{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:36Z","timestamp":1787337276260,"version":"build-2736575974"},"reference-count":21,"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":[[2003,1]]},"abstract":"<jats:p>\n                    A spectral element formulation of the atmospheric two-dimensional shallow water equations on the cubed-sphere is described. The equations are written in tensor form using the contravariant and covariant velocity components. A semi-implicit time discretization results in a reduced Schur complement system for the pressure. The Laplacian operator is approximated by the L\n                    <jats:sup>2<\/jats:sup>\n                    pseudo-Laplacian arising in the P\n                    <jats:sub>N<\/jats:sub>\n                    \/P\n                    <jats:sub>N<\/jats:sub>\n                    -2 spectral element formulation of the incompressible Stokes problem. The overlapping Schwarz preconditioner of Fischer, Miller, and Tufo [An overlapping Schwarz method for spectral element simulation of three-dimensional incompressible flows, in Parallel Solution of Partial Differential Equations, IMA Vol. Math. Appl. 120, Springer, New York, 2000, pp. 159--180] based on the fast diagonalization method, is extended to generalized curvilinear coordinates. To obtain a separable operator for the linear finite element tensor-product approximation within each spectral element, extrema of the inverse metric tensor and its determinant are employed. Convergence rates and parallel CPU timings are compared against a block-Jacobi preconditioner.\n                  <\/jats:p>","DOI":"10.1137\/s1064827502409420","type":"journal-article","created":{"date-parts":[[2003,11,13]],"date-time":"2003-11-13T21:00:59Z","timestamp":1068757259000},"page":"442-453","source":"Crossref","is-referenced-by-count":10,"title":["A Schwarz Preconditioner for the Cubed-Sphere"],"prefix":"10.1137","volume":"25","author":[{"given":"Stephen J.","family":"Thomas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John M.","family":"Dennis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Henry M.","family":"Tufo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul F.","family":"Fischer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"E. 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Ronquist (1988),\n                      Optimal Spectral Element Methods for the Unsteady Three Dimensional Navier Stokes Equations\n                      , Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0493(1972)100<0136:CFAOTP>2.3.CO;2"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0493(1997)125<0647:OFITDF>2.0.CO;2"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.5554"},{"key":"R19","doi-asserted-by":"publisher","unstructured":"S. Thomas, R. Loft, Semi\u2010implicit spectral element atmospheric model, Proceedings of the Fifth International Conference on Spectral and High Order Methods (ICOSAHOM\u201001) (Uppsala), Vol. 17, 2002, 339\u201335010.1023\/A:10151294208821910573","DOI":"10.1023\/A:1015129420882"},{"key":"R20","unstructured":"Olof Widlund, Some Schwarz methods for symmetric and nonsymmetric elliptic problems, SIAM, Philadelphia, PA, 1992, 19\u20133693j:65202"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9991(05)80016-6"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827502409420","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:53:53Z","timestamp":1787334833000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827502409420"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S1064827502409420"],"URL":"https:\/\/doi.org\/10.1137\/s1064827502409420","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}