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Overlapping Multi-Patch Structures in Isogeometric Analysis

Abstract : In isogeometric analysis (IGA) the domain of interest is usually represented by B-spline or NURBS patches, as they are present in standard CAD models. Complex domains can often be represented as a union of simple overlapping subdomains, parameterized by (tensor-product) spline patches. Numerical simulation on such overlapping multi-patch domains is a serious challenge in IGA. To obtain non-overlapping subdomains one would usually reparameterize the domain or trim some of the patches. Alternatively, one may use methods that can handle overlapping subdomains. In this paper, we propose a non-iterative, robust and efficient method defined directly on overlapping multi-patch domains. Consequently, the problem is divided into several sub-problems, which are coupled in an appropriate way. The resulting system can be solved directly in a single step. We compare the proposed method with iterative Schwarz domain decomposition approaches and observe that our method reduces the computational cost significantly, especially when handling subdomains with small overlaps. Summing up, our method significantly simplifies the domain parameterization problem, since we can represent any domain of interest as a union of overlapping patches without the need to introduce trimming curves/surfaces. The performance of the proposed method is demonstrated by several numerical experiments for the Poisson problem and linear elasticity in two and three dimensions.
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https://hal.inria.fr/hal-02197673
Contributor : Angelos Mantzaflaris <>
Submitted on : Tuesday, July 30, 2019 - 3:30:16 PM
Last modification on : Thursday, November 26, 2020 - 3:50:03 PM

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Somayeh Kargaran, Bert Jüttler, Stefan Kleiss, Angelos Mantzaflaris, Thomas Takacs. Overlapping Multi-Patch Structures in Isogeometric Analysis. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2019, 356, pp.325-353. ⟨10.1016/j.cma.2019.07.010⟩. ⟨hal-02197673⟩

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