Dense Matrix Inversion of Linear Complexity for Integral-Equation-Based Large-Scale 3-D Capacitance Extraction

@article{Chai2011DenseMI,
  title={Dense Matrix Inversion of Linear Complexity for Integral-Equation-Based Large-Scale 3-D Capacitance Extraction},
  author={Wenwen Chai and Dan Jiao},
  journal={IEEE Transactions on Microwave Theory and Techniques},
  year={2011},
  volume={59},
  pages={2404-2421}
}
State-of-the-art integral-equation-based solvers rely on techniques that can perform a dense matrix-vector multiplication in linear complexity. We introduce the H2 matrix as a mathematical framework to enable a highly efficient computation of dense matrices. Under this mathematical framework, as yet, no linear complexity has been established for matrix inversion. In this work, we developed a matrix inverse of linear complexity to directly solve the dense system of linear equations for the 3-D… CONTINUE READING
Highly Cited
This paper has 31 citations. REVIEW CITATIONS

Citations

Publications citing this paper.
Showing 1-10 of 25 extracted citations

Accuracy-Controlled and Structure-Preserved H2-Matrix-Matrix Product in Linear Complexity

2018 International Conference on Electromagnetics in Advanced Applications (ICEAA) • 2018
View 2 Excerpts

Direct Solution of General H2-Matrix with Controlled Accuracy and Change of Cluster Bases for Large-Scale Electromagnetic Analysis

2018 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO) • 2018
View 2 Excerpts

Linear-complexity direct integral equation solver with explicit accuracy control for large-scale interconnect extraction

2018 International Applied Computational Electromagnetics Society Symposium (ACES) • 2018
View 2 Excerpts

Accuracy directly controlled fast direct solutions of general H2-matrices and its application to electrically large electromagnetic analysis

2017 International Conference on Electromagnetics in Advanced Applications (ICEAA) • 2017
View 2 Excerpts

Accuracy directly controlled fast direct solutions of general h2-matrices

2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting • 2017
View 1 Excerpt

References

Publications referenced by this paper.
Showing 1-10 of 25 references

-Matrix Arithmetics in Linear Complexity

Computing • 2005
View 9 Excerpts
Highly Influenced

Sparse transformations and preconditioners for hierarchical 3-D capacitance extraction with multiple dielectrics

Proceedings. 41st Design Automation Conference, 2004. • 2004
View 5 Excerpts
Highly Influenced

Hierarchical Matrices, ser

S. Börm, L. Grasedyck, W. Hackbusch
Lecture Note 21. Bonn, Germany: Max Planck Inst. Math., • 2003
View 6 Excerpts
Highly Influenced

Matrix inversion lemma

H. Boltz
Wikipedia 2011. [Online]. Available: http://en.wikipedia.org/wiki/Invertible_matrix CHAI AND JIAO: DENSE MATRIX INVERSION OF LINEAR COMPLEXITY FOR IE-BASED LARGE-SCALE 3-D CAPACITANCE EXTRACTION 2421 • 2011
View 2 Excerpts

Fast direct solvers for integral equations in complex three-dimensional domains

L. Greengard, D. Gueyffier, P.-G. Martinnson, V. Rokhlin
Acta Numer., pp. 261–288, 2009. • 2009
View 1 Excerpt

Direct Solve of Electrically Large Integral Equations for Problem Sizes to 1 M Unknowns

IEEE Transactions on Antennas and Propagation • 2008
View 2 Excerpts

Modular Fast Direct Electromagnetic Analysis Using Local-Global Solution Modes

IEEE Transactions on Antennas and Propagation • 2008
View 2 Excerpts

Similar Papers

Loading similar papers…