TY - EJOU
AU - Chang, Chih-Wen
TI - A Regularized Integral Equation Scheme for Three-Dimensional Groundwater Pollution Source Identification Problems
T2 - Computer Modeling in Engineering \& Sciences
PY - 2012
VL - 88
IS - 2
SN - 1526-1506
AB - We utilize a regularized integral equation scheme to resolve the three-dimensional backward advection-dispersion equation (BADE) for identifying the groundwater pollution source identification problems in this research. First, the Fourier series expansion method is employed to estimate the concentration field C(x, y, z, t) at any time t < T. Second, we contemplate a direct regularization by adding an extra term a(x, y, z, 0) to transform a second-kind Fredholm integral equation for C(x, y, z, 0). The termwise separable property of the kernel function permits us to acquire a closed-form regularized solution. In addition, a tactic to determine the regularization parameter is recommended. We find that the proposed method is robust and applicable to the three-dimensional BADE when several numerical experiments with the large heterogeneous parameters and the noisy final time data are examined.
KW - Backward advection-dispersion equation
KW - Groundwater contaminant distribution
KW - Ill-posed problem
KW - Regularized solution
KW - Fourier series
KW - Fredholm integral equation
DO - 10.3970/cmes.2012.088.065