Linearized Initialization of the Newton Krylov Algorithm for Nonlinear Elliptic Problems

Abstract

Abstract. It is known that the Newton Krylov algorithm may not always converge if the initial assumption or initialization is far from the exact solution. We present a technique for initializing Newton Krylov solver for nonlinear elliptic problems. In this technique, initial guess is generated by solving linearised equation corresponding to the nonlinear equation. Here, nonlinear part is replaced by the equivalent linear part. Effectiveness of the technique is presented through numerical examples.