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Iterative solution of piecewise linear systems and applications to flows in porous media
 SIAM Journal on Scientific Computing
, 2009
"... Abstract. For the ecient mathematical modelling of freesurface hydrodynamic problems, it is required the solution of special linear systems whose coecient matrix is a piecewise constant function of the solution itself. In so doing one may fulll relevant physical constraints. In particular, the exis ..."
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Abstract. For the ecient mathematical modelling of freesurface hydrodynamic problems, it is required the solution of special linear systems whose coecient matrix is a piecewise constant function of the solution itself. In so doing one may fulll relevant physical constraints. In particular, the existence, the uniqueness, and two constructive iterative methods to solve a piecewise linear system of the form max[l;min(u;x)] + Tx = b; are analysed. The methods are shown to have a nite termination property, i.e., they converge to an exact solution in a nite number of steps and, actually, they converge very quickly, as conrmed by a few numerical tests, which are derived from the mathematical modelling of
ows in porous media.
method for nonlinear leastsquares problems with simple bounds
, 2011
"... the convergence of an inexact GaussNewton trustregion method ..."
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