A higher-order conformal decomposition finite element method for plane B-rep geometries

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Abstract

A higher-order accurate conformal decomposition finite element method (CDFEM) is proposed, using an explicit boundary description of the domain. A level-set concept is introduced which converts the explicit B-rep geometry based on NURBSs to an implicit representation. This concept also applies to higher-order fictitious domain methods (FDMs) which are often based on implicit descriptions. In the proposed CDFEM, an arbitrary, non-conforming background mesh is introduced and manipulated to capture non-smooth features of the boundary such as corners and to ensure shape-regular elements. Elements that are cut by the boundary are decomposed into conforming sub-elements. The final mesh composed by higher-order Lagrange elements enables higher-order accurate approximations in the context of the FEM. Special emphasis is on the fact that NURBSs feature reduced continuity between knot spans which must be properly considered in the mesh generation, not only at corners.
Original languageEnglish
JournalComputers & structures
DOIs
Publication statusPublished - Dec 2018

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Decomposition Method
NURBS
Finite Element Method
Higher Order
Decomposition
Finite element method
Geometry
Mesh
Fictitious Domain Method
Regular Element
Higher Order Approximation
Mesh generation
High-order Methods
Mesh Generation
Level Set
Lagrange
Knot
Convert
Arbitrary
Concepts

Cite this

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title = "A higher-order conformal decomposition finite element method for plane B-rep geometries",
abstract = "A higher-order accurate conformal decomposition finite element method (CDFEM) is proposed, using an explicit boundary description of the domain. A level-set concept is introduced which converts the explicit B-rep geometry based on NURBSs to an implicit representation. This concept also applies to higher-order fictitious domain methods (FDMs) which are often based on implicit descriptions. In the proposed CDFEM, an arbitrary, non-conforming background mesh is introduced and manipulated to capture non-smooth features of the boundary such as corners and to ensure shape-regular elements. Elements that are cut by the boundary are decomposed into conforming sub-elements. The final mesh composed by higher-order Lagrange elements enables higher-order accurate approximations in the context of the FEM. Special emphasis is on the fact that NURBSs feature reduced continuity between knot spans which must be properly considered in the mesh generation, not only at corners.",
author = "Steidl, {Jakob Werner} and Fries, {Thomas Peter}",
year = "2018",
month = "12",
doi = "10.1016/j.compstruc.2018.12.006",
language = "English",
journal = "Computers & structures",
issn = "0045-7949",
publisher = "Elsevier Limited",

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N2 - A higher-order accurate conformal decomposition finite element method (CDFEM) is proposed, using an explicit boundary description of the domain. A level-set concept is introduced which converts the explicit B-rep geometry based on NURBSs to an implicit representation. This concept also applies to higher-order fictitious domain methods (FDMs) which are often based on implicit descriptions. In the proposed CDFEM, an arbitrary, non-conforming background mesh is introduced and manipulated to capture non-smooth features of the boundary such as corners and to ensure shape-regular elements. Elements that are cut by the boundary are decomposed into conforming sub-elements. The final mesh composed by higher-order Lagrange elements enables higher-order accurate approximations in the context of the FEM. Special emphasis is on the fact that NURBSs feature reduced continuity between knot spans which must be properly considered in the mesh generation, not only at corners.

AB - A higher-order accurate conformal decomposition finite element method (CDFEM) is proposed, using an explicit boundary description of the domain. A level-set concept is introduced which converts the explicit B-rep geometry based on NURBSs to an implicit representation. This concept also applies to higher-order fictitious domain methods (FDMs) which are often based on implicit descriptions. In the proposed CDFEM, an arbitrary, non-conforming background mesh is introduced and manipulated to capture non-smooth features of the boundary such as corners and to ensure shape-regular elements. Elements that are cut by the boundary are decomposed into conforming sub-elements. The final mesh composed by higher-order Lagrange elements enables higher-order accurate approximations in the context of the FEM. Special emphasis is on the fact that NURBSs feature reduced continuity between knot spans which must be properly considered in the mesh generation, not only at corners.

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DO - 10.1016/j.compstruc.2018.12.006

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JO - Computers & structures

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