{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:30:26Z","timestamp":1787329826063,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[1995,9]]},"abstract":"<jats:p>We describe new high-order, momentum conserving methods for spreading charge to and interpolating potential from the mesh. These methods permit efficient grid-based algorithms to be used in high-order accurate n-body particle codes such as the fast multipole algorithm (FMM) of Greengard and Rokhlin [J. Comput. Phys., 73 (1987), pp. 325\u2013348]. We report on experiments showing that potential evaluation using our spreading and interpolating techniques are significantly more accurate than evaluation using multipole expansions directly. We describe, briefly, how to incorporate our methods into the FMM.<\/jats:p>","DOI":"10.1137\/0916062","type":"journal-article","created":{"date-parts":[[2005,3,1]],"date-time":"2005-03-01T03:42:54Z","timestamp":1109648574000},"page":"1082-1091","source":"Crossref","is-referenced-by-count":18,"title":["Grid-Multipole Calculations"],"prefix":"10.1137","volume":"16","author":[{"given":"C. Leonard","family":"Berman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,13]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0913055"},{"key":"R2","volume-title":"Vortex dynamics and vortex methods","author":"Anderson C. R.","year":"1991"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0906008"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160440202"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4655(91)90151-A"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1063\/1.463935"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"A. Dutt, V. Rokhlin,  on the rapid evaluation of trigonometric series, Tech. report, DCS\/RR-893, Yale University, New Haven, CT,  1992, March","DOI":"10.21236\/ADA249029"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90238-I"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/5750.001.0001"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/0911035"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(87)90140-9"},{"key":"R12","unstructured":"L. Greengard, V. Rokhlin,  On the efficient implementation of the fastmultipole algorithm, Research report, YALEU\/DCS\/RR-602, Yale University, New Haven, CT,  1988, February"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0089775"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/0912004"},{"key":"R15","volume-title":"Computer Simulation Using Particles","author":"Hockney R. W.","year":"1981"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1038\/324446a0"},{"key":"R17","unstructured":"A. Mayo,  On the accuracy of a class of momentum conserving particle mesh methods, and the interpolation of elliptic functions on uniform meshes, Technical rep., RC 14306, IBM Research, Yorktown Heights, NY,  1989, January"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/0915046"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(85)90002-6"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(90)90107-C"},{"key":"R21","unstructured":"J. K. Salmon, Ph.D. Thesis,  Parallel Hierarchical  N Body Methods, California Institute of Technology, Pasadena, CA,  1990"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1992-1106983-2"},{"key":"R23","volume-title":"Matrix computations","author":"Van Loan Charles F.","year":"1989"},{"key":"R24","volume-title":"Mathematical analysis of physical problems","author":"Wallace Philip R.","year":"1984"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/0916062","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:35:23Z","timestamp":1787326523000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/0916062"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,9]]},"references-count":24,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1995,9]]}},"alternative-id":["10.1137\/0916062"],"URL":"https:\/\/doi.org\/10.1137\/0916062","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,9]]}}}