A rapid hierarchical radiosity algorithm
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
The order of Appel's algorithm
Information Processing Letters
A sparse image method for BEM capacitance extraction
DAC '96 Proceedings of the 33rd annual Design Automation Conference
Matrix computations (3rd ed.)
A fast hierarchical algorithm for 3-D capacitance extraction
DAC '98 Proceedings of the 35th annual Design Automation Conference
The rapid evaluation of potential fields in particle systems
The rapid evaluation of potential fields in particle systems
Efficient inductance extraction via windowing
Proceedings of the conference on Design, automation and test in Europe
On the efficacy of simplified 2D on-chip inductance models
Proceedings of the 39th annual Design Automation Conference
Inductance Modeling for On-Chip Interconnects
Analog Integrated Circuits and Signal Processing
Proceedings of the 41st annual Design Automation Conference
CHIME: coupled hierarchical inductance model evaluation
Proceedings of the 41st annual Design Automation Conference
Proceedings of the 2004 Asia and South Pacific Design Automation Conference
Improving boundary element methods for parasitic extraction
ASP-DAC '03 Proceedings of the 2003 Asia and South Pacific Design Automation Conference
Efficient statistical capacitance variability modeling with orthogonal principle factor analysis
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Proceedings of the 44th annual Design Automation Conference
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The increasing interconnect density and operating frequencies of system-on-a-chip (SOC) designs necessitates extraction of parasitic electromagnetic couplings beyond the localized confines of functional design blocks. In addition, SOC design styles and gridless variable-width routing make it increasingly difficult to use precharacterized library shapes for parasitic extraction. A comprehensive capacitance and inductance extraction solution requires a hierarchical data representation and fast runtime algorithms. We illustrate through examples that both the multipole method and hierarchical refinement, which are the two most successful approaches for parasitic extraction to date, work efficiently only under certain, limiting conditions. To improve this situation we present an approach which combines the best of both methods into a concurrent multipole refinement representation of the electromagnetic interaction which is efficient for arbitrary interconnect configurations. We use a generalized formulation of electromagnetic interactions to exploit the similarities in capacitance and inductance extraction for greater efficiency.