A RTC-DG Method for Electrical-Thermal-Stress Analysis of 3-D Packages of Integrated Circuits with Micro-Fluidic Cooling

In this work, a Robin transmission condition (RTC) augmented discontinuous Galerkin (DG) method (RTC-DG) is proposed for electrical-thermal-stress analysis of 3-D integrated circuits with micro-fluidic cooling. Unlike the conventional DG method, the proposed DG scheme is directly applied to discretize the high-order governing partial-differential equations (PDEs), and the resulted numerical flux is used for the information communication among neighboring subdomains. To strictly confine the new variables introduced by the numerical flux, a firstorder RTC is derived at the interface of adjacent subdomains, which serves as an auxiliary equation in helping solving the new variables. In such a way, it only needs to solve the newly introduced variables at the interface of subdomains, thus the number of degrees of freedoms (DoFs) is significantly reduced in comparison with the convential DG method. In addition, to keep the domain decomposition capability of the DG method for steady-state issues, a finite-element-tearing-and-interconnecting (FETI) like procedure is resorted to decomposed the globally-coupled matrix equation into a number of small matrix equations that can be parallely solved by a direct solver. To validate the accuracy and efficiency of proposed algorithm, the proposed RTC-DG method is applied to electrical-thermal-stress simulation for a 3-D package with micro-fluidic channel.