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3D Mesh Generation in Geocomputing

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Advances in Geocomputing

Part of the book series: Lecture Notes in Earth Sciences ((LNEARTH,volume 119))

Abstract

Mesh generation has been widely used in engineering computing, but seems to be relatively “new" for geoscience community. This paper firstly lists such relevant progresses of mesh generation for the engineering computing and then discusses the possibility for applying/extending them to geoscience computing (i.e. geocomputing). for geoscience, the available input data are normally a large quantity of point data in the 3D space rather than the defined shapes and dimensions with reasonable tolerances provided by the industrial designers, thus quite different from the engineering cases. To deal with such geoscience data, this paper briefly introduces the relevant progresses on geometrical modeling, hexahedral and tetrahedral shaped mesh generation, and then focuses on the applying and/or extending the related methods to generate all hexahedral/tetrahedral shaped meshes in 3D for geoscience purposes, which is described through the different practical application examples, such as the all-hexahedral shaped mesh generation for a fracture dominated reservoir system, the South Australia interacting fault system and the entire earth model without or with the simplified/practical plate boundaries; and all-tetrahedral shaped mesh generation for a multi-layer un- derground geological model, and visualizing and meshing with the microseismicity data recorded during a hydraulic stimulation process in a geothermal reservoir.

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References

  • Baker TJ (1989) Automatic Mesh Generation for Complex Three-Dimensional Regions Using a Constrained Delaunay Triangulation. Engineering with Computers, Vol 5 pp 161–175

    Article  Google Scholar 

  • Blacker T and Stephenson MB (1991) Paving: A New Approach to Automated Quadrilateral Mesh Generation. International Journal for Numerical Methods in Engineering, Vol 32 pp 811–847

    Article  Google Scholar 

  • Borouchaki H and Frey PJ (1998) Adaptive Trangular-Quadrilateral Mesh Generation. International Journal for Numerical Methods in Engineering, Vol 41 pp 915–934

    Article  Google Scholar 

  • Borouchaki H and George PL (1997) Aspects of 2-D Delaunay Mesh Generation. International Journal for Numerical Methods in Engineering, Vol 40 pp 1957–1975

    Article  Google Scholar 

  • Borouchaki H, George PL and Lo SH (1996) Optimal Delaunay Point Insertion. International Journal for Numerical Methods in Engineering, Vol 39 pp 3407–3437

    Article  Google Scholar 

  • Borouchaki H, Laug P and George PL (2000) Parametric Surface Meshing Using a Combined Advancing-Front Generalized Delaunay Approach. International Journal for Numerical Methods in Engineering, Vol 49 pp 233–259

    Article  Google Scholar 

  • Borouchaki H and Lo SH (1995) Fast Delaunay Triangulation in Three Dimensions. Computer Methods in Applied Mechanics and Engineering, Vol 128 pp 153–167

    Article  Google Scholar 

  • Calvo NA and Idelsohm SR (2000) All-Hexahedral Element Meshing: Generation of the Dual Mesh by Recurrent Subdivision. Computer Methods in Applied Mechanics and Engineering, Vol 182 pp 371–378

    Article  Google Scholar 

  • Cheng GD and Li H (1996) New Method for Graded Mesh Generation of Quadrilateral Finite Elements. Computers and Structures, Vol 59 Num 5 pp 823–829

    Google Scholar 

  • Chiba N, Nishigaki I, Yamashita Y, Takizawa C and Fujishiro K (1998) A Flexible Automatic Hexahedral Mesh Generation by Boundary-Fit Method. Computer Methods in Applied Mechanics and Engineering, Vol 161 pp 145–154

    Article  Google Scholar 

  • Delaunay BN (1934) Sur la Sphere. Vide. Izvestia Akademia Nauk SSSR, VII Seria, Otdelenie Matematicheskii i Estestvennyka Nauk, Vol 7 pp 793–800

    Google Scholar 

  • Dewhirst D, Vangavolu S, Wattrick H (1995) The Combination of Hexahedral and Tetrahedral Meshing Algorithms. Proceeding 4th International Meshing Roundtable pp 291–304

