Evaluating Hex‐mesh Quality Metrics via Correlation Analysis
Hexahedral (hex‐) meshes are important for solving partial differential equations (PDEs) in applications of scientific computing and mechanical engineering. Many methods have been proposed aiming to generate hex‐meshes with high scaled Jacobians. While it is well established that a hex‐mesh should b...
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| Vydáno v: | Computer graphics forum Ročník 36; číslo 5; s. 105 - 116 |
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| Hlavní autoři: | , , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Oxford
Blackwell Publishing Ltd
01.08.2017
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | Hexahedral (hex‐) meshes are important for solving partial differential equations (PDEs) in applications of scientific computing and mechanical engineering. Many methods have been proposed aiming to generate hex‐meshes with high scaled Jacobians. While it is well established that a hex‐mesh should be inversion‐free (i.e. have a positive Jacobian measured at every corner of its hexahedron), it is not well‐studied that whether the scaled Jacobian is the most effective indicator of the quality of simulations performed on inversion‐free hex‐meshes given the existing dozens of quality metrics for hex‐meshes. Due to the challenge of precisely defining the relations among metrics, studying the correlations among different quality metrics and their correlations with the stability and accuracy of the simulations is a first and effective approach to address the above question. In this work, we propose a correlation analysis framework to systematically study these correlations. Specifically, given a large hex‐mesh dataset, we classify the existing quality metrics into groups based on their correlations, which characterizes their similarity in measuring the quality of hex‐elements. In addition, we rank the individual metrics based on their correlations with the accuracy and stability metrics for simulations that solve a number of elliptic PDE problems. Our preliminary experiments suggest that metrics that assess the conditioning of the elements are more correlated to the quality of solving elliptic PDEs than the others. Furthermore, an inversion‐free hex‐mesh with higher average quality (measured by any quality metrics) usually leads to a more accurate and stable computation of elliptic PDEs. To support our correlation study and address the lack of a publicly available large hex‐mesh dataset with sufficiently varying quality metric values, we also propose a two‐level perturbation strategy to generate the desired dataset from a small number of meshes to exclude the influences of element numbers, vertex connectivity, and volume sizes to our study. |
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| AbstractList | Hexahedral (hex‐) meshes are important for solving partial differential equations (PDEs) in applications of scientific computing and mechanical engineering. Many methods have been proposed aiming to generate hex‐meshes with high scaled Jacobians. While it is well established that a hex‐mesh should be inversion‐free (i.e. have a positive Jacobian measured at every corner of its hexahedron), it is not well‐studied that whether the scaled Jacobian is the most effective indicator of the quality of simulations performed on inversion‐free hex‐meshes given the existing dozens of quality metrics for hex‐meshes. Due to the challenge of precisely defining the relations among metrics, studying the correlations among different quality metrics and their correlations with the stability and accuracy of the simulations is a first and effective approach to address the above question. In this work, we propose a correlation analysis framework to systematically study these correlations. Specifically, given a large hex‐mesh dataset, we classify the existing quality metrics into groups based on