En prekondisjonert iterativ metode for et ikke-lineært sadelpunktproblem

Abstract

The subject of the text is numerical solutions of partial differential equations. Solving a PDE numerically involves reducing it to a linear system of equations. How a PDE can be discretized is discussed, but the emphasis is on methods for solving linear systems.

Different iterative methods are illustrated on the system originating from a 2D Poisson equation, and their performances are compared. The conjugate gradient method is combined with severeal preconditioners to enhance the method's performance. The aim is to program a method that is efficent also for large systems of equations. This method is then used in a program for solving a class of saddlepoint problems.

The purpose of the text is to develop a solver for a non-linear saddlepoint problem. Discretizing the problem gives us a non-linear system of equations which can not be solved directly. Newton's method is applied. In each iteration we must solve a saddlepoint problem of the kind that is solved earlier. Throughout the text more complex problems are solved by reducing them to problems that are easier to solve.