Testing line search techniques for finite element discretizations for unsaturated flow

Abstract

Unsaturated flow in porous media is often modeled using the finite element (FE) method. When employing an implicit version of the computational equations resulting from the FE discretization, a nonlinear system of equations is generated that must then be solved by techniques such as Newton's method. This paper reveals results of the effectiveness of three line search techniques when employed within the framework of the approximate Newton method. The methods of a bisection line search, a quadratic variation of the norm of the residual line search, and a relaxation technique are considered, all in the context of a parallel computing environment. © 2009 Springer Berlin Heidelberg.