zbMATH — the first resource for mathematics

Iterative solution of piecewise linear systems for the numerical solution of obstacle problems. (English) Zbl 1432.65079
Summary: 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 obstacle problem and the obstacle problem. We propose a class of effective semi-iterative Newton-type methods to find the exact solution of such piecewise linear systems. We prove that the semi-iterative Newton-type methods have a global monotonic convergence property, i.e., the iterates converge monotonically to the exact solution in a finite number of steps. Numerical examples are presented to demonstrate the effectiveness of the proposed methods.

65K10 Numerical optimization and variational techniques
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C53 Methods of quasi-Newton type
Full Text: Link