Quadrature schemes for arbitrary convex/concave volumes and integration of weak form in enriched partition of unity methods

Sudhakar, Y.; Wall, Wolfgang A.

doi:10.1016/j.cma.2013.01.007

Cited by 103 publications

(64 citation statements)

References 42 publications

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“…After spatial discretization, equation˛is going to be solved on mesh 1 andˇon 2 , respectively. Based on these partial differential equations, the discrete residuals r1 .p 1 ; q 1 / D 0 and r2 .p 2 ; q 2 / D 0 (45) 1564 P. FARAH ET AL.…”

Section: General Mesh Coupling Methodology For Monolithic Multiphysicsmentioning

confidence: 99%

Volumetric coupling approaches for multiphysics simulations on non‐matching meshes

Farah

Vuong

Wall

et al. 2016

Numerical Meth Engineering

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Summary In finite element analysis of volume coupled multiphysics, different meshes for the involved physical fields are often highly desirable in terms of solution accuracy and computational costs. We present a general methodology for volumetric coupling of different meshes within a monolithic solution scheme. A straightforward collocation approach is compared to a mortar‐based method for nodal information transfer. For the latter, dual shape functions based on the biorthogonality concept are used to build the projection matrices, thus further reducing the evaluation costs. We give a detailed explanation of the integration scheme and the construction of dual shape functions for general first‐order and second‐order Langrangian finite elements within the mortar method, as well as an analysis of the conservation properties of the projection operators. Moreover, possible incompatibilities due to different geometric approximations of curved boundaries are discussed. Numerical examples demonstrate the flexibility of the presented mortar approach for arbitrary finite element combinations in two and three dimensions and its applicability to different multiphysics coupling scenarios. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: General Mesh Coupling Methodology For Monolithic Multiphysicsmentioning

confidence: 99%

Volumetric coupling approaches for multiphysics simulations on non‐matching meshes

Farah

Vuong

Wall

et al. 2016

Numerical Meth Engineering

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“…Hence, in this work, we allow Γ i to exhibit large deformation, and the crack propagation through the structure introduces a thin opening in the fluid domain ( Figure 3). The recently developed robust numerical integration strategies [30][31][32] are used for the weak form integration. Advanced remeshing strategies are needed to handle these scenarios.…”

Section: The Strongly Coupled Partitioned Approachmentioning

confidence: 99%

A strongly coupled partitioned approach for fluid‐structure‐fracture interaction

Sudhakar

Wall

2018

Numerical Methods in Fluids

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Summary We present a novel method to model large deformation fluid‐structure‐fracture interaction, which is characterized by the fact that the fluid‐induced loads lead to fracture of the structure and the fluid medium fills the resulting crack opening; the mutual interaction between the crack faces and the surrounding fluid contributes substantially to the overall dynamics. A mesh refitting approach is used to model the quasi‐static fracture of the structure, and a robust embedded interface formulation is used to solve the fluid flow equations. The proposed method uses a strongly coupled partitioned scheme with Aitken's Δ2 method as convergence accelerator. Selected numerical examples of increasing complexity are presented to evaluate the performance of the proposed fluid‐structure‐fracture coupling algorithm. The most difficult simulation of the reported examples involves a number of complex phenomena: mixed‐mode crack propagation through the structure, fluid starts to fill the crack opening, complete fracture of the structure into two pieces of which one is carried away by the flow.

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“…These 2 approaches are satisfactory but can require quite large computational resources for the integration due to the large number of integration points, unless precomputed strategies like in the work of Yang et al 24 are considered. Recent contributions [25][26][27][28] propose to use moment fitting techniques [29][30][31] to construct integration rules on the fly. Blended integration cell methods have also been proposed to decrease the integration cost thanks to large mapped integration cells.…”

Section: Introductionmentioning

confidence: 99%

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

Legrain

Moës

2018

Numerical Meth Engineering

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Summary A novel integration scheme is proposed for fictitious domain finite element methods. It relies on the use of a surface tracking strategy based on anisotropic mesh adaptation. Thanks to an error estimator, the method builds iteratively an adapted anisotropic mesh that is refined near the geometrical interface and elongated in the direction of a small curvature. This strategy allows to decrease the integration cost, which can be problematic for high‐order fictitious domain methods. In addition, it opens the possibility for the creation of unfitted solid shell strategies that can be used for the treatment of thin structures. Numerical studies show that the method leads to promising results for both integration cost and behavior with respect to locking.

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Quadrature schemes for arbitrary convex/concave volumes and integration of weak form in enriched partition of unity methods

Cited by 103 publications

References 42 publications

Volumetric coupling approaches for multiphysics simulations on non‐matching meshes

Volumetric coupling approaches for multiphysics simulations on non‐matching meshes

A strongly coupled partitioned approach for fluid‐structure‐fracture interaction

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

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