Improved Babylonian Square Root Algorithm-Based Analytical Expressions for the Surface-to-Surface Solution to the Sommerfeld Half-Space Problem

PROJECT TITLE :

Improved Babylonian Square Root Algorithm-Based Analytical Expressions for the Surface-to-Surface Solution to the Sommerfeld Half-Space Problem

ABSTRACT:

In a recent work, analytical express expressions have been derived for the Sommerfeld integrals describing the surface fields of a vertical electric dipole placed near a plane air–earth boundary. Such formulas have the advantage of being precise, but sadly encompass slowly convergent infinite sums of special functions. As a consequence, accurate evaluation of the fields is obtained at the price of a non-negligible computational effort. The purpose of this Communication is to derive improved express expressions for the Sommerfeld integrals, which assure the identical degree of accuracy as the preceding ones, but are constituted by quick-convergent sums of Hankel functions.

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