A novel algorithm for the stochastic analysis of electric field problems considering material and spatial uncertainties

This paper aims to address the material and spatial uncertainties in the stochastic electric field problem by proposing two efficient algorithms based on the stable nodal integration method (SNIM). The random variables/fields are used to describe the material and spatial uncertainties and a generalized stochastic perturbation-SNIM (GS-SNIM) method is developed to address the random-variable scenario while a random field-SNIM (RF-SNIM) method is developed to address the random-field scenario. Numerical examples are studied to fully verify the accuracy and efficiency of the proposed GS/RF-SNIM. The analysis results demonstrate that (1) the GS-SNIM is able to solve the random-variable based uncertainties through different orders expansion; (2) the RF-SNIM can calculate the expected values and variances of the stochastic electric field problem; and (3) the present methods produce accurate stochastic analysis results and significantly reduce the computational cost.