Jacobian-based repair method for finite element meshes after registration
Registration methods are used in the meshing field to “adapt” a given mesh to a target domain. Finite element method (FEM) is applied to the resulting mesh to compute an approximate solution to the system of partial differential equations (PDE) representing the physical phenomena under study. Prior...
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Published in | Engineering with computers Vol. 27; no. 3; pp. 285 - 297 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
London
Springer-Verlag
01.07.2011
Springer Nature B.V Springer Verlag |
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Abstract | Registration methods are used in the meshing field to “adapt” a given mesh to a target domain. Finite element method (FEM) is applied to the resulting mesh to compute an approximate solution to the system of partial differential equations (PDE) representing the physical phenomena under study. Prior to FE analysis the Jacobian matrix determinant must be checked for all mesh elements. The value of this Jacobian depends on the configuration of the element nodes. If it is negative for a given node, the element is invalid and therefore the FE analysis cannot be carried out. Similarly, some elements, although valid, can present poor quality regarding Jacobian-based indicator values, such as the Jacobian ratio. Mesh registration procedures are likely to produce invalid and/or poor quality elements if the Jacobian parameter is ignored. To repair invalid and poor quality elements after mesh registration, we propose a relaxation procedure driven by specific validity and quality energy formulations derived from the Jacobian value. The algorithm first recovers mesh validity and further improves elements quality, focusing primarily on nodes that make the elements invalid or of poor quality. Our novel approach has been developed in the context of non-rigid mesh registration and validated on a data set of 60 clinical cases in the context of orthopaedic and orthognathic hard and soft tissues modelling studies. The proposed repair method achieves a valid state of the mesh and also raises the quality of the elements to a level suitable for commercial FE solvers. |
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AbstractList | Registration methods are used in the meshing field to "adapt" a given mesh to a target domain. Finite element method (FEM) is applied to the resulting mesh to compute an approximate solution to the system of partial differential equations (PDE) representing the physical phenomena under study. Prior to FE analysis the Jacobian matrix determinant must be checked for all mesh elements. The value of this Jacobian depends on the configuration of the element nodes. If it is negative for a given node, the element is invalid and therefore the FE analysis cannot be carried out. Similarly, some elements, although valid, can present poor quality regarding Jacobian-based indicator values, such as the Jacobian ratio. Mesh registration procedures are likely to produce invalid and/or poor quality elements if the Jacobian parameter is ignored. To repair invalid and poor quality elements after mesh registration, we propose a relaxation procedure driven by specific validity and quality energy formulations derived from the Jacobian value. The algorithm first recovers mesh validity and further improves elements quality, focusing primarily on nodes that make the elements invalid or of poor quality. Our novel approach has been developed in the context of non-rigid mesh registration and validated on a data set of 60 clinical cases in the context of orthopaedic and orthognathic hard and soft tissues modelling studies. The proposed repair method achieves a valid state of the mesh and also raises the quality of the elements to a level suitable for commercial FE solvers. Registration methods are used in the meshing field to "adapt" a given mesh to a target domain. Finite element method (FEM) is applied to the resulting mesh to compute an approximate solution to the system of partial differential equations (PDE) representing the physical phenomena under study. Prior to FE analysis the Jacobian matrix determinant must be checked for all mesh elements. The value of this Jacobian depends on the configuration of the element nodes. If it is negative for a given node, the element is invalid and therefore the FE analysis cannot be carried out. Similarly, some elements, although valid, can present poor quality regarding Jacobian-based indicator values, such as the Jacobian ratio. Mesh registration procedures are likely to produce invalid and/or poor quality elements if the Jacobian parameter is ignored. To repair invalid and poor quality elements after mesh registration, we propose a relaxation procedure driven by specific validity and quality energy formulations derived from the Jacobian value. The algorithm first recovers mesh validity and further improves elements quality, focusing primarily on nodes that make the elements invalid or of poor quality. Our novel approach has been developed in the context of non-rigid mesh registration and validated on a data set of 60 clinical cases in the context of orthopaedic and orthognathic hard and soft tissues modelling studies. The proposed repair method achieves a valid state of the mesh and also raises the quality of the elements to a level suitable for commercial FE solvers.[PUBLICATION ABSTRACT] |
