High derivatives for fast sensitivity analysis in linear magnetodynamics

We present a method of sensitivity analysis using high derivatives and Taylor development. The principle is to find a polynomial approximation of the finite elements solution towards the sensitivity parameters. While presenting our method, we explain why this method is applicable with special parameters only. We applied it on a magnetodynamic problem, simple enough to be able to find the analytical solution with a formal calculus tool. We then present the implementation and the good results obtained with the polynomial, first by comparing the derivatives themselves, then by comparing the approximate solution with the theoretical one. After this validation, we present results on a real 2D application and we underline the possibilities of reuse in other fields of physics