Optimality criteria method for optimal design in hyperbolic problems
Marko Vrdoljak · University of Zagreb University Computing Centre (SRCE) · 2010
Abstract. We consider an optimal design problem with a hyperbolic initial boundary value problem as the state equation. As a possible application consider a body made from a mixture of different materials which is vibrating under the given external force, subject to a prescribed boundary and initial values. The control function (the distribution of given materials in the given domain) uniquely determines the response (the state function) of the vibrating material. Our goal is to find a distribution of materials minimising given integral functional depending on state and control functions. We derive the necessary condition of optimality, which enables us to formulate an optimality criteria method for a numerical solution. Two numerical examples are presented. The same procedure can be applied in the case of multiple state equations as well.