Sensitivity Analysis of Electromagnetic Quantities in Time Domain by Means of FEM

Abstract

Sensitivity analysis belongs to the most important tools in optimization theory. It determines the dependence of global or local electromagnetic quantities on geometrical and physical parameters expressed in the form of an objective function. For several objective functions the sensitivity may be directly calculated differentiating the objective function versus one of material or geometric parameters. Such approach needs large computational effort, especially while evaluating in time domain. This paper presents effective methods for computing of sensitivity of nodal potentials in finite elements versus perturbations in conductivity of analyzed model in time domain. Derived equations are based on the method of stiffness and mass matrices derivative and Tellegen’s theorem known from circuit theory and have been expanded on field theory. Numerical example presented in the paper shows sensitivity of voltage induced in measurement coil versus variation of electrical conductivity in single finite element as function of time. The proposed methods calculate the sensitivity versus all finite elements in area of analysis at once. On the basis of sensitivity information the iterative algorithm for identification of shape and conductivity distribution of material flaws could be applied.