their correlations, which characterizes their similarity in measuring the quality of hex‐elements. In addition, we rank the individual metrics based on their correlations with the accuracy and stability metrics for simulations that solve a number of elliptic PDE problems. Our preliminary experiments suggest that metrics that assess the conditioning of the elements are more correlated to the quality of solving elliptic PDEs than the others. Furthermore, an inversion‐free hex‐mesh with higher average quality (measured by any quality metrics) usually leads to a more accurate and stable computation of elliptic PDEs. To support our correlation study and address the lack of a publicly available large hex‐mesh dataset with sufficiently varying quality metric values, we also propose a two‐level perturbation strategy to generate the desired dataset from a small number of meshes to exclude the influences of element numbers, vertex connectivity, and volume sizes to our study. |
| Author | Gao, Xifeng Huang, Jin Chen, Guoning Xu, Kaoji Pan, Zherong Deng, Zhigang |
| Author_xml | – sequence: 1 givenname: Xifeng surname: Gao fullname: Gao, Xifeng organization: New york University – sequence: 2 givenname: Jin surname: Huang fullname: Huang, Jin organization: Zhejiang University – sequence: 3 givenname: Kaoji surname: Xu fullname: Xu, Kaoji organization: University of Houston – sequence: 4 givenname: Zherong surname: Pan fullname: Pan, Zherong organization: University of North Carolina at Chapel Hill – sequence: 5 givenname: Zhigang surname: Deng fullname: Deng, Zhigang organization: University of Houston – sequence: 6 givenname: Guoning surname: Chen fullname: Chen, Guoning organization: University of Houston |
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| Cites_doi | 10.1016/j.cad.2007.05.016 10.1016/0045-7825(92)90154-C 10.1111/j.1467-8659.2011.02015.x 10.1137/S0895479899351805 10.1002/nme.768 10.1115/SBC2010-19427 10.1016/j.cma.2007.02.009 10.1111/j.1467-8659.2011.02014.x 10.1007/s00357-014-9161-z 10.1145/2070781.2024177 10.1016/j.cma.2012.12.020 10.1145/2602141 10.1145/2508363.2508388 10.1109/TVCG.2013.250 10.1002/(SICI)1097-0207(20000530)48:3<401::AID-NME880>3.0.CO;2-D 10.1007/s00366-008-0091-4 10.1111/j.1467-8659.2006.01000.x 10.1016/j.cad.2014.08.020 10.1111/cgf.13007 10.1145/2897824.2925976 10.1016/j.medengphy.2005.12.006 10.1007/978-3-540-46375-7_5 10.1214/ss/1177012580 10.1007/s00366-004-0296-0 10.1016/0168-874X(92)90040-J 10.1016/j.proeng.2014.10.376 10.4028/www.scientific.net/MSF.670.318 10.1002/(SICI)1097-0207(20000720)48:8<1165::AID-NME940>3.0.CO;2-Y 10.1145/3250694 10.1016/S0010-4485(03)00079-4 10.1016/j.jbiomech.2011.05.006 10.1137/1.9780898719208 10.1007/BF01898350 10.1111/cgf.13021 10.1145/2766932 10.1137/1.9780898718003 10.1137/S1064827594271421 10.1145/2766941 10.1145/1391989.1391995 10.1145/1201775.882290 10.1007/978-3-642-04319-2_5 10.1109/MCSE.2006.105 10.1145/2366145.2366196 10.1007/s00366-014-0368-8 |
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| References | 2007; 39 2015; 34 1989; 4 1985; 1 1996; 17 2000; 48 2011 2010 2000; 21 2000; 8 2009 2011; 30 2008 2003; 58 2007 1995 2008; 35 2006 2012; 18 2004 2003 2002 1992; 12 2016; 35 1992; 94 2012; 31 2014; 20 2013; 19 2001 2000 2013; 32 2004; 36 2006; 28 2006; 25 2007; 196 2011; 44 2009; 344 2008; 24 2016 2015 2014 2013 2014; 33 1967 2003; 22 2014; 31 Livesu M. (e_1_2_8_38_2) 2015; 34 e_1_2_8_28_2 Kaufman L. (e_1_2_8_33_2) 2009 e_1_2_8_24_2 e_1_2_8_45_2 e_1_2_8_26_2 e_1_2_8_47_2 e_1_2_8_68_2 e_1_2_8_9_2 e_1_2_8_5_2 e_1_2_8_7_2 e_1_2_8_20_2 e_1_2_8_41_2 e_1_2_8_66_2 e_1_2_8_22_2 e_1_2_8_62_2 e_1_2_8_60_2 Wang K. (e_1_2_8_64_2) 2012; 18 e_1_2_8_17_2 e_1_2_8_19_2 e_1_2_8_13_2 e_1_2_8_34_2 e_1_2_8_59_2 e_1_2_8_36_2 e_1_2_8_57_2 e_1_2_8_30_2 e_1_2_8_55_2 e_1_2_8_11_2 e_1_2_8_32_2 e_1_2_8_53_2 Fang X. (e_1_2_8_15_2) 2016; 35 e_1_2_8_51_2 e_1_2_8_29_2 e_1_2_8_23_2 e_1_2_8_46_2 e_1_2_8_25_2 e_1_2_8_48_2 e_1_2_8_67_2 Muller‐Hannemann M. (e_1_2_8_43_2) 2001 e_1_2_8_4_2 e_1_2_8_6_2 e_1_2_8_8_2 e_1_2_8_42_2 e_1_2_8_65_2 e_1_2_8_21_2 e_1_2_8_44_2 e_1_2_8_63_2 e_1_2_8_61_2 e_1_2_8_40_2 e_1_2_8_16_2 e_1_2_8_39_2 e_1_2_8_18_2 e_1_2_8_12_2 e_1_2_8_58_2 e_1_2_8_14_2 e_1_2_8_37_2 e_1_2_8_56_2 Batchelor G.K. (e_1_2_8_2_2) 1967 Kazhdan M. (e_1_2_8_27_2) 2006 Li B. (e_1_2_8_35_2) 2013; 19 Bathe K.J. (e_1_2_8_3_2) 1995 e_1_2_8_31_2 Pébay P.P. (e_1_2_8_49_2) 2008 e_1_2_8_54_2 e_1_2_8_10_2 e_1_2_8_52_2 e_1_2_8_50_2 |
