Semi-discrete time-domain sensitivity analysis of electromagnetic field

Purpose - The purpose of this paper is to present sensitivity analysis of electromagnetic fields in the time-domain. Design/methodology/approach - The method utilizing adjoint models is commonly used to evaluate sensitivity. In connection with widely applied finite element method, the time-stepping scheme for discretization of time functions is used. Findings - The proposed semi-discrete method allows us to obtain time-domain solution without time-stepping. For space discretization, the authors use finite elements, as usual. The semi-discrete method delivers analytical and continuous solution for any given time of analysis, which has a form of exponential functions. In order to obtain an analytical formula, there is necessary the integration of sensitivity equation. The paper finds possible solutions of this problem, either the application of Zassenhaus formula or improvement of commutation properties of two matrices. Research limitations/implications - Drawback of this method is matrices which are losing their symmetry and are no more banded. All calculations in this work were carried out with fully assigned matrices. Comparison of the efficiency of the semi-discrete method with classical method shows that, despite the high demand for memory, this method can compete in relation to finite elements with the time-stepping. Practical implications - The resultant gradient information may be used for solving inverse problems, such as optimization of magnetic circuits and identification of material conductivity distributions. Originality/value - The paper offers compact formula for sensitivity evaluation.