### Abstract

Boundary element methods (BEM) are often used for complex 3-D capacitance extraction because of their efficiency, ease of data preparation, and automatic handling of open regions. BEM capacitance extraction, however, yields a dense set of linear equations that makes solving via direct matrix methods such as Gaussian elimination prohibitive for large problem sizes. Although iterative, multipole-accelerated techniques have produced dramatic improvements in BEM capacitance extraction, accurate sparse approximations of the electrostatic potential matrix are still desirable for the following reasons. First, the corresponding capacitance models are sufficient for a large number of analysis and design applications. Moreover, even when the utmost accuracy is required, sparse approximations can be used to precondition iterative solution methods. In this paper, we propose a definition of electrostatic potential that can be used to formulate sparse approximations of the electrostatic potential matrix in both uniform and multilayered planar dielectrics. Any degree of sparsity can be obtained, and unlike conventional techniques which discard the smallest matrix terms, these approximations are provably positive definite for the troublesome cases with a uniform dielectric and without a groundplane.

Original language | English (US) |
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Pages (from-to) | 357-362 |

Number of pages | 6 |

Journal | Proceedings - Design Automation Conference |

State | Published - Jan 1 1996 |

Externally published | Yes |

Event | Proceedings of the 1996 33rd Annual Design Automation Conference - Las Vegas, NV, USA Duration: Jun 3 1996 → Jun 7 1996 |

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### ASJC Scopus subject areas

- Hardware and Architecture
- Control and Systems Engineering

### Cite this

*Proceedings - Design Automation Conference*, 357-362.

**Sparse image method for BEM capacitance extraction.** / Krauter, Byron; Xia, Yu; Dengi, Enis; Pileggi, Lawrence T.

Research output: Contribution to journal › Conference article

*Proceedings - Design Automation Conference*, pp. 357-362.

}

TY - JOUR

T1 - Sparse image method for BEM capacitance extraction

AU - Krauter, Byron

AU - Xia, Yu

AU - Dengi, Enis

AU - Pileggi, Lawrence T.

PY - 1996/1/1

Y1 - 1996/1/1

N2 - Boundary element methods (BEM) are often used for complex 3-D capacitance extraction because of their efficiency, ease of data preparation, and automatic handling of open regions. BEM capacitance extraction, however, yields a dense set of linear equations that makes solving via direct matrix methods such as Gaussian elimination prohibitive for large problem sizes. Although iterative, multipole-accelerated techniques have produced dramatic improvements in BEM capacitance extraction, accurate sparse approximations of the electrostatic potential matrix are still desirable for the following reasons. First, the corresponding capacitance models are sufficient for a large number of analysis and design applications. Moreover, even when the utmost accuracy is required, sparse approximations can be used to precondition iterative solution methods. In this paper, we propose a definition of electrostatic potential that can be used to formulate sparse approximations of the electrostatic potential matrix in both uniform and multilayered planar dielectrics. Any degree of sparsity can be obtained, and unlike conventional techniques which discard the smallest matrix terms, these approximations are provably positive definite for the troublesome cases with a uniform dielectric and without a groundplane.

AB - Boundary element methods (BEM) are often used for complex 3-D capacitance extraction because of their efficiency, ease of data preparation, and automatic handling of open regions. BEM capacitance extraction, however, yields a dense set of linear equations that makes solving via direct matrix methods such as Gaussian elimination prohibitive for large problem sizes. Although iterative, multipole-accelerated techniques have produced dramatic improvements in BEM capacitance extraction, accurate sparse approximations of the electrostatic potential matrix are still desirable for the following reasons. First, the corresponding capacitance models are sufficient for a large number of analysis and design applications. Moreover, even when the utmost accuracy is required, sparse approximations can be used to precondition iterative solution methods. In this paper, we propose a definition of electrostatic potential that can be used to formulate sparse approximations of the electrostatic potential matrix in both uniform and multilayered planar dielectrics. Any degree of sparsity can be obtained, and unlike conventional techniques which discard the smallest matrix terms, these approximations are provably positive definite for the troublesome cases with a uniform dielectric and without a groundplane.

UR - http://www.scopus.com/inward/record.url?scp=0029697872&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029697872&partnerID=8YFLogxK

M3 - Conference article

SP - 357

EP - 362

JO - Proceedings - Design Automation Conference

JF - Proceedings - Design Automation Conference

SN - 0738-100X

ER -