A domain decomposing reduced-order method for solving the multi-domain transient heat conduction problems

Abstract

In this article, a domain decomposition algorithm combined with a reduced-order model (ROM) is proposed to deal with the transient heat conduction problems in multi-domain structures. Using the domain decomposition algorithm and the finite element method (FEM), the original problem is decomposed into multiple non-overlapping subdomains, which can be solved independently under appropriate boundary conditions. However, additional inter-regional connected calculation will be brought through the simple geometry decomposition. Thus, the proper orthogonal decomposition (POD), a projection-based ROM technique, is utilized to further reduce the number of unknowns and the calculation time for each subdomain. To be more specific, the local POD bases of each subdomain are obtained by decomposing a snapshot matrix that gathered according to time by the application of the virtual boundary conditions on interfaces of the adjacent subdomains and other boundaries. Furthermore, the problems under different boundary conditions can be linked by the variable condensation technique on the interfaces, which enhances the efficiency of the numerical solver dramatically. Finally, the accuracy and efficiency of the proposed method are demonstrated by comparing the results calculated using both the proposed algorithm and the direct finite element simulation.