First- and second-order sensitivity analysis of finite element models using extended complex variables method

This paper proposed a robust novel method that is called the extended complex variables method (ECVM) for the first- and second-order sensitivity analysis. In the most previous versions of complex variables method, only an imaginary step was used to analyze the sensitivity. However, ECVM is employed both the real and imaginary parts to improve the efficiency of it. The proposed method is applied for several problems with a closed-form solution, and the results are compared by past methods. It is illustrated that the first-order sensitivity analysis is not influenced by the change of the step size for both the traditional and extended complex variables methods. However, it is shown that, unlike the complex variable's method, the efficiency of ECVM is high and it is independent of the step size for calculating the second-order sensitivity. The range of accurate results for second-order sensitivity analysis by ECVM is between two until four times more than CVM and FDM. Hence, this approach is suggested as an appropriate technique for calculating simultaneously the first- and second-order sensitivities with high accuracy as well as low computational cost.