Implementation of an adjoint thermal solver for inverse problems

Authors

Peter Jaksch - Siemens Industrial Turbomachinery AB

Abstract

This paper contains a derivation of the adjoint equations for transient heat conduction and describes how to include the adjoint solution in a nonlinear conjugate gradient method. The adjoint equations are useful for optimization problems where a scalar valued target function is optimized with respect to a large number of design variables. In this paper the target function is a least squares fit between calculated and measured transient metal temperatures. The design variables consist of heat transfer coefficients on a set of mesh facets for a finite element mesh. Contrary to intuition the sensitivity of the target function with respect to the different design variables can be evaluated by just two transient solutions; the direct problem and the adjoint problem, with roughly similar cost. If a brute force approach is used the transient problem has to be solved for each individual design variable. Since a typical mesh contains thousands of facets the speedup of the adjoint approach is enormous.