine GC dual basis functions for B-spline basis functions is the inversion of the Gram matrix. 32,37 In this case, the first step in the calculation of the dual basis requires the computation of the Gramian matrix for the primal basis…”

Section: Global Dual Basesmentioning

confidence: 99%

Inverse mass matrix for isogeometric explicit transient analysis via the method of localized Lagrange multipliers

González

Kopačka

Kolman

et al. 2018

Numerical Meth Engineering

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A variational framework is employed to generate inverse mass matrices for isogeometric analysis (IGA). As different dual bases impact not only accuracy but also computational overhead, several dual bases are extensively investigated.Specifically, locally discontinuous biorthogonal basis functions are evaluated in detail for B-splines of high continuity and Bézier elements with a standard C 0 continuous finite element structure. The boundary conditions are enforced by the method of localized Lagrangian multipliers after generating the inverse mass matrix for completely free body. Thus, unlike inverse mass matrix methods without employing the method of Lagrange multipliers, no modifications in the reciprocal basis functions are needed to account for the boundary conditions. Hence, the present method does not require internal modifications of existing IGA software structures. Numerical examples show that globally continuous dual basis functions yield better accuracy than locally discontinuous biorthogonal functions, but with much higher computational overhead. Locally discontinuous dual basis functions are found to be an economical alternative to lumped mass matrices when combined with mass parameterization. The resulting inverse mass matrices are tested in several vibration problems and applied to explicit transient analysis of structures. KEYWORDSBézier extraction, explicit transient analysis, free vibration, inverse mass matrix, isogeometric analysis, localized Lagrange multipliers Int J Numer Methods Eng. 2019;117:939-966. wileyonlinelibrary.com/journal/nme

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Isogeometric Bézier dual mortaring: Refineable higher-order spline dual bases and weakly continuous geometry

Cited by 35 publications

References 35 publications

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

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

A dual domain decomposition algorithm for the analysis of non-conforming isogeometric Kirchhoff–Love shells

Inverse mass matrix for isogeometric explicit transient analysis via the method of localized Lagrange multipliers

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