    Google Scholar 

  • Du Q and Wang DS (2003) Tetrahedral Mesh Generation and Optimization Based on Centroidal Voronoi Tessellations. International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 56 Num 9 pp 1355–1373

    Article  Google Scholar 

  • Dziewonski AD and Anderson DL (1981) Preliminary Reference Earth Model. Physics of the Earth and Planetary Interiors, Vol 25 Num 2 pp 97–356

    Google Scholar 

  • Frey P, Benoit S and Gautherie M (1994) Fully Automatic Mesh Generation for 3- D Domains Based Upon Voxel Sets. International Journal for Numerical Methods in Engineering, John Wiley, Num 37 pp 2735–2753

    Article  Google Scholar 

  • George PL (1997) Improvements on Delaunay-Based Three-Dimensional Automatic Mesh Generator. Finite Elements in Analysis and Design, Elsevier, Vol 25 pp 297–317

    Article  Google Scholar 

  • George PL, Hecht F and Saltel E (1991) Automatic Mesh Generator with Specified Boundary. Computer Methods in Applied Mechanics and Engineering, North-Holland, Vol 92 pp 269–288

    Google Scholar 

  • George PL and Seveno E (1994) The Advancing-Front Mesh Generation Method Revisited. International Journal for Numerical Methods in Engineering, Wiley, Vol 37 pp 3605–3619

    Article  Google Scholar 

  • Hariya M, Nishigaki I, Kataoka I, Hiro Y (2006) Automatic Hexahedral Mesh Generation with Feature Line Extraction. Proceeding 15th Round Table Meshing pp 453–468

    Google Scholar 

  • Joe B (1991a) GEOMPACK – A Software Package for the Generation of Meshes Using Geometric Algorithms. Advances in Engineering Software, Elsevier, Vol 13 Num 5 pp 325–331

    Google Scholar 

  • Joe B (1991b) Construction of Three-Dimensional Delaunay Triangulations Using Local Transformations. Computer Aided Geometric Design, Elsevier Science Publishers (North-Holland), Num 8 pp 123–142

    Article  Google Scholar 

  • Joe B (1991c) Delaunay Versus Max–Min Solid Angle Triangulations For Three- Dimensional Mesh Generation. International Journal for Numerical Methods in Engineering, John Wiley & Sons, Vol 31 pp 987–997

    Article  Google Scholar 

  • Joe B (1995) Construction of Three-Dimensional Improved-Quality Triangulations Using Local Transformations. SIAM Journal of Science Computing, Vol 16 pp 1292–1307

    Article  Google Scholar 

  • Kageyama A and Sato T (2004) The ‘Yin-Yang Grid’: An Overset Grid in Spherical Geometry. Geochem. Geophys. Geosyst., Q09005, doi:10.1029/2004GC000734

    Google Scholar 

  • Kanai T, Makinouchi A, Oishi Y (2000) Development of Tectonic CAD/Database Systems. In Abstracts of International Workshop on Solid Earth Simulation and ACES WG Meeting (Ed. Mitsu’ura M et al.). Tokyo, Jan 17–21

    Google Scholar 

  • Knupp PM (1998) Next-Generation Sweep Tool: A Method For Generating All- Hex Meshes on Two-And-One-Half Dimensional Geomtries. Proceedings the 7th International Meshing Roundtable pp 505–513

    Google Scholar 

  • Knupp PM (1999) Applications of Mesh Smoothing: Copy, Morph, and Sweep on Unstructured Quadrilateral Meshes. International Journal for Numerical Methods in Engineering, Wiley, Vol 45 pp 37–45

    Article  Google Scholar 

  • Lai MW, Benzley S and White D (2000) Automated Hexahedral Mesh Generation by Generalized Multiple Source to Multiple Target Sweeping. International Journal for Numerical Methods in Engineering, John Wiley, Vol 49 Num 1 pp 261–275

