Algebraically constrained extended edge element method (eXFEM-AC) for resolution of multi-material cells

Kramer, Richard Michael Jack; Bochev, Pavel B.; Siefert, Christopher; Voth, Thomas Eugene

doi:10.1016/j.jcp.2014.07.021

Cited by 5 publications

(9 citation statements)

References 24 publications

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“…The first major result is that the CDFEM spaces are subspaces of the corresponding XFEM-AC spaces. Two and three dimensional versions of this theorem have been developed [6,7,8].…”

Section: Equivalence Resultsmentioning

confidence: 99%

“…Rather than reproducing our previous articles, [6], [7], and [8], in their entirety here, we instead summarize their major results, both theoretical and computational. Two key theorems will be stated, but their proofs will be omitted since they have been published elsewhere.…”

Section: Xfem-ac and Cdfem For Nodes Edges And Facesmentioning

confidence: 97%

“…The second reason for choosing lowest order simplicies is that edge and face bases functions on these elements have very special properties. On a simplex, edge basis functions have a constant tangential component on any line [7,8] and face basis functions have a constant normal component on any plane [8]. These results are key to proving the equivalence of XFEM and CDFEM, which is summarized in Section 2.4.…”

Section: Discretizationsmentioning

confidence: 99%

“…CDFEM enriches cut elements by decomposing them into interfaceconforming sub-elements. Our XFEM-AC approach is applied to the full de Rahm complex (node, edges and faces) in 2D and 3D, and we develop a corresponding CDFEM method for cases where it has not previously been developed (edges and faces) [6,7,8]. We summarize these already published theoretical results in Chapter 2.…”

Section: Introductionmentioning

confidence: 99%

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Electromagnetic Extended Finite Elements for High-Fidelity Multimaterial Problems LDRD Final Report

Siefert

Bochev

Kramer

et al. 2014

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Surface effects are critical to the accurate simulation of electromagnetics (EM) as current tends to concentrate near material surfaces. Sandia EM applications, which include exploding bridge wires for detonator design, electromagnetic launch of flyer plates for material testing and gun design, lightning blast-through for weapon safety, electromagnetic armor, and magnetic flux compression generators, all require accurate resolution of surface effects. These applications operate in a large deformation regime, where body-fitted meshes are impractical and multimaterial elements are the only feasible option. State-of-the-art methods use various mixture models to approximate the multi-physics of these elements. The empirical nature of these models can significantly compromise the accuracy of the simulation in this very important surface region. We propose to substantially improve the predictive capability of electromagnetic simulations by removing the need for empirical mixture models at material surfaces. We do this by developing an eXtended Finite Element Method (XFEM) and an associated Conformal Decomposition Finite Element Method (CDFEM) which satisfy the physically required compatibility conditions at material interfaces. We demonstrate the effectiveness of these methods for diffusion and diffusion-like problems on node, edge and face elements in 2D and 3D. We also present preliminary work on h-hierarchical elements and remap algorithms.

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“…The first major result is that the CDFEM spaces are subspaces of the corresponding XFEM-AC spaces. Two and three dimensional versions of this theorem have been developed [6,7,8].…”

Section: Equivalence Resultsmentioning

confidence: 99%

Section: Xfem-ac and Cdfem For Nodes Edges And Facesmentioning

confidence: 97%

Section: Discretizationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electromagnetic Extended Finite Elements for High-Fidelity Multimaterial Problems LDRD Final Report

Siefert

Bochev

Kramer

et al. 2014

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“…The Conformal Decomposition Finite Element Method (CDFEM) [5,4] and the eXtended Finite Element Method with Algebraic Constraints (XFEM-AC) [2,3] are related approaches for resolution of sub-cell interfaces. In either case, a tetrahedral base (or 'parent') mesh supports an interface description, which does not conform to the mesh surfaces.…”

Section: Conformal Tetrahedron Cutting Introductionmentioning

confidence: 99%

Cutting Tetrahedra by Node Identifiers

Report

Kramer

2015

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This report briefly outlines an algorithm for dividing a tetrahedron intersected by a planar interface into conforming sub-tetrahedra. The problem of conformal decomposition of tetrahedral meshes arises in enriched finite element methods; in particular, we are concerned with the Conformal Decomposition Finite Element Method (CDFEM) and variants of the eXtended Finite Element Method (XFEM). The algorithm presented is based on the paper How to Subdivide Pyramids, Prisms and Hexahedra into Tetrahedra by Dompierre, Labbé, Vallet, and Camarero (1999), and here is applied and extended to the problem of fully defining and tracking all geometric features of the sub-tetrahedra generated when a tetrahedron is cut by a planar surface. Nodes Edges Faces 3/N4-F2 F

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An isoparametric tangled finite element method for handling higher-order elements with negative Jacobian

Prabhune

Suresh

2023

Comput Mech

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Algebraically constrained extended edge element method (eXFEM-AC) for resolution of multi-material cells

Cited by 5 publications

References 24 publications

Electromagnetic Extended Finite Elements for High-Fidelity Multimaterial Problems LDRD Final Report

Electromagnetic Extended Finite Elements for High-Fidelity Multimaterial Problems LDRD Final Report

Cutting Tetrahedra by Node Identifiers

An isoparametric tangled finite element method for handling higher-order elements with negative Jacobian

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