Object-oriented implementation of 3D DC adaptive finite-element method

详细信息    查看全文

• 作者：Zhengyong Ren (1) (2)
  Jingtian Tang (2)
  Feiyan Wang (2)
  Xiao Xiao (2)
  Changsheng Liu (2) (4)
  Rongwen Guo (2) (3)
  
• 关键词：object ; oriented strategy ; adaptive finite ; element method ; C ++ framework ; unstructured mesh
• 刊名：Frontiers of Earth Science
• 出版年：2010
• 出版时间：June 2010
• 年：2010
• 卷：4
• 期：2
• 页码：229-236
• 全文大小：327KB
• 参考文献：1. Akin J E, Singh M (2002). Object-oriented Fortran 90 P-adaptive finite element method. Advances in Engineering. Software, 33, (7-10): 461鈥?68 CrossRef
  2. Axness C, Carrera J, Bayer M (2004). Finite-element formulation for solving the hydrodynamic flow equation under radial flow conditions. Computers & Geosciences, 30(6): 663鈥?70 CrossRef
  3. Braun J (2003). Pecube: a new finite-element code to solve the 3D heat transport equation including the effects of a time-varying, finite amplitude surface topography. Computers & Geosciences, 29(6): 787鈥?94 CrossRef
  4. Brenner S C, Scott L R (2002). The Mathematical Theory of Finite Element Methods. Berlin: Springer
  5. Folch A, V谩zquez M, Codina R, Marti J. (1999). A fractional-step finite-element method for the Navier-Stokes equations applied to magma-chamber withdrawal. Computers & Geosciences, 25(3): 263鈥?75 CrossRef
  6. Haber E (2000). A mixed finite element method for the solution of the magnetostatic problem with highly discontinuous coefficients in 3D. Computational Geosciences, 4(4): 323鈥?36 CrossRef
  7. Key K, Weiss C (2006). Adaptive finite-element modeling using unstructured grids: The 2D magnetotelluric example. Geophysics, 71(6): G291鈥揋299 CrossRef
  8. Li Y G, Key K (2007). 2D marine controlled-source electromagnetic modeling: Part 1- An adaptive finite-element algorithm. Geophysics, 72(2): WA51鈥揥A62 CrossRef
  9. Ludwig K, Speiser B (2006). EChem ++-An object-oriented problem solving environment for electrochemistry: Part 4. Adaptive multilevel finite elements applied to electrochemical models Algorithm and benchmark calculations. Journal of Electroanalytical Chemistry, 588(1): 74鈥?7 CrossRef
  10. Nguyen S H, Mardon D (1995). A p-version finite-element formulation for modeling magnetic resonance relaxation in porous media. Computers & Geosciences, 21(1): 51鈥?0 CrossRef
  11. Niekamp R, Stein E (2002). An object-oriented approach for parallel two- and three-dimensional adaptive finite element computations. Computers & Structures, 80(3鈥?): 317鈥?28 CrossRef
  12. Phongthanapanich S, Dechaumphai P (2004). Adaptive Delaunay triangulation with object-oriented programming for crack propagation analysis. Finite Elements in Analysis and Design, 40(13鈥?4): 1753鈥?771 CrossRef
  13. Qiang J K, Luo Y Z (2007). The resistivity FEM numerical modeling on 3-D undulating topography. Chinese J Geophys, 50(5): 1606鈥?613. (in Chinese with English abstract)
  14. Ren Z Y, Tang J T (2009). 3D direct current resistivity modeling with an unstructured mesh by an adaptive finite-element method. Geophysics (in press)
  15. Rosenberg D, Fournier A, Fischer P, Pouquet A (2006). Geophysicalastrophysical spectral-element adaptive refinement (GASpAR): Object-oriented h-adaptive fluid dynamics simulation. Journal of Computational Physics, 215(1): 59鈥?0 CrossRef
  16. Scalicky T (1996). LASPack Reference Manual. Dresden: Dresden University of Technology, 39, http://www.netlib.org, accessed July 26, 2006
  17. Si H (2003). Tetgen: a quality tetrahedral mesh generator and 3D delaunay triangulation, http://tetgen.berlios.de, accessed July 01, 2006
  18. Stewart J R, Edwards H C (2004). A framework approach for developing parallel adaptive multiphysics applications. Finite Elements in Analysis and Design, 40(12): 1599鈥?617 CrossRef
  19. Wu X P (2003). A 3-D finite-element algorithm for DC resistivity modeling using the shifted incomplete Cholesky conjugate gradient method. Geophys J Int, 154: 947鈥?56 CrossRef
  20. Xu S Z, Zhao S K (1985). The boundary element method calculating electric field of a point source on three-dimension topography. Journal of Guilin College of Geology, 5(2): 163鈥?68 (in Chinese with English abstract)
  21. Zienkiewicz O C, Zhu J Z (1992a). The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique. Int j numer. methods eng, 33(7): 1331鈥?364 CrossRef
  22. Zienkiewicz O C, Zhu J Z (1992b). The superconvergent patch recovery and a posteriori error estimates. Part 2: error estimates and adaptivity. Int j numer. methods eng, 33(7): 1365鈥?382 CrossRef
  23. Zienkiewicz O C, Taylor R L (2000). The Finite-element Method (fifth edition) Volume I: The basic. Woburn MA: Butterworth-Heinemann
  
• 作者单位：Zhengyong Ren (1) (2)
  Jingtian Tang (2)
  Feiyan Wang (2)
  Xiao Xiao (2)
  Changsheng Liu (2) (4)
  Rongwen Guo (2) (3)
  
  1. Institute of Geophysics, ETH Zurich, Zurich, 8092, Switzerland
  2. School of Info-physics and Geomatics Engineering, Central South University, Changsha, 410083, China
  4. Changsha Aeronautical Vocational and Technical College, Changsha, 410014, China
  3. School of Earth and Ocean Sciences, University of Victoria, Victoria, 32100, Canada
  
• ISSN：2095-0209

文摘

In this paper, we introduced a clear object-oriented framework to implement the complicated adaptive procedure with C ++ programming language. In this framework, it consisted of the unstructured mesh generation, a-posterior error estimating, adaptive strategy, and the postprocessing. Unlike the procedure-oriented framework, which is commonly used in DC resistivity modeling with FORTRAN language, the object-oriented one, which is famous for its characteristic of encapsulation, could be used for a class of problems that would be executed by only making some changes on the user interface. To validate its flexibility, two synthetic DC examples were tested here.