Bubnov-Galerkin method for solving exterior alternating field problems

Abstract

It is demonstrated that the Bubnov-Galerkin method coupled with the separation of variables method can be applied for solving exterior alternating field problems. As an example illustrating the use of the method, the inner impedance of a rectangular conductor is calculated. Though the method is approximate, exact values of the impedance have been obtained by iterative numerical processes. The method can be used when the field or the vector potential do not vanish at infinity, and when the energy associated with the whole space is infinite.

Development and implementation of some BEM variants—A critical review

“…However, the implementation of the Galerkin-Bubnov scheme in boundary integral equation can be seen in the work of Rolics [221,222]. For the Galerkin-Bubnov scheme, the weighting function is obtained in the same form with the weight function for Galerkin approach (but with arbitrary coefficients).…”

Fixed‐point technique in computing nonlinear eddy current problems

“…A magnetic vector potential A defined as (Rolicz, 1982). The conductor cross section D I is surrounded by a contour S, the shape of which is chosen in the system of orthogonal coordinates (x 1 , x 2 ) in order to enable a separation of variables in the region outside S. The solution in the interior region D I , on the other hand, is approximated by the finite element method, as…”

Numerical solution of eddy current problems in ferromagnetic bodies travelling in a transverse magnetic field

“…In this paper, a hybrid approach [16] is applied based on Galerkin's ÿnite element formulation coupled with a separation of variables. According to the mentioned method a conducting region is surrounded by a contour S, the shape of which in orthogonal co-ordinates (x 1 ; x 2 ) enables the separation of variables in the surrounding empty space.…”

“…After algebraic transformations, (27) The symbols appearing above are illustrated in Figure 4. By virtue of (28), the coe cients C 1n ; C 2n have been eliminated from Equations (16). Taking advantage of a local basis of ÿnite elements, the matrices in (16) 29) where a m = x n y k − x k y n , b m = y n − y k , c m = x k − x n: , m; n; k are indices of the nodes, e is element area and f m; n = 2 for m = n 1 otherwise…”