SUMMARYAn iterative procedure is presented for the finite element computation of unbounded electrical fields created by voltaged conductors. The procedure is based on successive evaluations of the potential on a fictitious boundary enclosing all the conductors, according to the charge lying on their surface. The convergence of the procedure to the solution of the unbounded field problem is demonstrated. Indications for the optimal placement of the fictitious boundary are provided, also taking into account the accuracy of the solution. The way in which computational efficiency can be reached is also discussed. The main advantage of this procedure lies in its simplicity of implementation in the context of a standard FE code for bounded problems, because a very limited amount of additional software is required; moreover, 2-D and axisymmetric versions can be implemented with minor changes from a suitable 3-D one. Examples of application are given in order to illustrate the practical use of the procedure and to validate it by comparisons with available solutions.
A new numerical method, called Robin boundary condition iteration (RBCI), is proposed for the finite-element (FE) solution of electromagnetic scattering problems in open boundary domains. The unbounded domain is truncated to a bounded one by means of a fictitious boundary that contains the scatterer and on which a suitable nonhomogeneous Robin (mixed) boundary condition is assumed for the Helmholtz equation in the bounded domain. The Robin condition is expressed by means of an integral formula (the second Green identity) in terms of the field in the interior of the bounded domain, with the integration surface being a surface strictly enclosed by the truncation boundary. The discretized differential and integral equations are then coupled together to solve the problem. The formulation is completely immune from the well-known interior resonance problems. A simple and effective iterative solving scheme is described. Examples are also provided to validate RBCI and compare it with other methods. Index Terms-Finite-element (FE) methods, integral equations, scattering.
The paper proposes an iterative procedure, called current iteration, for the finite element solution of two-dimensional steady-state skin effect problems in open boundaries. In the procedure a fictitious boundary is introduced enclosing all the conductors. On it, the magnetic vector potential is first guessed and then iteratively updated according to the current density computed in the conductors. Conditions are obtained implying convergence to the exact solution of the unbounded problem whatever the initial guess. The choice of the fictitious boundary and the selection of the relaxation parameter in such a way that computational efficiency is obtained are discussed. The greatest advantage of the procedure is its ease of implementation in a pre-existing finite element code for bounded problems, An axisymmetric version of the procedure is also described since implementation only involves minor changes as compared with the 2-D one. Examples are provided in order to clarify and validate the procedure and compare it with other techniques.
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