Iterative Solution of Piecewise Linear Systems

Iterative Solution of Piecewise Linear Systems

Abstract. The correct formulation of numerical models for free-surface hydrodynamics often requires the solution of special linear systems whose coefficient matrix is a piecewise constant function of the solution itself. In so doing one may prevent the development of unrealistic negative water depths. The resulting piecewise linear systems are equivalent to particular linear complementarity pro...

Iterative Solution of Piecewise Linear Systems for the Numerical Solution of Obstacle Problems

We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the numerical solution of free-surface problems. In particular, we here study their application to the numerical solution of both the (linear) parabolic obstacl...

Iterative Solution of Linear Systems

Recent advances in the eld of iterative methods for solving large linear systems are reviewed. The main focus is on developments in the area of conjugate gradient-type algorithms and Krylov subspace methods for non-Hermitian matrices .

Piecewise Constant Controlled Linear Fuzzy Systems

Iterative Solution of Piecewise Linear Systems and Applications to Flows in Porous Media

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[l,m...