Three-dimensional magnetostatic problem

The paper is devoted to an approximation of the solution of Maxwell's equations in three‐dimensional space. We present two methods which couple a finite element method inside the magnetic materials with a boundary integral method which uses Poincaré–Steklov's operator to describe the exterior domain. A computer code has been implemented for each method and a number of numerical experiments have been performed to validate each proposed methodology. Namely, we present numerical results concerning a non‐linear magnetostatic problem in ℝ3. Copyright © 1999 John Wiley & Sons, Ltd.