Boundary Integral Equations for the Computational Modeling of Three-Dimensional Steady Groundwater Flow Problems

摘要

The subject of investigation of the present thesis is the application of the boundary-integral-equation method to the computational modeling of three-dimensional, steady groundwater flow problems. The authors have investigated a particular type of integral-equation technique, viz. the boundary-integral-equation method. The main attraction of this method as compared with the finite-difference and finite-element methods is that it achieves computational efficiency through a reduction in the problem's dimensionality. Especially in implementing three-dimensional problems, this advantage shows up. Moreover, the differential equations describing the groundwater flow in the interior of the relevant porous substance are in principle solved exactly; all approximations are made on the boundaries. Since, however, the boundary-integral-equation method can in practice only be handled for piecewise homogeneous subdomains in the flow configurations, it does not defeat the finite-difference and finite-element methods in all cases. In general, for groundwater flow problems concerned with flow in strongly inhomogeneous media, a finite-difference, finite-element, or a hybrid approach, may be a better choice.