    Article  Google Scholar 

  • Lau TS and Lo SH (1996) Finite Element Mesh Generation Over Analytical Surfaces. Computers and Structures, Elsevier Science Ltd., Vol 59 Num 2 pp 301–309

    Google Scholar 

  • Lee CK (2003) Automatic Metric 3D Surface Mesh Generation Using Subdivision Surface Geometrical Model. Part 2: Mesh Generation Algorithm and Examples. International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 56 Num 11 pp 1615–1646

    Article  Google Scholar 

  • Lee CK and Hobbs RE (1999) Automatic Adaptive Finite Element Mesh Generation Over Arbitrary Two-Dimensional Domain Using Advancing Front Technique. Computers and Structures Pergammon, Vol 71 pp 9–34

    Article  Google Scholar 

  • Lee YK and Lee CK (2002) Automatic Generation of Anisotropic Quadrilateral Meshes on Three-Dimensional Surfaces Using Metric Specifications. International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 53 Num 12 pp 2673–2700

    Article  Google Scholar 

  • Lee YK, Lee CK (2003) A New Indirect Anisotropic Quadrilateral Mesh Generation Scheme with Enhanced Local Mesh Smoothing Procedures. International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 58 Num 2 pp 277–300

    Article  Google Scholar 

  • Lee CK and Lo SH (1994) A New Scheme for the Generation of a Graded Quadrilateral Mesh. Computers and Structures Pergammon Vol 52 Num 5 pp 847–857

    Article  Google Scholar 

  • Lee DT and Schacter BJ (1980) Two Algorithms for Constructing a Delaunay Triangulation. International Journal of Computer and Information Sciences, Vol 3 Num 9 pp 219–242

    Article  Google Scholar 

  • Leland RW, Melander D, Meyers R, Mitchell S, Tautges T (1998) The Geode Algorithm: Combining Hex/Tet Plastering, Dicing and Transition Elements for Automatic, All-Hex Mesh Generation. Proceeding 7th International Meshing Roundtable pp 515–521

    Google Scholar 

  • Lo SH (1991a) Volume Discretization into Tetrahedra-I. Verification and Orientation of Boundary Surfaces. Computers and Structures, Pergamon Press, Vol 39 Num 5 pp 493–500

    Article  Google Scholar 

  • Lo SH (1991b) Volume Discretization into Tetrahedra – II. 3D Triangulation by Advancing Front Approach. Computers and Structures Pergamon, Vol 39 Num 5 pp 501–511

    Article  Google Scholar 

  • Lo SH (1992) Generation of High Quality Gradation Finite Element Mesh. Engineering Fracture Mechanics, Pergamon, Vol 2 Num 41 pp 191–202

    Article  Google Scholar 

  • Lohner R (1996a) Progress in Grid Generation via the Advancing Front Technique. Engineering with Computers, Springer-Verlag, Vol 12 pp 186–210

    Article  Google Scholar 

  • Lohner R (1996b) Extensions and Improvements of the Advancing Front Grid Generation Technique. Communications in Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 12 pp 683–702

    Article  Google Scholar 

  • Lohner R (1996c) Regridding Surface Triangulations. Journal of Computational Physics, Academic Press, Vol 126 pp 1–10

    Google Scholar 

  • Lohner R and Cebral JR (2000) Generation of Non-Isotropic Unstructured Grids via Directional Enrichment. International Journal for Numerical Methods in Engineering, John Wiley, Vol 49 Num 1 pp 219–232

    Article  Google Scholar 

  • Lohner R and Eugenio O (1998) An Advancing Front Point Generation Technique. Communications in Numerical Methods in Engineering, Wiley, Vol 14 pp 1097–1108

    Article  Google Scholar 

  • Loic M (2001) A New Approach to Octree-Based Hexahedral Meshing. Proceedings 10th International Meshing Roundtable, pp 209–221

    Google Scholar 

  • Owen SJ, Canann S, Siagal S (1997) Pyramid Elements for Maintaining Tetrahedra to Hexahedra Conformability. Trends in Unstructured Mesh Generation AMD, Vol 220 pp 123–129

