{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:29:57Z","timestamp":1787336997106,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>A strategy for determining the optimal number of grid points and subdomains in a spectral method with domain decomposition on a serial computer is presented. The rapidly growing computational cost for large numbers of grid points in each subdomain is balanced against the exponential convergence for spectral approximation of smooth functions, and the optimum is found as the number of grid points and subdomains that gives the minimal computational cost for a given accuracy. The typical length scale of the problem is found to influence the number of subdomains but not the number of grid points within each subdomain.<\/jats:p>","DOI":"10.1137\/s1064827597322306","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"617-632","source":"Crossref","is-referenced-by-count":9,"title":["Optimal Decomposition of the Domain in Spectral Methods for Wave-Like Phenomena"],"prefix":"10.1137","volume":"22","author":[{"given":"Carl Erik","family":"Wasberg","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Gottlieb","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"M. Abramowitz and I. A. Stegun,\n                      Handbook of Mathematical Functions\n                      , Dover, New York, 1970."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1023"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-84108-8"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0916073"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1177\/109434209701100105"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(91)90216-8"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1988-0935077-0"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"D. Gottlieb and S. A. Orszag,\n                      Numerical Analysis of Spectral Methods: Theory and Applications\n                      , SIAM, Philadelphia, 1977.","DOI":"10.1137\/1.9781611970425"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"E. Hairer, S. P. N\u00f8rsett, and G. 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R\u00f8nquist,\n                      Optimal Spectral Element Methods for the Unsteady Three\u2010Dimensional Incompressible Navier\u2010Stokes Equations\n                      , Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 1988."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(84)90128-1"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/0911058"},{"key":"R18","first-page":"75","volume":"1","author":"Quarteroni Alfio","year":"1991","journal-title":"Surveys Math. Indust."},{"key":"R19","unstructured":"C. E. Wasberg,\n                      On the Chebyshev Collocation Approximation and Domain Decomposition\n                      , Tech. report FFI\/RAPPORT\u201092\/7032, Norwegian Defence Research Establishment, N\u20102027 Kjeller, Norway, 1992."},{"key":"R20","unstructured":"C. E. Wasberg,\n                      Spectral Collocation Methods with Domain Decomposition for Fluid Dynamics\n                      , Doctoral thesis, Department of Mathematics, University of Bergen, Bergen, Norway 1995."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827597322306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:39:58Z","timestamp":1787333998000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827597322306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S1064827597322306"],"URL":"https:\/\/doi.org\/10.1137\/s1064827597322306","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}