Low frequency MOM for penetrable scatterers

We study the solution of integral equation using the method of moments such that it is stable all the way from static to some moderately low frequencies. As the frequency decreases, the electric and magnetic fields became decoupled. The unknown current consists of two components, a curl-free part and a divergence-free part. To maintain a physically finite charge as the frequency approaches zero, it is necessary that the divergence of the curl-free part scales as O(w) as the frequency approaches zero. No such frequency scaling is needed for the divergence-free part. The different frequency dependence of the current causes the so-called low frequency breakdown. Many researchers have investigated this problem. One way to overcome this difficulty is to use the loop-tree or loop-star basis function which can separate the contribution from the divergence-free current and the curl-free current. To improve the convergence property, a basis rearrangement is used. We also implement the method on the curvilinear-patches to reduce the number of unknowns.