A Nonconformal SETI-DP Method for Transient Thermal Simulation

This article proposes a novel nonconformal mesh-based dual-primal spectral element tearing and interconnecting (SETI-DP) method designed for the efficient transient simulation of complex large-scale heat conduction problems using a domain decomposition method (DDM). This method allows for the division of complex, large-scale problems into smaller subdomain problems. By applying Robin-type transmission conditions at the subdomain interfaces, rapid convergence of the global interface iterative solution is achieved for arbitrary nonconformal subdomain problems. This nonconformal DDM approach supports independent meshing of subdomains, eliminating the need to generate a globally continuous mesh for large-scale problems, thereby significantly enhancing meshing efficiency. In addition, this nonconformal meshing strategy enables high-contrast spatial discretization and mixed-order spectral interpolation between different subdomains. This significantly increases meshing flexibility, minimizes the number of degrees of freedom (DoFs) in multiscale problems, and reduces computational costs. In addition, by developing a subdomain-coupled time iteration scheme, the global corner problem of residual transfer is explicitly given, which greatly improves the versatility and flexibility of the algorithm. Finally, to demonstrate the accuracy, efficiency, and robustness of our algorithm, we conduct benchmark tests on several representative examples.