Accurate and efficient computation of the wire kernel

Accurate and efficient evaluation of the wire kernel is fundamental to compute the electromagnetic field due to the electric current along a wire. The thin wire kernel where the current is assumed as line current flowing along the central axis of the wire causes unstable solution of integral equation. The general kernel, which is also referred as exact kernel, is an azimuthal integral representing the potential from uniform current flowing along the cylindrical surface. Its close form is a series of spherical Hankel functions [1]. To evaluate the close form wire kernel efficiently and avoid the floating point overflow problem, the spherical Hankel function is usually first represented as polynomials [2]. This approach will involve double-fold summation. In addition, since the logarithmic singularity is not explicitly extracted in Wangpsilas formula [1], the wire kernel converges very slowly for near fields. In this paper, for distant fields, a normalized Hankel function is introduced for Wangpsilas formula. The kernel can be evaluated efficiently without any floating point overflow problem. For near fields, a new closed form formula which converges fast is derived.