{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T06:51:22Z","timestamp":1648709482985},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2011,9,23]],"date-time":"2011-09-23T00:00:00Z","timestamp":1316736000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2012,7]]},"DOI":"10.1007\/s10444-011-9200-9","type":"journal-article","created":{"date-parts":[[2011,9,22]],"date-time":"2011-09-22T11:04:01Z","timestamp":1316689441000},"page":"93-121","source":"Crossref","is-referenced-by-count":1,"title":["An overlapping additive Schwarz preconditioner for the Laplace-Beltrami equation using spherical splines"],"prefix":"10.1007","volume":"37","author":[{"given":"Duong","family":"Pham","sequence":"first","affiliation":[]},{"given":"Thanh","family":"Tran","sequence":"additional","affiliation":[]},{"given":"Simon","family":"Crothers","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,9,23]]},"reference":[{"key":"9200_CR1","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/0167-8396(95)00030-5","volume":"13","author":"P Alfeld","year":"1996","unstructured":"Alfeld, P., Neamtu, M., Schumaker, L.L.: Bernstein-B\u00e9zier polynomials on spheres and sphere-like surfaces. Comput. Aided Geom. Des. 13, 333\u2013349 (1996)","journal-title":"Comput. Aided Geom. Des."},{"key":"9200_CR2","doi-asserted-by":"crossref","first-page":"1482","DOI":"10.1137\/S0036141094276275","volume":"27","author":"P Alfeld","year":"1996","unstructured":"Alfeld, P., Neamtu, M., Schumaker, L.L.: Dimension and local bases of homogeneous spline spaces. SIAM J. Math. Anal. 27, 1482\u20131501 (1996)","journal-title":"SIAM J. Math. Anal."},{"key":"9200_CR3","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/0377-0427(96)00034-9","volume":"73","author":"P Alfeld","year":"1996","unstructured":"Alfeld, P., Neamtu, M., Schumaker, L.L.: Fitting scattered data on sphere-like surfaces using spherical splines. J. Comput. Appl. Math. 73, 5\u201343 (1996)","journal-title":"J. Comput. Appl. Math."},{"key":"9200_CR4","first-page":"25","volume-title":"Approximation theory XI: Gatlinburg 2004, Mod. Methods Math.","author":"V Baramidze","year":"2005","unstructured":"Baramidze, V., Lai, M.-J.: Error bounds for minimal energy interpolatory spherical splines. In: Approximation theory XI: Gatlinburg 2004, Mod. Methods Math., pp. 25\u201350. Nashboro Press, Brentwood, TN (2005)"},{"key":"9200_CR5","first-page":"75","volume-title":"Wavelets and splines: Athens 2005, Mod. Methods Math.","author":"V Baramidze","year":"2006","unstructured":"Baramidze, V., Lai, M.-J.: Spherical spline solution to a PDE on the sphere. In: Wavelets and splines: Athens 2005, Mod. Methods Math., pp. 75\u201392. Nashboro Press, Brentwood, TN (2006)"},{"key":"9200_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0619-4","volume-title":"Modern Graph Theory","author":"B Bollob\u00e1s","year":"1998","unstructured":"Bollob\u00e1s, B.: Modern Graph Theory. Springer Verlag, New York (1998)"},{"key":"9200_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3658-8","volume-title":"The Mathematical Theory of Finite Element Methods","author":"SC Brenner","year":"2002","unstructured":"Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods. Springer, Berlin (2002)"},{"key":"9200_CR8","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1090\/S0025-5718-08-02150-9","volume":"78","author":"QT Gia Le","year":"2009","unstructured":"Le Gia, Q.T., Sloan, I.H., Tran, T.: Overlapping additive Schwarz preconditioners for elliptic PDEs on the unit sphere. Math. Comput. 78, 79\u2013101 (2009)","journal-title":"Math. Comput."},{"key":"9200_CR9","volume-title":"Non-Homogeneous Boundary Value Problems and Applications I","author":"JL Lions","year":"1972","unstructured":"Lions, J.L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications I. Springer-Verlag, New York (1972)"},{"key":"9200_CR10","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1093\/imanum\/dri037","volume":"26","author":"J Maes","year":"2006","unstructured":"Maes, J., Bultheel, A.: A hierarchical basis preconditioner for the biharmonic equation on the sphere. IMA J. Numer. Anal. 26, 563\u2013583 (2006)","journal-title":"IMA J. Numer. Anal."},{"key":"9200_CR11","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1137\/050647414","volume":"45","author":"J Maes","year":"2007","unstructured":"Maes, J., Kunoth, A., Bultheel, A.: BPX-type preconditioners for second and fourth order elliptic problems on the sphere. SIAM J. Numer. Anal. 45, 206\u2013222 (2007, electronic)","journal-title":"SIAM J. Numer. Anal."},{"key":"9200_CR12","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1023\/B:ACOM.0000016430.93487.ec","volume":"21","author":"M Neamtu","year":"2004","unstructured":"Neamtu, M., Schumaker, L.L.: On the approximation order of splines on spherical triangulations. Adv. Comput. Math. 21, 3\u201320 (2004)","journal-title":"Adv. Comput. Math."},{"key":"9200_CR13","volume-title":"Acoustic and Electromagnetic Equations","author":"J-C N\u00e9d\u00e9lec","year":"2000","unstructured":"N\u00e9d\u00e9lec, J.-C.: Acoustic and Electromagnetic Equations. Springer-Verlag, New York (2000)"},{"key":"9200_CR14","doi-asserted-by":"crossref","unstructured":"Pham, T.D., Tran, T., Chernov, A.: Pseudodifferential equations on the sphere with spherical splines. M3AS (2011). doi: 10.1142\/S021820251100560X","DOI":"10.1142\/S021820251100560X"},{"key":"9200_CR15","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1145\/275323.275329","volume":"23","author":"RJ Renka","year":"1997","unstructured":"Renka, R.J.: Algorithm 772: STRIPACK: Delaunay triangulation and Voronoi diagram on the surface of a sphere. ACM Trans. Math. Softw. 23, 416\u2013434 (1997)","journal-title":"ACM Trans. Math. Softw."},{"key":"9200_CR16","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/b137868","volume-title":"Domain Decomposition Methods\u2014Algorithms and Theory","author":"A Toselli","year":"2005","unstructured":"Toselli, A., Widlund, O.: Domain Decomposition Methods\u2014Algorithms and Theory, volume 34 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (2005)"},{"key":"9200_CR17","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1515\/1569395042571265","volume":"12","author":"T Tran","year":"2004","unstructured":"Tran, T., Stephan, E.P.: An overlapping additive Schwarz preconditioner for boundary element approximations to the Laplace screen and Lam\u00e9 crack problems. J. Numer. Math. 12, 311\u2013330 (2004)","journal-title":"J. Numer. Math."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-011-9200-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-011-9200-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-011-9200-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,16]],"date-time":"2019-06-16T05:39:51Z","timestamp":1560663591000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-011-9200-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9,23]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,7]]}},"alternative-id":["9200"],"URL":"https:\/\/doi.org\/10.1007\/s10444-011-9200-9","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,9,23]]}}}