    Google Scholar 

  • Owen SJ, Saigal S (2000) H-Morph: An Indirect Approach to Advancing Front Hex Meshing. International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd.. Vol 49 Num 1–2 pp 289–312

    Google Scholar 

  • Owen SJ, Staten ML, Canann SA and Saigal S (1999) Q-Morph: An Indirect Approach to Advancing Front Quad Meshing. International Journal for Numerical Methods in Engineering, Wiley, Vol 9 Num 44 pp 1317–1340

    Article  Google Scholar 

  • Ray M, Tautges T, Tuchinsky P (1998) The “Hex-Tet" Hex-Dominant Meshing Algorithm as Implemented in CUBIT. Proceeding 7th International Meshing Roundtable pp 151–158

    Google Scholar 

  • Rosenbaum G, Lister GS and Duboz C (2002) Reconstruction of the tectonic evolution of the western Mediterranean since the Oligocene. In: Rosenbaum, G. and Lister, G. S. 2002. Reconstruction of the evolution of the Alpine- Himalayan Orogen. Journal of the Virtual Explorer, Vol 8 pp 107–126

    Google Scholar 

  • Schneiders R (1996) A Grid-Based Algorithm for the Generation of Hexahedral Element Meshes. Engineering with Computers, Vol 12 pp 168–177

    Article  Google Scholar 

  • Schneiders R (1997) An Algorithm for the Generation of Hexahedral Element Meshes Based on an Octree Technique. Proceedings 6th International Meshing Roundtable pp 183–194

    Google Scholar 

  • Schneiders R and Bunten R (1995) Automatic Generation of Hexahedral Finite Element Meshes. Computer Aided Geometric Design, Elsevier, Vol 12 pp 693–707

    Article  Google Scholar 

  • Schneiders R, Schindler R and Weiler F (1996) Octree-Based Generation of Hexahedral Element Meshes. Proceedings 5th International Meshing Roundtable pp 205–216

    Google Scholar 

  • Scott MA, Earp MN, Benzley SE and Stephenson MB (2005) Adaptive Sweeping Techniques. Proceedings the 14th International Meshing Roundtable pp 417–432

    Google Scholar 

  • Shephard MS and Marcel KG (1991) Automatic Three-Dimensional Mesh Generation by the Finite Octree Technique. International Journal for Numerical Methods in Engineering, Wiley, Vol 32 pp 709–749

    Article  Google Scholar 

  • Shephard MS and Marcel KG (1992) Reliability of Automatic 3D Mesh Generation. Computer Methods in Applied Mechanics and Engineering, North-Holland, Vol 101 pp 443–462

    Google Scholar 

  • Shepherd J, Mitchell SA, Knupp P, and White D (2000) Methods for Multisweep Automation. Proceedings of the 9 National Laboratories, pp. 77–87

    Google Scholar 

  • Shewchuk JR (2002) Delaunay Refinement Algorithms for Triangular Mesh Generation, Computational Geometry: Theory and Applications, Vol 22 Num 1–3 pp 21–74, May 2002

    Google Scholar 

  • Shin BY and Sakurai H (1996) Automated Hexahedral Mesh Generation by Swept Volume Decomposition and Recomposition. Proceeding 5th International Meshing Roundtable pp 273–280

    Google Scholar 

  • Staten ML, Canann SA and Owen SJ (1998) BMSWEEP: Locating Interior Nodes During Sweeping. Proceeding the 7th International Meshing Roundtable pp 7–18

    Google Scholar 

  • Staten ML, Owen SJ, Blacker TD (2005) Unconstrained Paving & Plastering: A New Idea for all Hexahedral Mesh Generation. Proceedings the 14th International Meshing Roundtable pp 399–416

    Google Scholar 

  • Taghavi R (2000) Automatic Block Decomposition Using Fuzzy Logic Analysis. Proceeding 9th International Meshing Roundtable pp 187–192

    Google Scholar 

  • Takahashi H and Shimizu H (1991) A General Purpose Automatic Mesh Generation Using Shape Recognition Technique. Compt. Engrg. ASME, Vol 1 pp 519–526

