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.