An Interior Penalty Domain Decomposition Method for Thermal Analysis of 3-D Integrated Systems

Abstract

This article presents a finite-element-based domain decomposition method (DDM) for thermal analysis of 3-D large-scale and geometrically complicated integrated systems. The presented DDM decomposes the entire problem domain into many nonoverlapping subdomains, and a novel transmission condition (TC) based on a fictitious thermal contact resistance is introduced and then imposed through an interior penalty (IP) Galerkin procedure to enforce continuity at the interfaces between subdomains. The major advantage of the novel TC combined with the IP Galerkin procedure is that no extra unknowns are introduced and the system matrix arising from the finite element method will be symmetric and positive definite. Furthermore, the solving procedure of matrix equation adopts the preconditioned conjugate gradient method with a two-level preconditioner. To verify the convergence and accuracy, this article calculates the transient temperature profile of a brick and compares the computed numerical approximation with the exact solution. Meanwhile, the solving advantage of the proposed DDM is shown by comparing with Robin-TC DDM. Finally, numerical results for a 3-D integration package are shown to demonstrate the accuracy and superior performance of the proposed DDM.