Structure-preserving space–time POD reduction method for solving variable-coefficient parabolic equations

This paper presents a structure-preserving space–time POD reduction method for solving variable-coefficient parabolic equations. A space–time coupled full-order model with Kronecker-product structure is first derived through space–time finite element discretization, leading to a space–time reduced-order model. This formulation inherently possesses spatiotemporal separation properties and enables simultaneous dimensionality reduction in both space and time. Moreover, an error estimate between the numerical solution and the reduced solution is provided. Numerical experiments demonstrate the effectiveness of the proposed approach. Compared with the existing space reduction techniques, the advantages of the proposed method lie in the derivation of a space–time coupled model with Kronecker-product form, which yields a natural spatiotemporal separable structure that is inherently well-suited for space–time model order reduction.