Three‐dimensional space variable–separated PGD in electrostatic field problems: A comparison between two implementations

Abstract

Proper generalized decomposition (PGD) is a promising model order reduction (MOR) technique to solve partial differential equations (PDEs). It usually bases on an explicit variable-separated formulation of the problems to be solved. However, it can be expensive to derive the separated formulations. Also, the PGD process can become inefficient because of the massive separated terms.Another way of implementing PGD is based on direct integration. In this work, we illustrate this kind of implementation algebraically by introducing tensors to represent the operator and right-hand side of the problem. The separated formulation-based PGD and tensor-based PGD are compared in computational complexity and accuracy. The pros and cons of both approaches are discussed.The methods are applied in three-dimensional (3D) electrostatic field problems.