Survey of numerical methods in field calculations

In magnetic field computations, Maxwell´s equations are often restricted to the Poisson equation. Several approaches to solving this type of equations are discussed together with the possible field defining potentials. Finite element and finite difference methods are compared, as are the numerical means available for solving the corresponding large systems of matrix equations. Successive overrelaxation, conjugate gradient and preconditioned conjugate gradient method are frequently applied. The integral equation method avoids limitations due to boundary conditions but has other inconveniences due to the fully occupied matrix equation which has to be solved. After mentioning the boundary integral method and techniques to tackle eddy current problems, some examples of proven computer codes for the numerical field calculation are briefly described.