| References_xml | – volume: 34 issue: 4 year: 2015 article-title: Computational hydrographic printing publication-title: ACM Trans. Graph – start-page: 24 year: 2006 – year: 2001 – volume: 1 start-page: 69 issue: 2 year: 1985 end-page: 91 article-title: The plane with parallel coordinates publication-title: The Visual Computer – start-page: 88 year: 2013 end-page: 100 – volume: 35 start-page: 123:1 issue: 4 year: 2016 end-page: 123:11 article-title: Hexex: Robust hexahedral mesh extraction publication-title: ACM Trans. Graph – volume: 30 start-page: 143:1 issue: 6 year: 2011 end-page: 143:8 article-title: Boundary aligned smooth 3d cross‐frame field publication-title: ACM Trans. Graph – volume: 36 start-page: 203 issue: 3 year: 2004 end-page: 215 article-title: Automatic hexahedral mesh generation for multi‐domain composite models using a hybrid projective grid‐based method publication-title: Computer‐Aided Design – volume: 4 start-page: 73 issue: 2 year: 1989 end-page: 79 article-title: Francis Galton's account of the invention of correlation publication-title: Statist. Sci – volume: 21 start-page: 1300 issue: 4 year: 2000 end-page: 1317 article-title: Constraint preconditioning for indefinite linear systems publication-title: SIAM Journal on Matrix Analysis and Applications – year: 2014 – start-page: 1 year: 2014 end-page: 15 – start-page: 286 year: 2004 end-page: 293 – volume: 344 year: 2009 – year: 2008 – start-page: 318 year: 2011 end-page: 324 – volume: 44 start-page: 2337 issue: 22 year: 2011 end-page: 2343 article-title: Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear publication-title: Journal of Biomechanics – volume: 33 start-page: 25:1 issue: 3 year: 2014 end-page: 25:11 article-title: L1‐based construction of polycube maps from complex shapes publication-title: ACM Trans. Graph – year: 2015 – volume: 19 start-page: 1539 issue: 9 year: 2013 end-page: 1551 article-title: Surface mesh to volumetric spline conversion with generalized poly‐cubes publication-title: IEEE TVCG – volume: 32 start-page: 171:1 issue: 6 year: 2013 end-page: 171:12 article-title: Polycut: Monotone graph‐cuts for polycube base‐complex construction publication-title: ACM Trans. Graph – volume: 39 start-page: 914 issue: 10 year: 2007 end-page: 928 article-title: Adaptive generation of hexahedral element mesh using an improved grid‐based method publication-title: Computer‐Aided Design – volume: 35 start-page: 22 issue: 3 year: 2008 article-title: Algorithm 887: Cholmod, supernodal sparse cholesky factorization and update/downdate publication-title: ACM Transactions on Mathematical Software (TOMS) – start-page: 101 year: 2014 end-page: 113 – volume: 30 start-page: 1397 issue: 5 year: 2011 end-page: 1406 article-title: Cubecover‐parameterization of 3d volumes publication-title: Comput. Graph. Forum – volume: 22 start-page: 445 year: 2003 end-page: 452 – year: 2007 – year: 2003 – start-page: 61 year: 2006 end-page: 70 – volume: 24 start-page: 195 issue: 3 year: 2008 end-page: 213 article-title: Hexahedral mesh generation constraints publication-title: Eng. with Comput – volume: 48 start-page: 401 year: 2000 end-page: 420 article-title: Achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities. part i‐a framework for surface mesh optimization publication-title: International Journal for Numerical Methods in Engineering – volume: 31 start-page: 177:1 issue: 6 year: 2012 end-page: 177:11 article-title: