Model order reduction and error estimation with an application to the parameter-dependent eddy current equation
In product development, engineers simulate the underlying partial differential equation many times with commercial tools for different geometries. Since the available computation time is limited, we look for reduced models with an error estimator that guarantees the accuracy of the reduced model. Using commercial tools the theoretical methods proposed by G. Rozza, D.B.P. Huynh and A.T. Patera [Reduced basis approximation and a posteriori error estimation for affinely parameterized elliptic coercive partial differential equations, Arch. Comput. Methods Eng. 15 (2008), pp. 229-275] lead to technical difficulties. We present how to overcome these challenges and validate the error estimator by applying it to a simple model of a solenoid actuator that is a part of a valve.
model order reduction eddy current equation a posteriori error estimator krylov subspace method reduced basis method