Discontinuous Galerkin finite element simulations with polyhedral elements

Waltz, Caleb; Lee, Jin‐Fa

doi:10.1109/aps.2012.6349012

Cited by 1 publication

(2 citation statements)

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“…Sequences of the differentiation in (22) can be altered accordingly for other integration orders. General equations for exact integration of trivariate monomials over a three-dimensional domain can be derived when the integration limits , , , , , and in (22)…”

Section: Generalized Equations For Exact Integration Integration Limmentioning

confidence: 99%

“…Subsequently, the 2D PFEM has been extended to 3D PFEM [15,16]. 3D PFEM have been developed and implemented in various methods and fields, such as variable-element topology finite element method (VETFEM) [17], computer graphics [18][19][20], nonlinear continuum mechanics [21], electromagnetic simulations [22], boundary-element-based finite element methods (BEM-based FEM) [23,24], flow simulations, material design, and fracture [25].…”

Section: Introductionmentioning

confidence: 99%

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A Novel Virtual Node Hexahedral Element with Exact Integration and Octree Meshing

Perumal

2016

Mathematical Problems in Engineering

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The method presented in this work is a 3-dimensional polyhedral finite element (3D PFEM) based on virtual node method. Novel virtual node polyhedral elements (termed as VPHE) are developed here, particularly virtual node hexahedral element (termed as VHE). Stiffness matrices of these polyhedral elements consist of simple polynomials. Thus, a new algorithm is introduced in this paper, which enables exact integration of monomials without a need for high number of integration points and weights. The number of nodes for VHE elements is not restricted, as opposed to the conventional hexahedral elements. This feature enables formulation of transition elements (termed as T-VHE) which are useful to adaptive computation. Performances of the new VHE elements in solid mechanics and conductive heat transfer phenomena are examined through numerical simulations. The new T-VHE elements are utilized in octree mesh. The VHE elements are found to produce good results and T-VHE elements help to reduce number of global nodes for the analysis.

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Section: Generalized Equations For Exact Integration Integration Limmentioning

confidence: 99%