SENSITIVITY ANALYSIS AND OPTIMIZATION FOR JOULE HEATING WITH TEMPERATURE-DEPENDENT CONDUCTIVITIES

Abstract

The physical phenomenon of interest in this study relates to the joule heating of solids with temperature-dependent thermal/electrical conductivities and coupled field equations. The sensitivity analysis (SA) expressions of a general integral functional with respect to material and “loading” functions in the thermal-electric field are derived by using the adjoint variable method. The SA expressions are generally used in the mathematical programming solution methods of the so-called inverse problems, such as optimization and identification problems. In particular, a two-dimensional example optimization problem is studied numerically by discretizing the primary and adjoint field equations by the finite-element method, while minimizing the objective function of optimization by nonlinear programming routines. The parametric studies performed with various mesh topologies and (finite) decision vectors indicate the feasibility and efficiency of the proposed numerical scheme.