Belgian URSI meeting location:Brussels date:10 July 2015
From the early times researchers found out that problems did occur at certain frequencies. It turned out that the corresponding matrix of the integral equation had a determinant close to zero, leading to numerical instabilities at those frequencies. This was due to internal resonances of closed objects. To resolve this Prof. Butler proposed combined field integral equations, solving the numerical instabilities at the resonance frequencies. However, at low frequencies, the problem is much more fundamental. A survey in 2010 showed that no commercial software had solved this problem. Indeed, the instability is introduced by the elimination of charges with the Lorentz gauge. To get rid of the problematic term in the equations, some tricks have been introduced, like rotational basis functions. However, they do not represent a complete set of basis functions, which can represent all possible cases of currents. By re-introducing and eliminating both electric and magnetic charges, an efficient procedure has been tested to solve general electromagnetic problems.