Accelerated Summation of the Green´s Function for the Rectangular Cavity

A new convergence acceleration scheme is presented for the infinite series representing the Green´s function for the rectangular cavity. The error function transformation is applied to the modified image series of the cavity Green´s function to convert it into the sum of two rapidly convergent series. The proposed method is based on the error function with real arguments rather than the complex error function of the existing Ewald sum based method and can achieve better numerical efficiency with similar convergence rate.