A Coarsening Algorithm on Adaptive Grids by Newest Vertex Bisection and Its Applications

Чэн, Лонг; Zhang, Chen-Song

doi:10.4208/jcm.1004.m3172

Cited by 7 publications

(5 citation statements)

References 35 publications

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“…It uses a beautiful data structure to represent the mesh and also provides efficient MATLAB subroutines to manipulate the mesh (e.g. see [10,1]). In particular, local refinement and coarsening can be done fairly easily.…”

Section: Numerical Testsmentioning

confidence: 99%

Open and traction boundary conditions for the incompressible Navier–Stokes equations

Liu

2009

Journal of Computational Physics

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Section: Numerical Testsmentioning

confidence: 99%

Open and traction boundary conditions for the incompressible Navier–Stokes equations

Liu

2009

Journal of Computational Physics

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“…Similar to the refinement criterion, a Dörfler criterion is defined for coarsening as well, with θ c as the user-defined coarsening parameter. The earlier created array that contains the information about the added nodes by bisection helps in identifying the nodes that are suitable for coarsening [37]. Hence we cannot coarsen below the initial number of elements that we start with.…”

Section: Adaptive Variational Formulationmentioning

confidence: 99%

An Interface-Driven Adaptive Variational Procedure for Fully Eulerian Fluid-Structure Interaction via Phase-field Modeling

Rath¹,

Mao²,

Jaiman³

2021

Preprint

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In this study, we present a novel interface-driven adaptive technique using a fully Eulerian description for fluidstructure interaction. The proposed fully-Eulerian approach involves a fixed background mesh on which the interface is treated implicitly. The fluid-structure coupling is modeled by the phase-field finite element formulation comprising the convective Allen-Cahn equation coupled with the unified momentum equation for both solid and fluid. A bounded and stable solution of the Allen-Cahn equation is ensured via the positivity preserving variational formulation. The left Cauchy-Green deformation tensor is convected at each time step to trace the material coordinates in the Eulerian reference frame based on its initial position to evaluate the stresses correctly. The adaptive refinement/coarsening for the unstructured grid is determined by appropriate indicators and carried out by the newest vertex bisection algorithm. The proposed nonlinear adaptive partitioned procedure carries out the refining/coarsening steps at the first or last nonlinear iterations, hence ensuring the convergence of the nonlinear governing differential equations. We perform a detailed convergence and accuracy analysis via two benchmark problems namely, the pure solid system and a coupled fluid-solid system with an interface in a rectangle domain. We next systematically assess the performance of the adaptive procedure for the increasing complexity of problems. Finally, we demonstrate our fully-Eulerian interface-driven adaptive FSI model to simulate the contact problem between an elastic and rigid solid using a well-known bouncing elastic ball problem.

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“…Inspired by the coarsening algorithm in [9], we introduce new refinement/coarsening algorithms for quadrilateral meshes. Unlike the classical recursive refinement/coarsening procedures, the proposed algorithms are non-recursive and require neither storing nor maintaining refinement tree information such as the parents, brothers, generation, etc.…”

Section: An Adaptive Algorithm For Quadrilateral Meshesmentioning

confidence: 99%

“…Chen and Zhang [9] proposed a non recursive refinement/coarsening algorithm for triangular meshes which does not require storing the bisection tree explicitly. They only store coordinates of vertices and connectivity of triangles which are the minimal information required to represent a mesh for standard finite element computation.…”

Section: Introductionmentioning

confidence: 99%

“…We derive, for the presented 5-node transition element, a first-order a priori error estimate which is uniform with respect to the Lamé constant λ. Besides, we introduce new refinement/coarsening algorithms for quadrilateral meshes, which are counterparts of the algorithms by Chen and Zhang [9] for triangular meshes. And we present an adaptive finite element method based on the proposed hybrid stress transition elements.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Adaptive Hybrid Stress Transition Quadrilateral Finite Element Method for Linear Elasticity

Huang¹,

Xie²,

Zhang

2016

JCM

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In this paper, we discuss an adaptive hybrid stress finite element method on quadrilateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid stress quadrilateral elements with 5 to 7 nodes. In particular, we derive a priori error estimation for the 5-node transition hybrid stress element to show that it is free from Poisson-locking, in the sense that the error bound in the a priori estimate is independent of the Lamé constant λ. We introduce, for quadrilateral meshes, refinement/coarsening algorithms, which do not require storing the refinement tree explicitly, and give an adaptive algorithm. Finally we provide some numerical results.

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A Coarsening Algorithm on Adaptive Grids by Newest Vertex Bisection and Its Applications

Cited by 7 publications

References 35 publications

Open and traction boundary conditions for the incompressible Navier–Stokes equations

Open and traction boundary conditions for the incompressible Navier–Stokes equations

An Interface-Driven Adaptive Variational Procedure for Fully Eulerian Fluid-Structure Interaction via Phase-field Modeling

An Adaptive Hybrid Stress Transition Quadrilateral Finite Element Method for Linear Elasticity

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