### Abstract

A unified strategy for the higher-order accurate integration of implicitly defined geometries is proposed. The geometry is represented by a higher-order level-set function. The task is to integrate either on the zero-level set or in the sub-domains defined by the sign of the level-set function. In three dimensions, this is either an integration on a surface or inside a volume. A starting point is the identification and meshing of the zero-level set by means of higher-order interface elements. For the volume integration, special sub-elements are proposed where the element faces coincide with the identified interface elements on the zero-level set. Standard Gauss points are mapped onto the interface elements or into the volumetric sub-elements. The resulting integration points may, for example, be used in fictitious domain methods and extended finite element methods. For the case of hexahedral meshes, parts of the approach may also be seen as a higher-order marching cubes algorithm.

Originalsprache | englisch |
---|---|

Seiten (von - bis) | 323-371 |

Seitenumfang | 49 |

Fachzeitschrift | International journal for numerical methods in engineering |

Jahrgang | 106 |

Ausgabenummer | 5 |

DOIs | |

Publikationsstatus | Veröffentlicht - 4 Mai 2016 |

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### Schlagwörter

### ASJC Scopus subject areas

- Numerische Mathematik
- !!Engineering(all)
- Angewandte Mathematik

### Dies zitieren

*International journal for numerical methods in engineering*,

*106*(5), 323-371. https://doi.org/10.1002/nme.5121

**Higher-order accurate integration of implicit geometries.** / Fries, Thomas Peter; Omerovic, Samir.

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Forschung › Begutachtung

*International journal for numerical methods in engineering*, Jg. 106, Nr. 5, S. 323-371. https://doi.org/10.1002/nme.5121

}

TY - JOUR

T1 - Higher-order accurate integration of implicit geometries

AU - Fries, Thomas Peter

AU - Omerovic, Samir

PY - 2016/5/4

Y1 - 2016/5/4

N2 - A unified strategy for the higher-order accurate integration of implicitly defined geometries is proposed. The geometry is represented by a higher-order level-set function. The task is to integrate either on the zero-level set or in the sub-domains defined by the sign of the level-set function. In three dimensions, this is either an integration on a surface or inside a volume. A starting point is the identification and meshing of the zero-level set by means of higher-order interface elements. For the volume integration, special sub-elements are proposed where the element faces coincide with the identified interface elements on the zero-level set. Standard Gauss points are mapped onto the interface elements or into the volumetric sub-elements. The resulting integration points may, for example, be used in fictitious domain methods and extended finite element methods. For the case of hexahedral meshes, parts of the approach may also be seen as a higher-order marching cubes algorithm.

AB - A unified strategy for the higher-order accurate integration of implicitly defined geometries is proposed. The geometry is represented by a higher-order level-set function. The task is to integrate either on the zero-level set or in the sub-domains defined by the sign of the level-set function. In three dimensions, this is either an integration on a surface or inside a volume. A starting point is the identification and meshing of the zero-level set by means of higher-order interface elements. For the volume integration, special sub-elements are proposed where the element faces coincide with the identified interface elements on the zero-level set. Standard Gauss points are mapped onto the interface elements or into the volumetric sub-elements. The resulting integration points may, for example, be used in fictitious domain methods and extended finite element methods. For the case of hexahedral meshes, parts of the approach may also be seen as a higher-order marching cubes algorithm.

KW - Fictitious domain method

KW - GFEM

KW - Interface capturing

KW - Level-set method

KW - Numerical integration

KW - XFEM

UR - http://www.scopus.com/inward/record.url?scp=84962815220&partnerID=8YFLogxK

U2 - 10.1002/nme.5121

DO - 10.1002/nme.5121

M3 - Article

VL - 106

SP - 323

EP - 371

JO - International journal for numerical methods in engineering

JF - International journal for numerical methods in engineering

SN - 0029-5981

IS - 5

ER -