The accurate evaluation of higher order nearly singular integrals is one of the key technologies in accurate simulation by electromagnetic surface integral equations (SIE).However

the present methods mainly focus on low order nearly singular integrals for the planar element modeling

rather than on 3-order nearly singular integrals in higher order geometry modeling.Based on the former research of the Double Arctan-Transformation (DAT)

the Improved Double Arctan-Transformation (IDAT) is proposed to improve the stability and accuracy of the nearly singular integrals with singular kernel RR/R5

R/R4 and 1/R3 for higher order geometry modeling.Specifically

the exponential transformation is utilized to stabilize the integrals when the field points are extremely close to the source surface.Furthermore

the shape-function transformation is adopted to stabilize the integrals when the projection point approaches to the border of source surface.The proposed IDAT is also effective for the lower orders of the nearly singular integral kernels.With theoretical analysis and typical testing cases

the accuracy and stability performance of IDAT is fairly evaluated.