{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:50Z","timestamp":1787337290058,"version":"build-2736575974"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>We describe the implementation of a parallel algorithm that solves a computational geometry problem arising in meshfree methods. We solve the following problem: Given a collection of N d\u2010rectangles $S_i$ and Q points $x_k$ in $\\mathbb{R}^d$, compute $I_k = \\{ i \\mid x_k \\in S_i \\}$. This task is necessary for computing values of the meshfree basis functions $\\Psi_i(x_k)$ and can be used to efficiently compute the mass and stiffness matrices for the meshfree Galerkin method.<\/jats:p>","DOI":"10.1137\/s1064827502414321","type":"journal-article","created":{"date-parts":[[2006,8,24]],"date-time":"2006-08-24T15:30:58Z","timestamp":1156433458000},"page":"1318-1334","source":"Crossref","is-referenced-by-count":5,"title":["Parallel Support Set Searches for Meshfree Methods"],"prefix":"10.1137","volume":"28","author":[{"given":"C.","family":"Cartwright","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Oliveira","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D. E.","family":"Stewart","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(96)01078-X"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0117039"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501391588"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539799359361"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"A. Huerta, T. Belytchko, S. Fern\u00e1ndez\u2010M\u00e9ndez, and T. Rabczuk,\n                      Meshfree methods\n                      , in Encyclopedia of Computational Mechanics, Vol. 1, John Wiley & Sons, New York, 2004, pp. 279\u2013309.","DOI":"10.1002\/0470091355.ecm005"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/s004660050478"},{"key":"R7","unstructured":"Message Passing Interface Forum,\n                      MPI\n                      \u20102:\n                      Extensions to the Message\u2010Passing Interface\n                      , http:\/\/www.mpi\u2010forum.org\/docs\/docs.html (1997)."},{"key":"R8","unstructured":"P. Pacheco,\n                      Parallel Programming with MPI\n                      , Morgan Kaufmann, San Francisco, 1997."},{"key":"R9","unstructured":"H. Samet,\n                      The Design and Analysis of Spatial Data Structures\n                      , Ser. Comput. Sci., Addison\u2013Wesley, Reading, MA, 1990."},{"key":"R10","doi-asserted-by":"crossref","unstructured":"D. Shepard,\n                      A two\u2010dimensional function for irregularly spaced data\n                      , in Proceedings of the 23rd National Conference of the ACM, 1968, pp. 517\u2013524.","DOI":"10.1145\/800186.810616"},{"key":"R11","unstructured":"M. Snir, S. Otto, S. Huss\u2010Lederman, D. Walker, and J. Dongarra,\n                      MPI: The Complete Reference\n                      , MIT Press, Boston, 1996."},{"key":"R12","unstructured":"V. V. Vazirani,\n                      Approximation Algorithms\n                      , Springer\u2010Verlag, Berlin, 2001."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827502414321","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:54:49Z","timestamp":1787334889000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827502414321"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/S1064827502414321"],"URL":"https:\/\/doi.org\/10.1137\/s1064827502414321","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}