Charge iteration: A procedure for the finite element computation of unbounded electrical fields

An 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.

[1]  Peter P. Silvester,et al.  Universal finite element matrices for tetrahedra , 1982 .

[2]  S. Coco,et al.  Axisymmetric Unbounded Electrical field computation by Charge Iteration , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[3]  Peter P. Silvester,et al.  Construction of triangular finite element universal matrices , 1978 .

[4]  P. Silvester,et al.  Exterior finite elements for 2-dimensional field problems with open boundaries , 1977 .

[5]  O. Zienkiewicz,et al.  The coupling of the finite element method and boundary solution procedures , 1977 .

[6]  Ruey-Beei Wu,et al.  Exploiting structure periodicity and symmetry in capacitance calculations for three dimensional multiconductor systems , 1988 .

[7]  J. D'Angelo,et al.  Applications of the hybrid finite element-boundary element method in electromagnetics , 1988 .

[8]  V. Postoyalko,et al.  Green's Function Treatment of Edge Singularities in the Quasi-TEM Analysis of Microstrip , 1986 .

[9]  Salvatore Coco,et al.  ELFIN: an N-dimensional finite-element code for the computation of electromagnetic fields , 1988 .

[10]  E. M. Freeman,et al.  A sparse matrix open boundary method for finite element analysis , 1989 .

[11]  Peter P. Silvester,et al.  Finite Elements for Electrical Engineers , 1983 .

[12]  P. Bettess.  Finite element modelling of exterior electromagnetic problems , 1988 .

[13]  P. Silvester,et al.  Solution of 2-dimensional field problems by boundary relaxation , 1968 .

[14]  Salvatore Coco,et al.  Charge iteration for N-dimensional unbounded electrical field computations , 1992 .

[15]  P. Benedek,et al.  Capacitance of Parallel Rectangular Plates Separated by a Dielectric Sheet , 1972 .

[16]  P. Morse,et al.  Methods of theoretical physics , 1955 .