H2-matrix-based finite element linear solver for fast transient thermal analysis of high-performance ICs

Summary In this article, we propose H2‐based finite element (FE) solver for transient thermal analysis of high‐performance integrated circuits (ICs). H2‐matrix is a special subclass of hierarchical matrix or H‐matrix, which was shown to provide a data‐sparse way to approximate the matrices and their...

Full description

Saved in:
Bibliographic Details
Published in:International journal of circuit theory and applications 2015-12, Vol.43 (12), p.1953-1970
Main Authors: Chen, Hai-Bao, Tan, Sheldon X.-D., Shin, David H., Huang, Xin, Wang, Hai, Shi, Guoyong
Format: Article
Language:English
Subjects:
finite element method
H2-matrix
integrated circuits
thermal analysis
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Summary In this article, we propose H2‐based finite element (FE) solver for transient thermal analysis of high‐performance integrated circuits (ICs). H2‐matrix is a special subclass of hierarchical matrix or H‐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 H2‐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 H2‐representations with controlled error. Then, we demonstrate that both storage and time complexities of the new solver are bounded by ON, 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. We propose H2‐based finite element solver for transient thermal analysis of high‐performance integrated circuits (ICs). Both storage and time complexities of the new solver are bounded by ON, where N is the matrix size. 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.
ISSN:0098-9886
1097-007X
DOI:10.1002/cta.2051