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Proper Generalized Decomposition for Edge Elements in Magnetostatics With Adaptive Stopping Criterion

The proper generalized decomposition (PGD) is an a priori model-order reduction (MOR) method based on a variable-separated expression of the problem. Two iterative loops are needed in the PGD algorithm, namely, the outer loop for enriching the reduction modes progressively and the inner loop for solving each mode by fixed point iterations. Setting the stopping criterion of these two loops blindly can cause either the inaccuracy of the PGD or a waste of iterations. In this article, a special variable-separated PGD with edge elements is proposed and implemented on a hexahedral mesh in magnetostatics. Also, an adaptive stopping criterion based on dual formulations is applied to balance different error components, namely, the discretization error and error for outer and inner loops of PGD. A numerical example is given to illustrate the proposed approach.