Author | Hitschfeld, Nancy Bucki, Marek Lobos, Claudio Payan, Yohan |
Author_xml | – sequence: 1 givenname: Marek surname: Bucki fullname: Bucki, Marek organization: TIMC-IMAG UMR CNRS 5525, Pavillon Taillefer, Faculté de Médecine, Domaine de la Merci – sequence: 2 givenname: Claudio surname: Lobos fullname: Lobos, Claudio email: clobos@inf.utfsm.cl organization: Departamento de Informática, Universidad Técnica Federico Santa María – sequence: 3 givenname: Yohan surname: Payan fullname: Payan, Yohan organization: TIMC-IMAG UMR CNRS 5525, Pavillon Taillefer, Faculté de Médecine, Domaine de la Merci – sequence: 4 givenname: Nancy surname: Hitschfeld fullname: Hitschfeld, Nancy organization: Departamento de Ciencias de la Computación, Universidad de Chile |
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Cites_doi | 10.1016/S0965-9978(02)00065-0 10.1142/S021946781000372X 10.1016/S0165-1684(98)00143-1 10.1145/1073204.1073238 10.1080/10255840903505139 10.1016/j.media.2004.06.025 10.1016/j.cma.2005.02.016 10.1016/j.media.2010.02.003 10.1023/A:1008157432188 10.1016/S0021-9290(00)00055-5 10.1006/jcph.2001.6969 10.1002/(SICI)1097-0207(20000210)47:4<887::AID-NME804>3.0.CO;2-H 10.1016/j.cma.2003.08.004 10.1002/(SICI)1097-0207(20000720)48:8<1165::AID-NME940>3.0.CO;2-Y 10.1002/1097-0207(20000910/20)49:1/2<109::AID-NME925>3.0.CO;2-U 10.1080/10255840500289921 10.1007/3-540-45468-3_69 10.1007/3-540-45468-3_130 10.1007/978-3-540-30126-4_13 |
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Keywords | Finite element method Quality improvement Meshing Registration Mesh repair |
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References | Nesme, Faure, Payan (CR26) 2010; 10 Garimella, Shashkov, Knupp (CR11) 2004; 193 Montagnat, Delingette (CR24) 1998; 71 Montagnat, Delingette (CR25) 2005; 9 CR19 CR17 Delingette (CR7) 1999; 32 CR15 Freitag, Plassmann (CR10) 2000; 49 CR14 CR13 Knupp (CR16) 2000; 48 CR33 CR31 CR30 Bucki, Nazari, Payan (CR4) 2010; 14 George, Borouchaki, Laug (CR12) 2002; 33 Couteau, Payan, Lavallee (CR6) 2000; 33 CR2 Field (CR8) 2000; 47 CR5 Bucki, Lobos, Payan (CR3) 2010; 14 CR29 CR28 CR9 CR27 CR23 CR22 CR20 Knupp, Margolin, Shashkov (CR18) 2002; 176 Luboz, Chabanas, Swider, Payan (CR21) 2005; 8 Alliez, Cohen-Steiner, Yvinec, Desbrun (CR1) 2005; 24 Zhang, Bajaj (CR32) 2006; 195 198_CR28 198_CR29 198_CR27 R Garimella (198_CR11) 2004; 193 M Nesme (198_CR26) 2010; 10 V Luboz (198_CR21) 2005; 8 M Bucki (198_CR4) 2010; 14 D Field (198_CR8) 2000; 47 Y Zhang (198_CR32) 2006; 195 198_CR33 198_CR31 B Couteau (198_CR6) 2000; 33 198_CR30 198_CR19 198_CR5 198_CR2 198_CR17 198_CR15 L Freitag (198_CR10) 2000; 49 198_CR13 198_CR14 J Montagnat (198_CR24) 1998; 71 PM Knupp (198_CR18) 2002; 176 198_CR9 P Knupp (198_CR16) 2000; 48 P Alliez (198_CR1) 2005; 24 H Delingette (198_CR7) 1999; 32 M Bucki (198_CR3) 2010; 14 198_CR22 P George (198_CR12) 2002; 33 198_CR23 198_CR20 J Montagnat (198_CR25) 2005; 9 |
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Snippet | Registration methods are used in the meshing field to “adapt” a given mesh to a target domain. Finite element method (FEM) is applied to the resulting mesh to... Registration methods are used in the meshing field to "adapt" a given mesh to a target domain. Finite element method (FEM) is applied to the resulting mesh to... |
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SubjectTerms | Algorithms Bioengineering Biomechanics CAE) and Design Calculus of Variations and Optimal Control; Optimization Classical Mechanics Computer Science Computer-Aided Engineering (CAD Control Engineering Sciences Finite element method Focusing Jacobians Life Sciences Math. Applications in Chemistry Mathematical analysis Mathematical and Computational Engineering Mathematical models Mechanics Original Article Partial differential equations Physics Repair Systems Theory |
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Title | Jacobian-based repair method for finite element meshes after registration |
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