A Novel Method for Intrusive Stochastic Estimation of Geometric Tolerance Effects in Finite Element Electromagnetic Analysis

The robust design of microwave, millimeter-wave, or Terahertz components and structures incorporating manufacturing process tolerances would enhance the fabrication yield and thereby reduce the overall production cost. Based on the spectral stochastic finite element method (SSFEM) for material variations, a novel geometrical SSFEM (GSSFEM) is proposed to analyze dimensional uncertainty in 3-D microwave models. The Jacobian for Piola mapping is represented as a function of stochastic variables to capture mesh level uncertainties. Polynomial chaos expansion is used to approximate the electric field as a random process. The technique is validated by applying it to waveguide problems with uncertainty in geometric dimensions. GSSFEM results are compared with analytical formulations of the transmission coefficient for a physical insight and further with the Monte Carlo simulations for quantitative evaluation. The results using the proposed approach are in excellent agreement with conventional methods and are found to be faster than sparse grid stochastic collocation, while the scaling of the computational requirements with the number of degrees of freedom and stochastic dimension is as good as this efficient scheme. Furthermore, this approach has been employed to analyze uncertainty in multiple geometric parameters to compare their sensitivity. The proposed GSSFEM can be employed for analyzing the impact of fabrication tolerance of passive waveguide components at microwave frequencies and beyond.