Abstract

Since accurate thermal analysis plays a critical role in the thermal design and management of the 3-D system-level integration, in this paper, a discontinuous Galerkin time-domain (DGTD) algorithm is proposed to achieve this purpose. Such as the parabolic partial differential equation (PDE), the transient thermal equation cannot be directly solved by the DGTD method. To address this issue, the heat flux, as an auxiliary variable, is introduced to reduce the Laplace operator to a divergence operator. The resulting PDE is hyperbolic, which can be further written into a conservative form. By properly choosing the definition of the numerical flux used for the information exchange between neighboring elements, the hyperbolic thermal PDE can be solved by the DGTD together with the auxiliary differential equation. The proposed algorithm is a kind of element-level domain decomposition method, which is suitable to deal with multiscale geometries in 3-D integrated systems. To verify the accuracy and robustness of the developed DGTD algorithm, several representative examples are benchmarked.

Department(s)

Electrical and Computer Engineering

Keywords and Phrases

Auxiliary-differential equation (ADE) method; discontinuous Galerkin time-domain (DGTD) method; integrated circuit package; numerical flux; transient thermal analysis

International Standard Serial Number (ISSN)

2156-3950

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Institute of Electrical and Electronics Engineers; Electronics Packaging Society, All rights reserved.

Publication Date

01 Jun 2017

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