Application of multilevel scheme and two level discretization for POD based model order reduction of nonlinear transient heat transfer problems

In the present paper, a method to reduce the computational cost associated with solving a nonlinear transient heat conduction problem is presented. The proposed method combines the ideas of two level discretization and the multilevel time integration schemes with the proper orthogonal decomposition model order reduction technique. The accuracy and the computational efficiency of the proposed methods is discussed. Several numerical examples are presented for validation of the approach. Compared to the full finite element model, the proposed method significantly reduces the computational time while maintaining an acceptable level of accuracy.