1.Institute of Geophysics,
ETH Zurich, Zurich 8092, Switzerland；School of Info-physics
and Geomatics Engineering, Central South University, Changsha 410083,
China; 2.School of Info-physics
and Geomatics Engineering, Central South University, Changsha 410083,
China; 3.School of Info-physics
and Geomatics Engineering, Central South University, Changsha 410083,
China；Changsha Aeronautical
Vocational and Technical College, Changsha 410014, China; 4.School of Info-physics
and Geomatics Engineering, Central South University, Changsha 410083,
China；School of Earth and
Ocean Sciences, University of Victoria, Victoria 32100, Canada;
Abstract：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, whichis 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.
Akin J E, Singh M(2002). Object-oriented Fortran 90 P-adaptive finite element method. Advances in Engineering. Software, 33, (7―10): 461―468 doi: 10.1016/S0965-9978(02)00048-0
Axness C, Carrera J, Bayer M(2004). Finite-elementformulation for solving the hydrodynamic flow equation under radialflow conditions. Computers & Geosciences, 30(6): 663―670 doi: 10.1016/j.cageo.2004.03.013
Braun J(2003). Pecube: a new finite-element codeto solve the 3D heat transport equation including the effects of atime-varying, finite amplitude surface topography. Computers & Geosciences, 29(6): 787―794 doi: 10.1016/S0098-3004(03)00052-9
Brenner S C, Scott L R(2002). The Mathematical Theory of Finite Element Methods. Berlin: Springer
Folch A, Vázquez M, Codina R, Marti J. (1999). A fractional-step finite-elementmethod for the Navier-Stokes equations applied to magma-chamber withdrawal. Computers & Geosciences, 25(3): 263―275 doi: 10.1016/S0098-3004(98)00164-2
Haber E(2000). A mixed finite element method forthe solution of the magnetostatic problem with highly discontinuouscoefficients in 3D. Computational Geosciences, 4(4): 323―336 doi: 10.1023/A:1011540222718
Key K, Weiss C(2006). Adaptive finite-element modeling using unstructured grids: The 2Dmagnetotelluric example. Geophysics, 71(6): G291―G299 doi: 10.1190/1.2348091
Li Y G, Key K(2007). 2D marine controlled-source electromagnetic modeling: Part 1- Anadaptive finite-element algorithm. Geophysics, 72(2): WA51―WA62 doi: 10.1190/1.2432262
Ludwig K, Speiser B(2006). EChem++ —An object-oriented problem solving environmentfor electrochemistry: Part 4. Adaptive multilevel finite elementsapplied to electrochemical models Algorithm and benchmark calculations. Journal of Electroanalytical Chemistry, 588(1): 74―87 doi: 10.1016/j.jelechem.2005.12.003
Nguyen S H, Mardon D(1995). A p-version finite-element formulation for modelingmagnetic resonance relaxation in porous media. Computers & Geosciences, 21(1): 51―60 doi: 10.1016/0098-3004(94)00059-4
Niekamp R, Stein E(2002). An object-oriented approach for parallel two- and three-dimensionaladaptive finite element computations. Computers& Structures, 80(3―4): 317―328 doi: 10.1016/S0045-7949(02)00004-4
Phongthanapanich S, Dechaumphai P(2004). Adaptive Delaunay triangulation with object-orientedprogramming for crack propagation analysis. Finite Elements in Analysis and Design, 40(13―14): 1753―1771 doi: 10.1016/j.finel.2004.01.002
Qiang J K, Luo Y Z(2007). The resistivity FEM numerical modeling on 3-D undulating topography. Chinese J Geophys, 50(5): 1606―1613. (in Chinesewith English abstract)
Ren Z Y, Tang J T(2009). 3D direct current resistivity modeling with an unstructured meshby an adaptive finite-element method. Geophysics (in press)
Stewart J R, Edwards H C(2004). A framework approach for developing parallel adaptivemultiphysics applications. Finite Elementsin Analysis and Design, 40(12): 1599―1617 doi: 10.1016/j.finel.2003.10.006
Wu X P(2003). A 3-D finite-element algorithm forDC resistivity modeling using the shifted incomplete Cholesky conjugategradient method. Geophys J Int, 154: 947―956 doi: 10.1046/j.1365-246X.2003.02018.x
Xu S Z, Zhao S K(1985). The boundary element method calculating electric field of a pointsource on three-dimension topography. Journalof Guilin College of Geology, 5 (2): 163–168 (in Chinese with English abstract)
Zienkiewicz O C, Zhu J Z(1992a). The super convergent patch recovery and a posteriori error estimates.Part 1: the recovery technique. Int j numer.methods eng, 33(7): 1331―1364 doi: 10.1002/nme.1620330702
Zienkiewicz O C, Zhu J Z(1992b). The super convergent patch recovery and a posteriori error estimates.Part 2: error estimates and adaptivity. Int j numer. methods eng, 33(7): 1365―1382 doi: 10.1002/nme.1620330703
Zienkiewicz O C, Taylor R L(2000). The Finite-element Method (fifth edition) Volume I:The basic. Woburn MA: Butterworth-Heinemann
