System-Level Thermal Modeling Using Nonconformal Domain Decomposition and Model-Order Reduction

To keep up with increasing modeling complexity arising from 3-D integration, novel thermal modeling methods are required to tackle large-scale 3-D systems. In this paper, we propose a system-level thermal modeling method using nonconformal domain decomposition and Krylov space-based model-order reduction (MOR) for both steady-state and transient analysis. To efficiently model a 3-D system, the system is divided into separate domains with independent meshing grids using nonconformal domain decomposition. As a result, reduced-order models can be created for individual domains with MOR ports, which can reduce the computational challenge of performing MOR for the entire system with a large number of unknowns and ports. The connectivity between domains is captured using coupling matrices via Lagrange multipliers and Schur complements. In addition, the proposed method can efficiently handle varying design parameters, such as air convection coefficient and thermal conductivity without performing parameterized MOR. The modeling results show that the proposed method can efficiently simulate 3-D systems with hundreds of ports with a speed-up of 20×, compared with just thermal modeling using domain decomposition.