High-order Frequency Derivatives in Variational Eddy Current System

In a linear eddy current system excited by a current source, a high-order frequency sensitivity is derived in variational formulation instead of as a discretized state equation. An analytic sensitivity formulation of order ${n}$ is obtained by sequentially differentiating the variational eddy current system with respect to angular frequency. The high-order frequency sensitivity is implemented through a commercial finite element method. A frequency sensitivity analysis conducted based on two numerical examples verifies the results.