All‐hex meshing using singularity‐restricted field publication-title: ACM Trans. Graph – start-page: 65 year: 2009 end-page: 84 – year: 2016 – volume: 34 issue: 4 year: 2015 article-title: Practical hex‐mesh optimization via edge‐cone rectification publication-title: Transactions on Graphics (Proc. SIGGRAPH 2015) – start-page: 535 year: 2008 end-page: 552 – volume: 25 start-page: 809 year: 2006 end-page: 836 – volume: 31 start-page: 274 issue: 3 year: 2014 end-page: 295 article-title: Ward's hierarchical agglomerative clustering method: Which algorithms implement ward's criterion? publication-title: Journal of Classification – year: 2010 – volume: 196 start-page: 2943 issue: 29 year: 2007 end-page: 2959 article-title: Patient‐specific vascular nurbs modeling for isogeometric analysis of blood flow publication-title: Computer methods in applied mechanics and engineering – start-page: 173 year: 2000 end-page: 183 – volume: 58 start-page: 319 issue: 2 year: 2003 end-page: 332 article-title: A method for hexahedral mesh shape optimization publication-title: International Journal for Numerical Methods in Engineering – year: 1967 – volume: 35 issue: 4 year: 2016 article-title: All‐hex meshing using closed‐form induced polycube publication-title: Transactions on Graphics (Proc. SIGGRAPH 2016) – year: 2002 – volume: 30 start-page: 1407 issue: 5 year: 2011 end-page: 1416 article-title: All‐hex mesh generation via volumetric polycube deformation publication-title: Computer Graphics Forum (Special Issue of Symposium on Geometry Processing 2011) – volume: 18 issue: 5 year: 2012 article-title: Restricted trivariate polycube splines for volumetric data modeling publication-title: IEEE Transactions on Visualization and Computer Graphics – start-page: 239 year: 2003 end-page: 250 – volume: 20 start-page: 1189 issue: 8 year: 2014 end-page: 1199 article-title: Frame field singularity correction for automatic hexahedralization publication-title: IEEE Trans. Vis. Comput. Graphics – volume: 34 start-page: 142:1 issue: 4 year: 2015 end-page: 142:10 article-title: Hexahedral mesh reparameterization from aligned base‐complex publication-title: ACM Trans. Graph – year: 1995 – volume: 8 start-page: 1165 year: 2000 end-page: 1185 article-title: Achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities. part ii‐a framework for volume mesh optimization and the condition number of the jacobian matrix publication-title: International Journal for numerical methods in engineering – start-page: 179 year: 1995 end-page: 191 – volume: 94 start-page: 13 issue: 1 year: 1992 end-page: 23 article-title: An orthogonal accelerated deflation technique for large symmetric eigenproblems publication-title: Computer methods in applied mechanics and engineering – volume: 12 start-page: 313 year: 1992 end-page: 318 article-title: A performance study of tetrahedral and hexahedral elements in 3‐d finite element structural analysis publication-title: Finite Elements in Analysis and Design – volume: 28 start-page: 916 issue: 9 year: 2006 end-page: 924 article-title: Tetrahedral versus hexahedral finite elements in numerical modelling of the proximal femur publication-title: Medical Engineering & Physics – volume: 17 start-page: 1135 issue: 5 year: 1996 end-page: 1149 article-title: A sparse approximate inverse preconditioner for the conjugate gradient method publication-title: SIAM Journal on Scientific Computing – volume: 35 start-page: 97 year: 2016 end-page: 106 – start-page: 53 year: 2007 end-page: 62 – volume: 35 start-page: 237 year: 2016 end-page: 246 – volume: 18 issue: 5 year: 2012 ident: e_1_2_8_64_2 article-title: Restricted trivariate polycube splines for volumetric data modeling publication-title: IEEE Transactions on Visualization and Computer Graphics – ident: e_1_2_8_68_2 doi: 10.1016/j.cad.2007.05.016 – ident: e_1_2_8_19_2 doi: 10.1016/0045-7825(92)90154-C – ident: e_1_2_8_20_2 doi: 10.1111/j.1467-8659.2011.02015.x – ident: e_1_2_8_28_2 doi: 10.1137/S0895479899351805 – ident: e_1_2_8_32_2 doi: 10.1002/nme.768 – ident: e_1_2_8_8_2 – ident: e_1_2_8_61_2 doi: 10.1115/SBC2010-19427 – ident: e_1_2_8_65_2 doi: 10.1016/j.cma.2007.02.009 – ident: e_1_2_8_47_2 doi: 10.1111/j.1467-8659.2011.02014.x – ident: e_1_2_8_44_2 doi: 10.1007/s00357-014-9161-z – ident: e_1_2_8_23_2 doi: 10.1145/2070781.2024177 – ident: e_1_2_8_53_2 – start-page: 61 volume-title: Proceedings of the fourth Eurographics symposium on Geometry processing year: 2006 ident: e_1_2_8_27_2 – volume: 34 issue: 4 year: 2015 ident: e_1_2_8_38_2 article-title: Practical hex‐mesh optimization via edge‐cone rectification publication-title: Transactions on Graphics (Proc. SIGGRAPH 2015) – ident: e_1_2_8_66_2 doi: 10.1016/j.cma.2012.12.020 – ident: e_1_2_8_18_2 – ident: e_1_2_8_26_2 – volume-title: Finding groups in data: an introduction to cluster analysis year: 2009 ident: e_1_2_8_33_2 – ident: e_1_2_8_31_2 – volume-title: Finite Element Procedures in Engineering Analysis year: 1995 ident: e_1_2_8_3_2 – ident: e_1_2_8_22_2 doi: 10.1145/2602141 – ident: e_1_2_8_39_2 doi: 10.1145/2508363.2508388 – ident: e_1_2_8_25_2 doi: 10.1109/TVCG.2013.250 – ident: e_1_2_8_29_2 doi: 10.1002/(SICI)1097-0207(20000530)48:3<401::AID-NME880>3.0.CO;2-D – ident: e_1_2_8_57_2 doi: 10.1007/s00366-008-0091-4 – ident: e_1_2_8_46_2 doi: 10.1111/j.1467-8659.2006.01000.x – ident: e_1_2_8_40_2 doi: 10.1016/j.cad.2014.08.020 – volume-title: An introduction to fluid dynamics year: 1967 ident: e_1_2_8_2_2 – ident: e_1_2_8_14_2 doi: 10.1111/cgf.13007 – ident: e_1_2_8_55_2 – ident: e_1_2_8_34_2 doi: 10.1145/2897824.2925976 – ident: e_1_2_8_51_2 doi: 10.1016/j.medengphy.2005.12.006 – ident: e_1_2_8_5_2 – ident: e_1_2_8_21_2 doi: 10.1007/978-3-540-46375-7_5 – ident: e_1_2_8_59_2 doi: 10.1214/ss/1177012580 – ident: e_1_2_8_60_2 doi: 10.1007/s00366-004-0296-0 – ident: e_1_2_8_16_2 – volume: 35 issue: 4 year: 2016 ident: e_1_2_8_15_2 article-title: All‐hex meshing using closed‐form induced polycube publication-title: Transactions on Graphics (Proc. SIGGRAPH 2016) – volume: 19 start-page: 1539 issue: 9 year: 2013 ident: e_1_2_8_35_2 article-title: Surface mesh to volumetric spline conversion with generalized poly‐cubes publication-title: IEEE TVCG – ident: e_1_2_8_12_2 doi: 10.1016/0168-874X(92)90040-J – ident: e_1_2_8_50_2 doi: 10.1016/j.proeng.2014.10.376 – ident: e_1_2_8_45_2 doi: 10.4028/www.scientific.net/MSF.670.318 – ident: e_1_2_8_54_2 – ident: e_1_2_8_30_2 doi: 10.1002/(SICI)1097-0207(20000720)48:8<1165::AID-NME940>3.0.CO;2-Y – ident: e_1_2_8_56_2 doi: 10.1145/3250694 – ident: e_1_2_8_58_2 doi: 10.1016/S0010-4485(03)00079-4 – ident: e_1_2_8_62_2 doi: 10.1016/j.jbiomech.2011.05.006 – ident: e_1_2_8_11_2 doi: 10.1137/1.9780898719208 – ident: e_1_2_8_24_2 doi: 10.1007/BF01898350 – ident: e_1_2_8_37_2 doi: 10.1111/cgf.13021 – ident: e_1_2_8_42_2 – ident: e_1_2_8_67_2 doi: 10.1145/2766932 – ident: e_1_2_8_52_2 doi: 10.1137/1.9780898718003 – ident: e_1_2_8_6_2 doi: 10.1137/S1064827594271421 – ident: e_1_2_8_17_2 doi: 10.1145/2766941 – ident: e_1_2_8_9_2 doi: 10.1145/1391989.1391995 – ident: e_1_2_8_63_2 doi: 10.1145/1201775.882290 – ident: e_1_2_8_41_2 doi: 10.1007/978-3-642-04319-2_5 – start-page: 535 volume-title: New Applications of the Verdict Library for Standardized Mesh Verification Pre, Post, and End‐to‐End Processing year: 2008 ident: e_1_2_8_49_2 – ident: e_1_2_8_7_2 – volume-title: Anisotropic Validation of Hexahedral Meshes for Composite Materials in Biomechanics year: 2001 ident: e_1_2_8_43_2 – ident: e_1_2_8_13_2 doi: 10.1109/MCSE.2006.105 – ident: e_1_2_8_4_2 – ident: e_1_2_8_36_2 doi: 10.1145/2366145.2366196 – ident: e_1_2_8_10_2 – ident: e_1_2_8_48_2 doi: 10.1007/s00366-014-0368-8 |
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| Title | Evaluating Hex‐mesh Quality Metrics via Correlation Analysis |
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