Proceedings ArticleDOI
From O(k 2 N) to O(N): A fast complex-valued eigenvalue solver for large-scale on-chip interconnect analysis
Jongwon Lee,Venkataramanan Balakrishnan,Cheng-Kok Koh,Dan Jiao +3 more
- pp 181-184
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TLDR
This work reduces the computational complexity of the Arnoldi iteration from O(k2N) to O(N), thus paving the way for full-wave extraction of very large-scale on-chip interconnects, the k of which is hundreds of thousands.Abstract:
In general, the optimal computational complexity of Arnoldi iteration is O(k2N) for solving a generalized eigenvalue problem, with k being the number of dominant eigenvalues and N the matrix size. In this work, we reduce the computational complexity of the Arnoldi iteration from O(k2N) to O(N), thus paving the way for full-wave extraction of very large-scale on-chip interconnects, the k of which is hundreds of thousands. Numerical and experimental results have demonstrated the accuracy and efficiency of the proposed fast eigenvalue solver.read more
Citations
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Journal ArticleDOI
A Theoretically Rigorous Full-Wave Finite-Element-Based Solution of Maxwell's Equations From dc to High Frequencies
Jianfang Zhu,Dan Jiao +1 more
TL;DR: In this article, a theoretically rigorous method is presented to fundamentally eliminate the low-frequency breakdown problem, where the original frequency-dependent deterministic problem can be rigorously solved from a generalized eigenvalue problem that is frequency independent.
Journal ArticleDOI
A Rigorous Solution to the Low-Frequency Breakdown in Full-Wave Finite-Element-Based Analysis of General Problems Involving Inhomogeneous Lossless/Lossy Dielectrics and Nonideal Conductors
Jianfang Zhu,Dan Jiao +1 more
TL;DR: In this article, a rigorous method that does not utilize low-frequency approximations is developed to eliminate the low frequency breakdown problem for the full-wave finite-element based analysis of general 3D problems involving inhomogeneous lossless and/or lossy dielectrics and nonideal conductors.
Journal ArticleDOI
A Quadratic Eigenvalue Solver of Linear Complexity for 3-D Electromagnetics-Based Analysis of Large-Scale Integrated Circuits
TL;DR: This paper successfully solves a quadratic eigenvalue problem of over 2.5 million unknowns associated with a large-scale 3-D on-chip circuit embedded in inhomogeneous materials in 40 min on a single 3 GHz 8222SE AMD Opteron processor.
Journal ArticleDOI
Fast Full-Wave Solution That Eliminates the Low-Frequency Breakdown Problem in a Reduced System of Order One
Jianfang Zhu,Dan Jiao +1 more
TL;DR: In this article, a fast finite-element-based solution is developed to eliminate the low-frequency breakdown problem in a reduced system of order one, which is applicable to general 3D problems involving ideal conductors as well as nonideal conductors immersed in inhomogeneous, lossless, lossy, and dispersive materials.
Posted Content
Exploiting constant trace property in large-scale polynomial optimization
TL;DR: It is proved that every semidfinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant trace property (CTP) and extended to large-scale POPs with different sparsity structures.
References
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Proceedings ArticleDOI
A novel technique for full-wave modeling of large-scale three-dimensional high-speed on/off-chip interconnect structures
TL;DR: This method can generate S-parameters, full-wave RLGC, propagation constants, characteristic impedances, voltage, current, and field distributions, and hence yield a comprehensive representation of interconnect structures, and experimental and numerical results demonstrate its accuracy and efficiency.
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On-chip interconnect modeling by wire duplication
TL;DR: A novel wire duplication-based interconnect modeling technique that exploits the sparsity of the L−1 matrix, where L is the inductance matrix, and constructs a sparse and stable equivalent RLC circuit by windowing the original inductance Matrix.
Journal ArticleDOI
A Fast Frequency-Domain Eigenvalue-Based Approach to Full-Wave Modeling of Large-Scale Three-Dimensional On-Chip Interconnect Structures
TL;DR: This paper presents a novel, high-capacity, and fast approach to the full-wave modeling of 3-D on- chip interconnect structures, and develops a new mode-matching technique applicable to on-chip interconnects to solve large-scale3-D problems by using 2-D-like CPU time and memory.
Journal ArticleDOI
On-chip interconnect modeling by wire duplication
TL;DR: The authors present a novel wire duplication-based interconnect modeling technique that exploits the sparsity of the L/sup -1/ matrix, where L is the inductance matrix, and constructs a sparse and stable equivalent circuit by windowing the original inductance Matrix.
Proceedings ArticleDOI
A linear-time eigenvalue solver for finite-element-based analysis of large-scale wave propagation problems in on-chip interconnect structures
TL;DR: An algorithm is presented that provides a solution to the generalized eigenvalue problem with O(M) complexity, thus paving the way for the full-wave simulation of next generation VLSI circuits.
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