A new static field solver with open boundary conditions in the 3D-CAD-system MAFIA

The numerical solution of Maxwell´s equations involves calculation in a finite volume enclosing the structure of interest. Using simple Dirichlet or Neumann boundary conditions causes inaccuracies or requires excessively large meshes. For a static problem, which can be reduced to a scalar potential problem that can be described by Poisson´s equation, it is shown that one can formulate more accurate boundary conditions. A multipole expansion of the well-known solutions of the Poisson equation can be used to yield better boundary values from the neighboring inner potentials. This modified formulation is used in solving electrostatic and magnetostatic problems with the recently developed solver of the 3-D CAD system MAFIA, which solves Maxwell´s equations for a very broad range of applications