An isogeometric shape optimization method for groundwater flow in porous media

This work introduces a novel isogeometric method for addressing steady, saturated groundwater flow as a free-boundary problem. The innovation lies in adopting a double spline parameterization technique for accurately representing both the porous medium and the fully saturated zone. To linearise the governing equation, we differentiate them with respect to the coefficients of the geometric parameterization. This process results in a quasi-Newton method. Several benchmark numerical tests demonstrate the applicability and effectiveness of the proposed technique.