    Google Scholar 

  • Tu T and O’Hallaron DR (2004) Extracting Hexahedral Mesh Structures from Balanced Linear Octrees. Proceedings 13th International Meshing Roundtable Williamsburg VA pp 191–200

    Google Scholar 

  • Watson DF (1981) Computing the Delaunay Tesselation with Application to Voronoi Polytopes. The Computer Journal, Vol 24 Num 2 pp 167–172

    Article  Google Scholar 

  • Weatherill NP and Hassan O (1994) Efficient Three-dimensional Delaunay Triangulation with Automatic Point Creation and Imposed Boundary Constraints. International Journal for Numerical Methods in Engineering, Wiley, Num 37 pp 2005–2039

    Article  Google Scholar 

  • White D, Saigal S and Owen S (2004) CCSweep: Automatic Decomposition of Multi-Sweep Volumes. Engineering with Computers, Vol 20 pp 222–236

    Article  Google Scholar 

  • White D, Tautges T and Timothy J (2000) Automatic Scheme Selection for Toolkit Hex Meshing. International Journal for Numerical Methods in Engineering, Vol 49 pp 127–144

    Article  Google Scholar 

  • Wright JP and Alan GJ (1994) Aspects of Three-Dimensional Constrained Delaunay Meshing. International Journal for Numerical Methods in Engineering, Wiley, Num 37 pp 1841–1861

    Article  Google Scholar 

  • Xing HL, Miyamura T, Makinouchi A, Homma T, Kanai T, Oishi Y (2001) Development of High Performance Finite Element Software System for Simula- tion of Earthquake Nucleation and Development, Exploration Geodynamics. (Eds. Moresi L, Muller D and Hobbs B). Western Australia, pp 178–188

    Google Scholar 

  • Xing HL, Makinouchi A and Mora P (2007a) Finite Element Modeling of Interacting Fault System, Physics of the Earth and Planetary Interiors, Vol 163 pp 106–121. DOI 10.1016/j.pepi.2007.05.006

    Article  Google Scholar 

  • Xing HL and Mora P (2003) Mesh Generation Software Survey, Technical Report of ACcESS (ESSCC, The University of Queensland). pp 1–20

    Google Scholar 

  • Xing HL and Mora P (2006) Construction of an Intraplate Fault System Model of South Australia, and Simulation Tool for the iSERVO Institute Seed Project. Pure and Applied Geophysics, Vol 163 pp 2297–2316. DOI 10.1007/s00024- 006-0127-x

    Article  Google Scholar 

  • Xing HL, Zhang J and Yin C (2007b) A Finite Element Analysis of Tidal Deformation of the Entire Earth with a Discontinuous Outer Layer. Geophysical Journal International, Vol 170 Num 3 pp 961–970. DOI 10.1111/j.1365-246X.2007.03442.x

    Article  Google Scholar 

  • Yamakawa S and Shimada K (2003) Anisotropic Tetrahedral Meshing via Bubble Packing and Advancing Front. International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 57 Num 13 pp 1923–1942

    Article  Google Scholar 

  • Yerry MA and Shephard MS (1984) Automatic Three-Dimensional Mesh Generation by the Modified Octree Technique. International Journal for Numerical Methods in Engineering, John Wiley, Num 20 pp 1965–1990

    Article  Google Scholar 

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Authors and Affiliations

  1. The University of Queensland, Earth Systems Science Computational Centre, St. Lucia Brisbane, QLD 4072, Australia

    Huilin Xing, Wenhui Yu & Ji Zhang

  2. Department of Engineering Mechanics, Dalian University of Technology, Dalian, China

    Wenhui Yu

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  1. Huilin Xing
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  2. Wenhui Yu
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  3. Ji Zhang
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Xing, H., Yu, W., Zhang, J. (2009). 3D Mesh Generation in Geocomputing. In: Advances in Geocomputing. Lecture Notes in Earth Sciences, vol 119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85879-9_2

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