{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T22:54:56Z","timestamp":1777676096906,"version":"3.51.4"},"reference-count":24,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[1999,11,1]],"date-time":"1999-11-01T00:00:00Z","timestamp":941414400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of High Performance Computing Applications"],"published-print":{"date-parts":[[1999,11]]},"abstract":"<jats:p>Multilevel algorithms are a successful class of optimization techniques that address the mesh partitioning problem for mapping meshes onto parallel computers. They usually combine a graph contraction algorithm together with a lo-cal optimization method that refines the partition at each graph level. To date, these algorithms have been used al-most exclusively to minimize the cut-edge weight in the graph with the aim of minimizing the parallel communication overhead. However, it has been shown that for certain classes of problems, the convergence of the underlying solution algorithm is strongly influenced by the shape or aspect ratio of the subdomains. Therefore, in this paper, the authors modify the multilevel algorithms to optimize a cost function based on the aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.<\/jats:p>","DOI":"10.1177\/109434209901300404","type":"journal-article","created":{"date-parts":[[2005,3,8]],"date-time":"2005-03-08T14:23:33Z","timestamp":1110291813000},"page":"334-353","source":"Crossref","is-referenced-by-count":18,"title":["Multilevel Mesh Partitioning for Optimizing Domain Shape"],"prefix":"10.1177","volume":"13","author":[{"given":"C.","family":"Walshaw","sequence":"first","affiliation":[{"name":"School of Computing and Mathematical Sciences, University of Greenwich,\r                        London, U.K."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Cross","sequence":"additional","affiliation":[{"name":"School of Computing and Mathematical Sciences, University of Greenwich,\r                        London, U.K."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"Diekmann","sequence":"additional","affiliation":[{"name":"Hilti AG, Corporate Research, FL-9494 Schaan, Principality of Liechtenstein"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"Schlimbach","sequence":"additional","affiliation":[{"name":"School of Computing and Mathematical Sciences, University of Greenwich,\r                        London, U.K."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[1999,11,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1002\/cpe.4330060203"},{"key":"atypb2","volume-title":"Flow simulation with high performance computers II: Notes on numerical fluid mechanics","author":"Blazy, S.","year":"1995"},{"key":"atypb3","unstructured":"Bouhmala, N. 1998. Partitioning of unstructured meshes for parallel\n                processing. Ph.D. dissertation, Inst. d\u2019Informatique, Univ. Neuchatel."},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1986-0842125-3"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1096-9128(199801)10:1<53::AID-CPE288>3.0.CO;2-W"},{"key":"atypb6","first-page":"170","volume-title":"Proceedings of Irregular \u201898: Solving irregularly structured problems in parallel","author":"Diekmann, R."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620380608"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(94)90068-X"},{"key":"atypb9","first-page":"175","volume-title":"Proceedings of the 19th IEEE Design Automation Conference","author":"Fiduccia, C. M."},{"issue":"1","key":"atypb10","first-page":"171","volume":"41","author":"Gupta, A.","year":"1996","journal-title":"IBM Journal of Re-search and Development"},{"key":"atypb11","volume-title":"A multilevel algorithm for partitioning graphs","author":"Hendrickson, B.","year":"1993"},{"key":"atypb12","volume-title":"Proceedings of Supercomputing \u201895","author":"Hendrickson, B."},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1096-9128(199805)10:6<467::AID-CPE325>3.0.CO;2-A"},{"key":"atypb14","volume-title":"A fast and high quality multi-level scheme for partitioning irregular graphs","author":"Karypis, G.","year":"1995"},{"key":"atypb15","volume-title":"Multilevel k-way partitioning scheme for irregular graphs","author":"Karypis, G.","year":"1995"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1970.tb01770.x"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1126\/science.220.4598.671"},{"key":"atypb18","first-page":"212","volume-title":"Proceedings of ACM Conference on Computer Geometry","author":"Mitchell, S. A."},{"key":"atypb19","unstructured":"Schlimbach, F. 1998. Load balancing heuristics optimising sub-domain aspect\n                ratios for adaptive finite element simulations. Diploma thesis, Department of\n                Mathematics and Computer Science, University of Paderborn."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(96)01024-9"},{"key":"atypb21","first-page":"611","volume-title":"Parallel processing for scientific computing","author":"Vanderstraeten, D.","year":"1995"},{"key":"atypb22","volume-title":"Mesh partitioning: A multi-level balancing and refinement algorithm","author":"Walshaw, C.","year":"1998"},{"key":"atypb23","first-page":"381","volume-title":"Proceedings of VecPar\u201998, Porto, Portugal","author":"Walshaw, C."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1006\/jpdc.1997.1407"}],"container-title":["The International Journal of High Performance Computing Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/109434209901300404","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/109434209901300404","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T08:17:39Z","timestamp":1777450659000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/109434209901300404"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,11]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1999,11]]}},"alternative-id":["10.1177\/109434209901300404"],"URL":"https:\/\/doi.org\/10.1177\/109434209901300404","relation":{},"ISSN":["1094-3420","1741-2846"],"issn-type":[{"value":"1094-3420","type":"print"},{"value":"1741-2846","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,11]]}}}