SIMPLE AUTOMATIC DERIVATIVES IN SHAPE OPTIMIZATION

Abstract. Simulation of many physical phenomena requires the numerical solution of non-linear partial differential equations. In addition to simulation, one often wishes to identify or optimize some parameters of the system (including geometry). In this work we present how exact Jacobian with respect to state variables can be produced fully automatically for a simula-tion problem by using the technique of automatic differentiation of computer programs. Under some additional hypothesis, exact gradient can be produced semi-automatically with respect to geometrical variables, too. The presented approach is quite general and does not require very sophisticated computer implementation of the automatic differentiation technique itself. The advantages of exact derivatives in a shape optimization is demonstrated by a numerical example on shape optimization governed by incompressible fluid flow.