A reduced basis method for parameter optimization of multiscale problems

Abstract

Many natural or technical processes can be described by parameterized partial dierffential equations (P2DEs) that include dierent length-scales. Typical applications include parameter studies or optimal control where the model has to be solved for a huge variety of dierent parameters 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 eciency of the model reduction approach in multiscale optimization problems.