Abstract
The correct numerical modeling of free-surface hydrodynamic problems often requires to have the solution of special linear systems whose coefficient matrix is a piecewise constant function of the solution itself. In doing so, one may fulfill relevant physical constraints. The existence, the uniqueness, and two constructive iterative methods to solve a piecewise linear system of the form $\max[\boldsymbol{l},\min(\boldsymbol{u},\mathbf{x})]+T\mathbf{x}=\mathbf{b}$ are analyzed. The methods are shown to have a finite termination property; i.e., they converge to an exact solution in a finite number of steps and, actually, they converge very quickly, as confirmed by a few numerical tests, which are derived from the mathematical modeling of flows in porous media.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
