{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,5]],"date-time":"2025-08-05T12:46:47Z","timestamp":1754398007389,"version":"3.41.0"},"reference-count":23,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2012,6,1]],"date-time":"2012-06-01T00:00:00Z","timestamp":1338508800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000143","name":"Division of Computing and Communication Foundations","doi-asserted-by":"publisher","award":["CCF-0634802"],"award-info":[{"award-number":["CCF-0634802"]}],"id":[{"id":"10.13039\/100000143","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Des. Autom. Electron. Syst."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p>\n            Accurate and efficient thermal analysis for a VLSI chip is crucial, both for sign-off reliability verification and for design-time circuit optimization. To determine an accurate temperature profile, it is important to simulate a die together with its thermal mounts: this requires solving Poisson's equation on a nonrectangular 3D domain. This article presents a class of eigendecomposition-based Fast Poisson Solvers (FPS) for chip-level thermal analysis. We start with a solver that solves a rectangular 3D domain with mixed boundary conditions in O(\n            <jats:italic>N<\/jats:italic>\n            \u22c5 log\n            <jats:italic>N<\/jats:italic>\n            ) time, where\n            <jats:italic>N<\/jats:italic>\n            is the dimension of the finite difference matrix. Then we reveal, for the first time in the literature, a strong relation between fast Poisson solvers and Green-function-based methods. Finally, we propose an FPS method that leverages the preconditioned conjugate gradient method to solve nonrectangular 3D domains efficiently. We demonstrate this approach on thermal analysis of an industrial microprocessor, showing accurate results verified by a commercial tool, and that it solves a system of dimension 4.54e6 in only 13 conjugate gradient iterations, with a runtime of 65 seconds, a 15X speedup over the popular ICCG solver.\n          <\/jats:p>","DOI":"10.1145\/2209291.2209305","type":"journal-article","created":{"date-parts":[[2012,8,1]],"date-time":"2012-08-01T17:35:16Z","timestamp":1343842516000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["Fast poisson solvers for thermal analysis"],"prefix":"10.1145","volume":"17","author":[{"given":"Haifeng","family":"Qian","sequence":"first","affiliation":[{"name":"IBM T. J. Watson Research Center, NY"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sachin S.","family":"Sapatnekar","sequence":"additional","affiliation":[{"name":"University of Minnesota, MN"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eren","family":"Kursun","sequence":"additional","affiliation":[{"name":"IBM T. J. Watson Research Center, NY"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2012,7,5]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479894278952"},{"key":"e_1_2_1_2_1","unstructured":"ANSYS Thermal Modeling Reference. 2012. http:\/\/www1.ansys.com\/customer\/content\/documentation\/121\/ans_the.pdf.  ANSYS Thermal Modeling Reference. 2012. http:\/\/www1.ansys.com\/customer\/content\/documentation\/121\/ans_the.pdf."},{"volume-title":"Proceedings of the International Conference on Thermal Issues in Emerging Technologies, Theory and Applications. 111--118","author":"Bagnoli P. E.","key":"e_1_2_1_3_1","unstructured":"Bagnoli , P. E. , Casarosa , C. , and Stefani , F . 2007. DJOSER: Analytical thermal simulator for multilayer electronic structures. Theory and numerical implementation . In Proceedings of the International Conference on Thermal Issues in Emerging Technologies, Theory and Applications. 111--118 . Bagnoli, P. E., Casarosa, C., and Stefani, F. 2007. DJOSER: Analytical thermal simulator for multilayer electronic structures. Theory and numerical implementation. In Proceedings of the International Conference on Thermal Issues in Emerging Technologies, Theory and Applications. 111--118."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/43.759076"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/4.494196"},{"volume-title":"Proceedings of the 13th International Workshop on Thermal Investigation of ICs and Systems. 18--25","author":"Heriz V. M.","key":"e_1_2_1_6_1","unstructured":"Heriz , V. M. , Park , J. , Kemper , T. , Kang , S. , and Shakouri , A . 2007. Method of images for the fast calculation of temperature distributions in packaged VLSI chips . In Proceedings of the 13th International Workshop on Thermal Investigation of ICs and Systems. 18--25 . Heriz, V. M., Park, J., Kemper, T., Kang, S., and Shakouri, A. 2007. Method of images for the fast calculation of temperature distributions in packaged VLSI chips. In Proceedings of the 13th International Workshop on Thermal Investigation of ICs and Systems. 18--25."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2006.876103"},{"volume-title":"Proceedings of the IEEE\/IFIP VLSI System on Chip Conference. 276--279","author":"Jimenez V.","key":"e_1_2_1_8_1","unstructured":"Jimenez , V. , Gioiosa , R. , Kursun , E. , Cazorla , F. J. , Cher , C. , Buyuktosunoglu , A. , Bose , P. , and Valero , M . 2010. Trends and techniques for energy efficient architectures . In Proceedings of the IEEE\/IFIP VLSI System on Chip Conference. 276--279 . Jimenez, V., Gioiosa, R., Kursun, E., Cazorla, F. J., Cher, C., Buyuktosunoglu, A., Bose, P., and Valero, M. 2010. Trends and techniques for energy efficient architectures. In Proceedings of the IEEE\/IFIP VLSI System on Chip Conference. 276--279."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.1984.1270066"},{"key":"e_1_2_1_10_1","volume-title":"METIS: Unstructured graph partitioning and sparse matrix ordering system, version 2.0","author":"Karypis G.","year":"1995","unstructured":"Karypis , G. and Kumar , V . 1995 . METIS: Unstructured graph partitioning and sparse matrix ordering system, version 2.0 . http:\/\/glaros.dtc.umn.edu\/gkhome\/views\/metis. Karypis, G. and Kumar, V. 1995. METIS: Unstructured graph partitioning and sparse matrix ordering system, version 2.0. http:\/\/glaros.dtc.umn.edu\/gkhome\/views\/metis."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1147\/rd.516.0639"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCAD.2004.1382594"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1687399.1687447"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1109\/43.703820"},{"volume-title":"Iterative Methods for Sparse Linear Systems","author":"Saad Y.","key":"e_1_2_1_15_1","unstructured":"Saad , Y. 2003. Iterative Methods for Sparse Linear Systems . SIAM , Philadelphia, PA . Saad, Y. 2003. Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, PA."},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2011.2164540"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/1629911.1629961"},{"volume-title":"Proceedings of the IEEE\/ACM International Conference on Computer-Aided Design (Digest of Technical Papers). 463--470","author":"Sridhar A.","key":"e_1_2_1_18_1","unstructured":"Sridhar , A. , Vincenzi , A. , Ruggiero , M. , Brunschwiler , T. , and Atienza , D . 2010. 3D-ICE: Fast compact transient thermal modeling for 3D ICs with inter-tier liquid cooling . In Proceedings of the IEEE\/ACM International Conference on Computer-Aided Design (Digest of Technical Papers). 463--470 . Sridhar, A., Vincenzi, A., Ruggiero, M., Brunschwiler, T., and Atienza, D. 2010. 3D-ICE: Fast compact transient thermal modeling for 3D ICs with inter-tier liquid cooling. 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