A Simultaneous Numerical Integration Routine for the Fast Calculation of Similar Integrations

Abstract

In this paper, a fast and simultaneous integration routine tailored for obtaining results of multiple numerical integrations is introduced. In the routine, the same nodes are used when integrating different functions along the same integration path. In the paper it is demonstrated by several examples that if the integrands of interest are similar on the integration path, then using the same nodes decreases the computational costs dramatically. While the method is introduced by updating the popular Gauss-Kronrod quadrature rule, the same steps given in the paper can be applied to any other numerical integration rule.

Keywords

• electromagnetic line sources
• gauss-kronrod quadrature
• layered media green’s functions
• numerical integration
• simultaneous integration.