Reparameterization and Adaptive Quadrature for the Isogeometric Discontinuous Galerkin Method

Seiler, Agnes; Jüttler, Bert

doi:10.1007/978-3-319-67885-6_14

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…The advantage of implementing this approach is that we can develop a flexible DG-IGA code which can treat patch unions with matching and nonmatching interfaces in a similar way. Note also that the previous approach can be easily combined with the adaptive numerical quadrature methods presented in [31], in order to discretize the problem using non-matching structured meshes on the overlapping faces. Overlapping regions with boundary consisting of more than two faces are shown in Fig.…”

Section: Implementation and Numerical Tests 41 Implementation Remarksmentioning

confidence: 99%

Discontinuous Galerkin isogeometric analysis for segmentations generating overlapping regions

Hofer

Toulopoulos

2019

Applicable Analysis

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In the Isogeometric Analysis (IGA) framework, the computational domain has very often a multipatch representation. The multipatch domain can be obtained by a volume segmentation of a boundary represented domain, e.g., provided by a Computer Aided Design (CAD) model. Typically, small gap and overlapping regions can appear at the patch interfaces of such multipatch representations. In the current work we consider multipatch representations having only small overlapping regions between the patches. We develop a Discontinuous Galerkin (DG)-IGA method which can be immediately applied to these representations. Our method appropriately connects the fluxes of the one face of the overlapping region with the flux of the opposite face. We provide a theoretical justification of our approach by splitting the whole error into two components: the first is related to the incorrect representation of the patches (consistency error) and the second to the approximation properties of the IGA space. We show bounds for both components of the error. We verify the theoretical error estimates in a series of numerical examples.

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Section: Implementation and Numerical Tests 41 Implementation Remarksmentioning

confidence: 99%

Discontinuous Galerkin isogeometric analysis for segmentations generating overlapping regions

Hofer

Toulopoulos

2019

Applicable Analysis

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“…However, this method has no guarantees and the integration error cannot be controlled easily. In engineering practice local adaptive quadrature is used on top of it, that is, subdivision is performed around the trimmed region and quadrature nodes are placed in each sub-cell [8,13,28]. This approach can generate an extensive number of quadrature points, thus posing efficiency barriers.…”

Section: Introductionmentioning

confidence: 99%

First Order Error Correction for Trimmed Quadrature in Isogeometric Analysis

Scholz

Mantzaflaris

Jüttler

2019

Lecture Notes in Computational Science and Engineering

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In this work, we develop a specialized quadrature rule for trimmed domains, where the trimming curve is given implicitly by a real-valued function on the whole domain. We follow an error correction approach: In a first step, we obtain an adaptive subdivision of the domain in such a way that each cell falls in a predefined base case. We then extend the classical approach of linear approximation of the trimming curve by adding an error correction term based on a Taylor expansion of the blending between the linearized implicit trimming curve and the original one. This approach leads to an accurate method which improves the convergence of the quadrature error by one order compared to piecewise linear approximation of the trimming curve. It is at the same time efficient, since essentially the computation of one extra one-dimensional integral on each trimmed cell is required. Finally, the method is easy to implement, since it only involves one additional line integral and refrains from any point inversion or optimization operations. The convergence is analyzed theoretically and numerical experiments confirm that the accuracy is improved without compromising the computational complexity.

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Reparameterization and Adaptive Quadrature for the Isogeometric Discontinuous Galerkin Method

Cited by 2 publications

References 13 publications

Discontinuous Galerkin isogeometric analysis for segmentations generating overlapping regions

Discontinuous Galerkin isogeometric analysis for segmentations generating overlapping regions

First Order Error Correction for Trimmed Quadrature in Isogeometric Analysis

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