On the use of the magnetic vector potential in the nodal and edge finite element analysis of 3D magnetostatic problems

Network models of three-dimensional electromagnetic fields

“…Gauging of the solution is an important issue and appropriate conditions are often added to the governing equations. However, some recent publications on numerical methods suggest that gauging may not always be necessary [2,7,17]. By using numerical techniques such as relaxation methods or ICCG, one of the possible solutions is found satisfying the equations for potentials.…”

“…By using numerical techniques such as relaxation methods or ICCG, one of the possible solutions is found satisfying the equations for potentials. Finding one of the solutions may be faster than searching for the only one satisfying the gauge conditions [2,17].…”

“…Using an appropriate iterative method, such as ICCG or block relaxation, it is possible to solve these equations, or -to be more precise -find one of the equations satisfying EEM. The iterative process of seeking one of the solutions is converging faster than the process of finding one unique solution of a well posed system [2,17]. The authors have conducted some tests using the FM-EE model.…”

“…In the FM-EE and EM-FE models a well posed system will be accomplished by adding the conditions V=0 and Ω=0. Unfortunately, the known iterative procedures for solving large system of equations are in this case known to be converging rather slowly [2,17].…”

Computational electromagnetics for design optimisation: the state of the art and conjectures for the future

“…Another milestone development was the introduction of 'Edge Elements' and differential forms. Known more generally as 'Whitney forms' these elements were first presented to the CEM community by Bossavit [39,40], followed by Biro et al [41] and Tsibouikis et al [42]. It is also argued that, in comparison to the vector calculus description, differential forms make electromagnetism simpler, clearer, and more intuitive [43,44] as the relationships may be illustrated by simple diagrams [45].…”