Direct finite-element-based solver for 3D-IC thermal analysis via H-matrix representation

Li, Ying-Chi; Tan, Sheldon X.-D.; Yu, Tan; Huang, Xin; Wong, Ngai

doi:10.1109/isqed.2014.6783351

Cited by 2 publications

(1 citation statement)

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“…The

scriptH

‐matrix structure has been used in solving electrostatic and magneto‐static problems in which the resulting electromagnetic wave PDEs are hyperbolic . Recently, we proposed an FE‐based method for transient thermal analysis of high‐performance ICs, which is a parabolic problem, based on the

scriptH

‐matrix representation . We approved that the

scriptH

‐matrix based approach can still work for the parabolic problems.…”

Section: Introductionmentioning

confidence: 99%

²‐matrix‐based finite element linear solver for fast transient thermal analysis of high‐performance ICs

Chen

Tan

Shin

et al. 2014

Circuit Theory & Apps

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Summary In this article, we propose scriptH2‐based finite element (FE) solver for transient thermal analysis of high‐performance integrated circuits (ICs). scriptH2‐matrix is a special subclass of hierarchical matrix or scriptH‐matrix, which was shown to provide a data‐sparse way to approximate the matrices and their inverses with almost linear space and time complexities. In this work, we show that scriptH2‐based mathematical framework can also be applied to FE‐based transient analysis of thermal parabolic partial differential equations. We show how the thermal matrix can be approximated by scriptH2‐representations with controlled error. Then, we demonstrate that both storage and time complexities of the new solver are bounded by scriptO()N, where N is the matrix size. The method can be applied to any thermal structures for both steady and transient analysis. The numerical results from 3D ICs demonstrate the linear scalability of the proposed method in terms of both memory footprint and CPU time. The comparison with existing product‐quality LU solvers, CSPARSE and UMFPACK, on a number of 3D IC thermal matrices, shows that the new method is much more memory efficient than these methods, which however prevents the demonstration of the potential speedup of the proposed method over those methods. Copyright © 2014 John Wiley & Sons, Ltd.

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“…The

scriptH

scriptH

‐matrix representation . We approved that the

scriptH

‐matrix based approach can still work for the parabolic problems.…”

Section: Introductionmentioning

confidence: 99%

²‐matrix‐based finite element linear solver for fast transient thermal analysis of high‐performance ICs

Chen

Tan

Shin

et al. 2014

Circuit Theory & Apps

Self Cite

View full text Add to dashboard Cite

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ThermTap: An online power analyzer and thermal simulator for Android devices

Dousti

Ghasemi-Gol

Nazemi

et al. 2015

2015 IEEE/ACM International Symposium on Low Power Electronics and Design (ISLPED)

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Direct finite-element-based solver for 3D-IC thermal analysis via H-matrix representation

Cited by 2 publications

References 12 publications

²‐matrix‐based finite element linear solver for fast transient thermal analysis of high‐performance ICs

²‐matrix‐based finite element linear solver for fast transient thermal analysis of high‐performance ICs

ThermTap: An online power analyzer and thermal simulator for Android devices

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Direct finite-element-based solver for 3D-IC thermal analysis via H-matrix representation

Cited by 2 publications

References 12 publications

2‐matrix‐based finite element linear solver for fast transient thermal analysis of high‐performance ICs

2‐matrix‐based finite element linear solver for fast transient thermal analysis of high‐performance ICs

ThermTap: An online power analyzer and thermal simulator for Android devices

Contact Info

Product

Resources

About

²‐matrix‐based finite element linear solver for fast transient thermal analysis of high‐performance ICs

²‐matrix‐based finite element linear solver for fast transient thermal analysis of high‐performance ICs