The PCGM For Cauchy Inverse Problems In 3D Potential
Free (open access)
297 - 305
Huanlin Zhou, Buxi Bian, Changzheng Cheng & Zhongrong Niu
The preconditioned conjugate gradient method (PCGM) in combination with the boundary element method (BEM) is developed for reconstructing the boundary conditions in 3-D potential. Morozov’s discrepancy principle is employed to select the iteration step. The semi-analytical integral algorithm is proposed to treat the nearly singular integrals when the interior points are very close to the boundary. The numerical results confirm that the PCGM produces convergent and stable numerical solutions with respect to decreasing the amount of noise added into the input data. The numerical solutions are sensitive to the locations of the interior points when these points are distributed near the boundary without boundary conditions. The results are more accurate when these points are closer to the boundary. Keywords: BEM, inverse problems, Cauchy problems, potential, preconditioned conjugate gradient method.
BEM, inverse problems, Cauchy problems, potential, preconditioned conjugate gradient method