In this article, a discontinuous Galerkin time-domain (DGTD) method hybridized with Robin transmission condition (RTC-DGTD) is proposed for the transient thermal analysis of 3-D integrated circuits (ICs). As a kind of domain decomposition method (DDM), the DGTD method employs a term named numerical flux for the information exchange of solutions between neighboring subdomains. The numerical flux is a function of both temperature T and heat flux q, and thus for the heat equation, apart from T, the variable q has to be solved as well. To reach this, the traditional DGTD method decomposes the second-order partial-differential thermal equation into two first-order ones, which results that both T and q need to be solved in the whole computational domain, thereby the computational cost is extremely expensive. In this work, to get this trouble-treated, the proposed DGTD method is directly applied to discretize the second-order heat equation. An RTC is established at the interfaces of subdomains, which serves as the second governing equation and meanwhile bridges another connection of solutions in adjacent subdomains. In this way, the new variable q is now only present at the interfaces of subdomains. Consequently, the total number of unknowns is significantly reduced compared with that in the traditional DGTD method. To further speed up the time-marching scheme, an adaptive time-stepping method in terms of the proportional-integral-derivative (PID) control algorithm is employed. Besides, by introducing a restriction operator, the globally coupled matrix equation is torn into a number of small matrix equations pertinent to each subdomain, which is later solved via a finite-element tearing and interconnecting (FETI)-like method. To validate and verify the accuracy and efficiency of the proposed algorithm, several representative examples are studied and compared with COMSOL simulations.


Electrical and Computer Engineering

Keywords and Phrases

Adaptive time-stepping; discontinuous Galerkin time-domain (DGTD) method; domain decomposition method (DDM); Robin transmission condition (RTC); transient thermal analysis

International Standard Serial Number (ISSN)

2156-3985; 2156-3950

Document Type

Article - Journal

Document Version


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Publication Date

01 Sep 2022