Tetrahedral Edge Elements Research Articles

Comparison between two formulations in terms of potential for the coupling of magnetic and electric circuit equations

The 3D numerical simulation of electromagnetic systems accounting for the electric circuit equation is studied for strand conductors. Two formulations in terms of potential (A and T/sub 0/ Omega ) are compared and discussed. The finite element method is used to solve the magnetic equations with tetrahedral edge elements and tetrahedral nodal elements for, respectively, the A and T/sub 0/ Omega formulation. As an example of application, an iron-core coil and a current transformer have been simulated. In the latter the numerical results are compared with the experimental results.

Hybrid FEM-BIM formulation using electric and magnetic variables

A hybrid finite-element-boundary-integral method using a mixed electric-magnetic formulation for 3-D eddy current computation is presented. The finite element formulation using tetrahedral edge elements in terms of electric field is employed in the conducting region. The boundary integral method in terms of magnetic field is used in the air space. The use of a vector variable in the air space together with a boundary spanning tree technique makes it possible to solve multiply connected problems and leads to a diminution of boundary unknowns. The electric and the magnetic variables are coupled on the boundary of the domain through the boundary continuity of electric and magnetic fields; the coupling matrices thus obtained are the transposes of one another. Results concerning this mixed coupling method and comparison with the other hybrid methods are reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Eigenvalue analysis in anisotropically loaded electromagnetic cavities using 'edge' finite elements

The eigenmodes in an arbitrarily shaped, electromagnetic (EM) cavity loaded with an anisotropic material are computed using linear tetrahedral edge elements and curvilinear hexahedral edge elements. The permeability tensor is assumed to have off-diagonal entries (gyromagnetic), and the permittivity and conductivity tensors are diagonal (typically for composite materials). Therefore, the divergence-free condition is not always satisfied inside a finite element. Yet, the procedure is found to yield good prediction of the lower resonant frequencies, and no spurious modes are encountered in this range of interest. In the examples considered, numerical solutions are consistent with quasi-analytical solutions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A single scalar potential method for 3D magnetostatics using edge elements

It is demonstrated that it is possible to use a single, continuous, scalar potential to solve magnetostatic problems in three dimensions without the loss of accuracy associated with the reduced potential. This method makes use of tetrahedral edge elements and does not require the initial calculation of the field of the currents in the absence of magnetic materials. The method requires no numerical integration, has no restrictions on the current flow or the iron topology, and needs the solution of only one matrix problem. Results obtained by the method for translational and axisymmetric problems agree well with those computed by two-dimensional analysis with a vector potential. The method can be used to obtain accurate flux densities in both air and iron regions of three-dimensional problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>