High accuracy complete elliptic integrals for solving the Hertzian elliptical contact problems

Complete Elliptic integrals are widely used for solving different types of real problems. For instance, it is required by the Hertzian elliptical contact model, which is the fundament of contact mechanics and establishes the relationship between the stress and the deformation for two elastic solids. Since there is a singular point in the definition domain, traditional approaches often behave badly there. Moreover, no research has noticed the importance of the IEEE quadruple-precision standard on the high accuracy calculation of elliptic integrals. This paper presents a fast high accuracy method that incorporates the 128-bit quadruple-precision floating-point (ISO/IEC/IEEE 60559:2011, IEEE Std 754-2008). The method is used for solving the Hertzian elliptical contact problems. The experiments show that the method can achieve very high accuracy results.