Methods for connecting dissimilar three-dimensional finite element meshes

Dohrmann, Clark R.; Key, Samuel W.; Heinstein, Martin W.

doi:10.1002/(sici)1097-0207(20000220)47:5<1057::aid-nme821>3.0.co;2-g

Cited by 59 publications

(30 citation statements)

References 10 publications

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“…14c. While searching the intersecting line, we also get four hex sets called intersecting-adjacent hex sets (IAH [4]), which surround the intersecting line (shown in different colors in Fig. 14d).…”

Section: Procedures For Determining the Quad Setmentioning

confidence: 99%

“…Considering a reuse-based scenario, for a complex CAD model, instead of meshing it from scratch, its hexahedral meshes are created by combining existing mesh models available by searching with CAD models. Obviously, the searched mesh models hardly conform on their interfaces.Currently, to obtain an integral solution based on the mesh model with non-conforming interfaces, it is necessary to impose constraints on the non-conforming interfaces, such as gap elements and multi-point constraints [2][3][4]. Nevertheless, when the mesh models are large and Abstract Mesh matching is an effective way to convert the non-conforming interfaces between two hexahedral meshes into conforming ones, which is very important for achieving high-quality finite element analysis.…”

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confidence: 99%

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An improved hexahedral mesh matching algorithm

Chen

Gao

Zhu

2015

Engineering with Computers

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generation. Until now, however, it has been too difficult to generate hexahedral meshes of complex CAD models automatically. As a result, a complex model that cannot be well meshed as a whole is usually decomposed into a number of components, each of which can be meshed automatically by certain algorithms, and then the hexahedral meshes of all the components are combined together as the resultant meshes of the whole CAD model. One problem regarding this method is that the interfaces between the hexahedral meshes of the components are usually non-conforming.Assembly meshing is a typical example. We usually mesh the assembly components, i.e., parts, separately, instead of the whole assembly together. Because each part of the assembly may be meshed by different FEA engineers, or using different meshing techniques, or taking different element density, the meshes of the parts often become non-conforming on the assembly interfaces.In addition to the assembly meshing problem, reusing of the existing hexahedral mesh models also encounters a problem regarding the non-conforming interfaces. Because the high-quality hexahedral mesh generation of complex CAD models is very difficult and time-consuming, the ability to reuse the existing hexahedral mesh models in the library whose size keeps expanding is becoming increasingly important. Considering a reuse-based scenario, for a complex CAD model, instead of meshing it from scratch, its hexahedral meshes are created by combining existing mesh models available by searching with CAD models. Obviously, the searched mesh models hardly conform on their interfaces.Currently, to obtain an integral solution based on the mesh model with non-conforming interfaces, it is necessary to impose constraints on the non-conforming interfaces, such as gap elements and multi-point constraints [2][3][4]. Nevertheless, when the mesh models are large and Abstract Mesh matching is an effective way to convert the non-conforming interfaces between two hexahedral meshes into conforming ones, which is very important for achieving high-quality finite element analysis. However, the existing mesh matching algorithm is neither efficient nor effective enough to handle complex interfaces and selfintersecting sheets. In this paper, the algorithm is improved in three aspects: (1) by introducing a more precise criteria for chord matching and the concept of partition chord set, complex interfaces with internal loops can be handled more effectively; (2) by proposing a new solution, self-intersecting sheet can be inflated and extracted locally; and (3) by putting forward a mesh quality evaluation method, the sheet extraction operation during mesh matching can be done more efficiently. Our improved mesh matching algorithm is fully automatic, and its effectiveness is demonstrated by several examples in different matching situations.

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Section: Procedures For Determining the Quad Setmentioning

confidence: 99%

mentioning

confidence: 99%

An improved hexahedral mesh matching algorithm

Chen

Gao

Zhu

2015

Engineering with Computers

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“…Surface coupling methods [8][9][10][11][12]18] start by selecting one of the non-matching interfaces as a master and the other as a slave surface. The approach of [10][11][12] defines Lagrange multipliers on the slave surface and uses a projection operator from the master surface.…”

Section: Specifics Of Mesh Tyingmentioning

confidence: 99%

“…The approach of [10][11][12] defines Lagrange multipliers on the slave surface and uses a projection operator from the master surface. The mesh-tying methods considered in [8,9,17,18] build additional mesh structures between the slave and master interfaces using tools that range from mesh imprinting to local L 2 projections. A disadvantage of these methods is that in order to maintain accuracy, typically six levels of uniform 3D mesh refinement are required near the boundary to pass the patch test approximately.…”

Section: Specifics Of Mesh Tyingmentioning

confidence: 99%

Analysis and computation of a least-squares method for consistent mesh tying

Day

Bochev

2008

Journal of Computational and Applied Mathematics

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In the finite element method, a standard approach to mesh tying is to apply Lagrange multipliers. If the interface is curved, however, discretization generally leads to adjoining surfaces that do not coincide spatially. Straightforward Lagrange multiplier methods lead to discrete formulations failing a first-order patch test [T.A. Laursen, M.W. Heinstein, Consistent mesh-tying methods for topologically distinct discretized surfaces in non-linear solid mechanics, Internat. J. Numer. Methods Eng. 57 (2003) 1197-1242].This paper presents a theoretical and computational study of a least-squares method for mesh tying [P. Bochev, D.M. Day, A leastsquares method for consistent mesh tying, Internat. J. Numer. Anal. Modeling 4 (2007) 342-352], applied to the partial differential equation −∇ 2 + = f . We prove optimal convergence rates for domains represented as overlapping subdomains and show that the least-squares method passes a patch test of the order of the finite element space by construction. To apply the method to subdomain configurations with gaps and overlaps we use interface perturbations to eliminate the gaps. Theoretical error estimates are illustrated by numerical experiments.

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“…In direct methods, the nodal variables on one interface are interpolated in terms of the variables on the other(s) [1][2][3][4]. Methods such as nearest neighbor interpolation [5], nearest element interpolation [6][7][8][9], radial basis interpolation schemes [10], variable-node methods [11][12][13] fall into this category. In the method of classical Lagrange multipliers, Lagrange multipliers are introduced as independent third variables and a weak form of the interface constraints are enforced.…”

Section: Introductionmentioning

confidence: 99%

A gap element for treating non-matching discrete interfaces

2015

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A family of gap elements are developed for treating non-matching interfaces occurring in partitioned analysis of mechanical systems. The proposed gap elements preserve linear and angular momentum and can be specialized to equivalent dual mortar methods, if desired. The proposed gap elements continue to be applicable when the interface gaps disappear, i.e., for flat interface surfaces and are free of energy injection or dissipation. Two dimensional numerical examples are offered to illustrate the basic features of the present gap elements.

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Methods for connecting dissimilar three-dimensional finite element meshes

Cited by 59 publications

References 10 publications

An improved hexahedral mesh matching algorithm

An improved hexahedral mesh matching algorithm

Analysis and computation of a least-squares method for consistent mesh tying

A gap element for treating non-matching discrete interfaces

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