A reduced basis method for parameter optimization of multiscale problems

Abstract. Many natural or technical processes can be described by parameterized partial differ-ential equations (P2DEs) that include different length-scales. Typical applications include parameter studies or optimal control where the model has to be solved for a huge variety of different parame-ters resulting in enormous computational times for classical discretization techniques. The reduced basis method was introduced to overcome this problem. The aim of this contribution is to extend the reduced basis methodology to optimization problems that are constrained by a parameterized multiscale problem. We introduce the methodoly in detail and give numerical experiments that demonstrate the efficiency of the model reduction approach in multiscale optimization problems