An Efficient 3D-to-2D Reduction Technique for Frequency-Domain Layered Finite Element Analysis of Large-Scale High-Frequency Integrated Circuits

Sheng, Feng; Chakravarty, S.; Jiao, Dan

doi:10.1109/epep.2007.4387185

Cited by 5 publications

(3 citation statements)

References 6 publications

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“…12(a) and (b) shows the CPU cost and memory consumption in factorization, respectively. The conventional method has to factorize the entire system matrixT in (15), whereas the proposed method only needs to invert P ii in (26), which has a 1-D size and is tridiagonal. Fig.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Since the surface vector bases N i (i = 1 − 6, 10 − 15) are perpendicular to volume vector bases N i (i = 7 − 9), as can be seen from Fig. 1, andT in (15) solely comprises matrices formed by the inner product of N i and N j , all the Q matrices in Fig. 2(b) vanish.…”

Section: B Orfe-rr Methodsmentioning

confidence: 99%

“…Since P ii is a tridiagonal matrix, as shown in [15], its inverse can be stored efficiently in two sequences {u j } and {v j }, j = 1, 2, . .…”

Section: By Using P As the Preconditioner (22) Is Solved Iteratively Asmentioning

confidence: 99%

See 2 more Smart Citations

Time-Domain Orthogonal Finite-Element Reduction-Recovery Method for Electromagnetics-Based Analysis of Large-Scale Integrated Circuit and Package Problems

Chen

Jiao

2009

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Abstract-A time-domain orthogonal finite-element reductionrecovery method is developed to overcome the large problem sizes encountered in the simulation of large-scale integrated-circuit and package problems. In this method, a set of orthogonal prism vector basis functions is developed. Based on this set of bases, an arbitrary 3-D multilayered system such as a combined package and die is reduced to a single-layer system with negligible computational cost. More importantly, the reduced single-layer system is diagonal and, hence, can be solved readily. From the solution of the reduced system, the solution of the other unknowns is recovered in linear complexity. The method entails no theoretical approximation. It applies to any arbitrarily shaped multilayer structure involving inhomogeneous materials or any structure that can be geometrically modeled by triangular prism elements. In addition, it permits nonlinear device modeling and broadband simulation within one run. Numerical and experimental results have demonstrated its accuracy and high capacity in simulating on-chip, package, and die-package interface problems.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: B Orfe-rr Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Time-Domain Orthogonal Finite-Element Reduction-Recovery Method for Electromagnetics-Based Analysis of Large-Scale Integrated Circuit and Package Problems

Chen

Jiao

2009

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Fast iterative solution algorithms for the frequency-domain layered finite-element based analysis of large-scale on-chip interconnect structures

Sheng

Jiao

2008

2008 IEEE-EPEP Electrical Performance of Electronic Packaging

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Time-domain orthogonal finite-element reduction-recovery (OrFE-RR) method for fast and accurate broadband simulation of die-package interaction

Chen

Jiao

2008

2008 IEEE-EPEP Electrical Performance of Electronic Packaging

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The co-simulation of a die and a package results in numerical problems of ultra-large scale, requiring billions of parameters to describe them accurately. In this paper, an orthogonal finite-element reduction-recovery method is proposed to overcome the large problem sizes encountered in the simulation of an integrated die-package system. In this method, a set of orthogonal prism vector basis functions are developed to render the surface-unknown-based matrix in each layer diagonal. An arbitrary 3D multilayered system such as a combined package and die is then reduced to a single-layer system with negligible computational cost. The reduced single-layer system is diagonal due to the orthogonal bases, and hence can be solved readily. From the solution of the reduced single-layer system, the solution in other layers is recovered in linear complexity. The method entails no approximation. It applies to arbitrarily-shaped multilayer structures and arbitrary inhomogeneity. In addition, it permits nonlinear device modeling and broadband simulation within one run. Numerical and experimental results have demonstrated its accuracy and high capacity in simulating on-chip, package, and die-package interface problems.

show abstract

An Efficient 3D-to-2D Reduction Technique for Frequency-Domain Layered Finite Element Analysis of Large-Scale High-Frequency Integrated Circuits

Cited by 5 publications

References 6 publications

Time-Domain Orthogonal Finite-Element Reduction-Recovery Method for Electromagnetics-Based Analysis of Large-Scale Integrated Circuit and Package Problems

Time-Domain Orthogonal Finite-Element Reduction-Recovery Method for Electromagnetics-Based Analysis of Large-Scale Integrated Circuit and Package Problems

Fast iterative solution algorithms for the frequency-domain layered finite-element based analysis of large-scale on-chip interconnect structures

Time-domain orthogonal finite-element reduction-recovery (OrFE-RR) method for fast and accurate broadband simulation of die-package interaction

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