2.5-D and 3-D DC resistivity modelling using an extrapolation cascadic multigrid method

Multigrid methods are well known for their high efficiency in solving elliptic boundary value problems. In this study, an improved extrapolation cascadic multigrid (EXCMG) method is presented to solve large sparse systems of linear equations, which are discretized from both 2.5-D and 3-D DC resistiv...

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Vydané v:Geophysical journal international Ročník 197; číslo 3; s. 1459 - 1470
Hlavní autori: Pan, Kejia, Tang, Jingtian
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Oxford University Press 01.06.2014
Predmet:
Electrical properties
Numerical approximations and analysis
Numerical solutions
ISSN:0956-540X, 1365-246X
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Shrnutí:Multigrid methods are well known for their high efficiency in solving elliptic boundary value problems. In this study, an improved extrapolation cascadic multigrid (EXCMG) method is presented to solve large sparse systems of linear equations, which are discretized from both 2.5-D and 3-D DC resistivity modelling using the finite element methods. To increase the accuracy, the singularity generated by the source term is removed by reformulating the solution with the secondary potential. In addition, a set of new and efficient Fourier coefficient is presented to transform the solutions in the 2.5-D Fourier domain to the 3-D Cartesian domain. To show the efficiency and the ease-to-implement of EXCMG, we first implement the EXCMG methods to a two-layered model of both 2-D and 3-D and compare the results with the analytical solutions. It has been shown that the maximum relative error in apparent resistivity is no more than 0.4 per cent provided an appropriate grid size is chosen. Then the comparisons of EXCMG with two other iterative solvers [symmetric successive over-relaxation conjugate gradient (SSORCG) and incomplete Cholesky conjugate gradient (ICCG)] show that converging at a rate independent of the grid size, the EXCMG method is much more efficient than SSORCG and ICCG solvers. Moreover, the EXCMG method has been shown its potential for being generalized to large-scale 3-D problems, due to the fact that it becomes more efficient as the size of the problem increases.
ISSN:0956-540X
1365-246X
DOI:10.1093/gji/ggu094