Parametric model order reduction based on parallel tensor compression

In this paper, we for the first time explore the model order reduction (MOR) of parametric systems based on the tensor techniques and a parallel tensor compression algorithm. For the parametric system characterising multidimensional parameter space and nonlinear parametric dependence, we first approximate the system matrices by tensor functions of the parameters, whose first-order coefficients are third-order tensors. In order to effectively reduce the computational cost and the storage burden, we propose a parallel tensor compression algorithm based on Tensor-SVD to deal with the tensors in the tensor functions. Then, we obtain the low-rank approximation in Kruskal form of third-order tensors. After that, by computing the first several expansion coefficients of the state variable with the selected parameter vectors, the projection matrix is constructed to obtain the reduced parametric system. Theoretical analysis shows that the reduced parametric system can match the first several expansion coefficients of the output variable of the original system at the selected parameter vectors. Moreover, the stability of the proposed MOR method is discussed. Finally, the efficiency of the proposed method is illustrated by two numerical examples.