A parallel and incremental extraction of variational capacitance with stochastic geometric moments
This paper presents a parallel and incremental solver for stochastic capacitance extraction. The random geometrical variation is described by stochastic geometrical moments, which lead to a densely augmented system equation. To efficiently extract the capacitance and solve the system equation, a par...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2012
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| Online Access: | https://hdl.handle.net/10356/99888 http://hdl.handle.net/10220/8560 |
| _version_ | 1811676849423515648 |
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| author | Gong, Fang Yu, Hao Wang, Lingli He, Lei |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Gong, Fang Yu, Hao Wang, Lingli He, Lei |
| author_sort | Gong, Fang |
| collection | NTU |
| description | This paper presents a parallel and incremental solver for stochastic capacitance extraction. The random geometrical variation is described by stochastic geometrical moments, which lead to a densely augmented system equation. To efficiently extract the capacitance and solve the system equation, a parallel fast-multipole-method (FMM) is developed in the framework of stochastic geometrical moments. This can efficiently estimate the stochastic potential interaction and its matrix-vector product (MVP) with charge. Moreover, a generalized minimal residual (GMRES) method with incremental update is developed to calculate both the nominal value and the variance. Our overall extraction show is called piCAP. A number of experiments show that piCAP efficiently handles a large-scale on-chip capacitance extraction with variations. Specifically, a parallel MVP in piCAP is up 3 × to faster than a serial MVP, and an incremental GMRES in piCAP is up to 15× faster than non-incremental GMRES methods. |
| first_indexed | 2024-10-01T02:28:00Z |
| format | Journal Article |
| id | ntu-10356/99888 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:28:00Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | ntu-10356/998882020-03-07T14:00:31Z A parallel and incremental extraction of variational capacitance with stochastic geometric moments Gong, Fang Yu, Hao Wang, Lingli He, Lei School of Electrical and Electronic Engineering DRNTU::Engineering::Electrical and electronic engineering This paper presents a parallel and incremental solver for stochastic capacitance extraction. The random geometrical variation is described by stochastic geometrical moments, which lead to a densely augmented system equation. To efficiently extract the capacitance and solve the system equation, a parallel fast-multipole-method (FMM) is developed in the framework of stochastic geometrical moments. This can efficiently estimate the stochastic potential interaction and its matrix-vector product (MVP) with charge. Moreover, a generalized minimal residual (GMRES) method with incremental update is developed to calculate both the nominal value and the variance. Our overall extraction show is called piCAP. A number of experiments show that piCAP efficiently handles a large-scale on-chip capacitance extraction with variations. Specifically, a parallel MVP in piCAP is up 3 × to faster than a serial MVP, and an incremental GMRES in piCAP is up to 15× faster than non-incremental GMRES methods. Accepted version 2012-09-18T06:40:58Z 2019-12-06T20:13:02Z 2012-09-18T06:40:58Z 2019-12-06T20:13:02Z 2011 2011 Journal Article Gong, F., Yu, H., Wang, L., & He, L. (2011). A parallel and incremental extraction of variational capacitance with stochastic geometric moments. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 20(9), 1729-1737. 1063-8210 https://hdl.handle.net/10356/99888 http://hdl.handle.net/10220/8560 10.1109/TVLSI.2011.2161352 162551 en IEEE transactions on very large scale integration (VLSI) systems © 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: [http://dx.doi.org/10.1109/TVLSI.2011.2161352]. application/pdf |
| spellingShingle | DRNTU::Engineering::Electrical and electronic engineering Gong, Fang Yu, Hao Wang, Lingli He, Lei A parallel and incremental extraction of variational capacitance with stochastic geometric moments |
| title | A parallel and incremental extraction of variational capacitance with stochastic geometric moments |
| title_full | A parallel and incremental extraction of variational capacitance with stochastic geometric moments |
| title_fullStr | A parallel and incremental extraction of variational capacitance with stochastic geometric moments |
| title_full_unstemmed | A parallel and incremental extraction of variational capacitance with stochastic geometric moments |
| title_short | A parallel and incremental extraction of variational capacitance with stochastic geometric moments |
| title_sort | parallel and incremental extraction of variational capacitance with stochastic geometric moments |
| topic | DRNTU::Engineering::Electrical and electronic engineering |
| url | https://hdl.handle.net/10356/99888 http://hdl.handle.net/10220/8560 |
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