Proceedings ArticleDOI
A fast hierarchical algorithm for 3-D capacitance extraction
Weiping Shi,Jianguo Liu,Naveen K. Kakani,Tiejun Yu +3 more
- pp 212-217
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TLDR
A new algorithm for computing the capacitance of three-dimensional perfect electrical conductors of complex structures that is significantly faster and uses muc h less memory than previous best algorithms, and is kernel independent.Abstract:
We present a new algorithm for computing the capacitance of three-dimensional perfect electrical conductors of complex structures. The new algorithm is significantly faster and uses much less memory than previous best algorithms, and is kernel independent. The new algorithm is based on a hierarchical algorithm for the n-body problem, and is an acceleration of the boundary element method for solving the integral equation associated with the capacitance extraction problem. The algorithm first adaptively subdivides the conductor surfaces into panels according to an estimation of the potential coefficients and a user-supplied error bound. The algorithm stores the potential coefficient matrix in a hierarchical data structure of size O(n), although the matrix is size n/sup 2/ if expanded explicitly, where n is the number of panels. The hierarchical data structure allows us to multiply the coefficient matrix with any vector in O(n) time. Finally, we use a generalized minimal residual algorithm to solve m linear systems each of size n/spl times/n in O(mn) time, where m is the number of conductors. The new algorithm is implemented and the performance is compared with previous best algorithms. For the k/spl times/k bus example, our algorithm is 100 to 40 times faster than FastCap, and uses 1/100 to 1/60 of the memory used by FastCap. The results computed by the new algorithm are within 2.7% from that computed by FastCap.read more
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Journal ArticleDOI
Parasitic extraction: current state of the art and future trends
TL;DR: The state of the art in parasitic extraction for resistance, capacitance, and inductance is surveyed and some future trends on parasitic extraction, model reduction and interconnect modeling are discussed and a fairly complete list of references is given.
RecentProgress in NumericalMethods forthePoisson- Boltzmann Equation in Biophysical Applications
TL;DR: Recent developments in boundaryelement methods, interface methods, adaptive methods, finite element methods, and other approaches for the Poisson-Boltzmann equation as well as related mesh generation techniques are reviewed.
Proceedings ArticleDOI
Parasitic extraction: current state of the art and future trends
TL;DR: The state of the art in parasitic extraction for resistance, capacitance and inductance is surveyed and other related topics such as interconnect modeling, delay calculation and signal integrity issues such as crosstalk are covered.
Journal ArticleDOI
Fast capacitance extraction of actual 3-D VLSI interconnects using quasi-multiple medium accelerated BEM
TL;DR: In this article, a quasi-multiple medium (QMM) method based on the direct boundary element method (BEM) is presented to extract the capacitance of three-dimensional (3-D) very large scale integration interconnects with multiple dielectrics.
References
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Book
Introduction to Algorithms
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Journal ArticleDOI
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
Youcef Saad,Martin H. Schultz +1 more
TL;DR: An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace.
Journal ArticleDOI
A fast algorithm for particle simulations
TL;DR: An algorithm is presented for the rapid evaluation of the potential and force fields in systems involving large numbers of particles whose interactions are Coulombic or gravitational in nature, making it considerably more practical for large-scale problems encountered in plasma physics, fluid dynamics, molecular dynamics, and celestial mechanics.
Book
The Rapid Evaluation of Potential Fields in Particle Systems
TL;DR: In this paper, an algorithm for the rapid evaluation of the potential and force fields in large-scale ensembles of particles is presented, which requires an amount of work proportional to the number of particles.
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