{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T23:00:36Z","timestamp":1771455636649,"version":"3.50.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,4,21]],"date-time":"2017-04-21T00:00:00Z","timestamp":1492732800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","doi-asserted-by":"publisher","award":["200020_156178"],"award-info":[{"award-number":["200020_156178"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,1]]},"DOI":"10.1007\/s10915-017-0431-x","type":"journal-article","created":{"date-parts":[[2017,4,21]],"date-time":"2017-04-21T05:56:22Z","timestamp":1492754182000},"page":"267-289","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["OpenCL Based Parallel Algorithm for RBF-PUM Interpolation"],"prefix":"10.1007","volume":"74","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6076-4115","authenticated-orcid":false,"given":"Roberto","family":"Cavoretto","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5969-636X","authenticated-orcid":false,"given":"Teseo","family":"Schneider","sequence":"additional","affiliation":[]},{"given":"Patrick","family":"Zulian","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,4,21]]},"reference":[{"issue":"4","key":"431_CR1","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1109\/5.92042","volume":"79","author":"RJ Anderson","year":"1991","unstructured":"Anderson, R.J., Snyder, L.: A comparison of shared and nonshared memory models of parallel computation. Proc. IEEE 79(4), 480\u2013487 (1991). doi: 10.1109\/5.92042","journal-title":"Proc. IEEE"},{"key":"431_CR2","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1002\/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N","volume":"40","author":"I Babu\u0161ka","year":"1997","unstructured":"Babu\u0161ka, I., Melenk, J.M.: The partition of unity method. Int. J. Numer. Methods Eng. 40, 727\u2013758 (1997)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"431_CR3","first-page":"317","volume":"216","author":"M Bozzini","year":"2010","unstructured":"Bozzini, M., Lenarduzzi, L., Rossini, M.: Polyharmonic splines: an approximation method for noisy scattered data of extra-large size. Appl. Math. Comput. 216, 317\u2013331 (2010)","journal-title":"Appl. Math. Comput."},{"key":"431_CR4","unstructured":"Brent, R.P.: Algorithms for Minimization Without Derivatives. Courier Corporation (2013)"},{"key":"431_CR5","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511543241","volume-title":"Radial Basis Functions: Theory and Implementation, Cambridge Monographs on Applied and Computational Mathematics","author":"MD Buhmann","year":"2003","unstructured":"Buhmann, M.D.: Radial Basis Functions: Theory and Implementation, Cambridge Monographs on Applied and Computational Mathematics, vol. 12. Cambridge University Press, Cambridge (2003)"},{"key":"431_CR6","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s40314-013-0104-9","volume":"34","author":"R Cavoretto","year":"2015","unstructured":"Cavoretto, R.: A numerical algorithm for multidimensional modeling of scattered data points. Comput. Appl. Math. 34, 65\u201380 (2015)","journal-title":"Comput. Appl. Math."},{"key":"431_CR7","doi-asserted-by":"crossref","first-page":"A1891","DOI":"10.1137\/140989157","volume":"37","author":"R Cavoretto","year":"2015","unstructured":"Cavoretto, R., De Rossi, A.: A trivariate interpolation algorithm using a cube-partition searching procedure. SIAM J. Sci. Comput. 37, A1891\u2013A1908 (2015)","journal-title":"SIAM J. Sci. Comput."},{"key":"431_CR8","doi-asserted-by":"crossref","first-page":"2568","DOI":"10.1016\/j.camwa.2016.04.021","volume":"71","author":"R Cavoretto","year":"2016","unstructured":"Cavoretto, R., De Rossi, A., Perracchione, E.: Efficient computation of partition of unity interpolants through a block-based searching technique. Comput. Math. Appl. 71, 2568\u20132584 (2016)","journal-title":"Comput. Math. Appl."},{"key":"431_CR9","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s10915-015-0143-z","volume":"68","author":"R Cavoretto","year":"2016","unstructured":"Cavoretto, R., De Rossi, A., Perracchione, E., Venturino, E.: Robust approximation algorithms for the detection of attraction basins in dynamical systems. J. Sci. Comput. 68, 395\u2013415 (2016)","journal-title":"J. Sci. Comput."},{"key":"431_CR10","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s11075-014-9850-z","volume":"68","author":"R Cavoretto","year":"2015","unstructured":"Cavoretto, R., Fasshauer, G.E., McCourt, M.: An introduction to the Hilbert\u2013Schmidt SVD using iterated Brownian bridge kernels. Numer. Algorithms 68, 393\u2013422 (2015)","journal-title":"Numer. Algorithms"},{"key":"431_CR11","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1007\/s10543-014-0537-6","volume":"55","author":"S Marchi De","year":"2015","unstructured":"De Marchi, S., Santin, G.: Fast computation of orthonormal basis for rbf spaces through Krylov space methods. BIT 55, 949\u2013966 (2015)","journal-title":"BIT"},{"key":"431_CR12","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.cam.2015.12.016","volume":"300","author":"F Dell\u2019Accio","year":"2016","unstructured":"Dell\u2019Accio, F., Di Tommaso, F.: Complete Hermite\u2013Birkhoff interpolation on scattered data by combined Shepard operators. J. Comput. Appl. Math. 300, 192\u2013206 (2016)","journal-title":"J. Comput. Appl. Math."},{"key":"431_CR13","doi-asserted-by":"crossref","first-page":"A2745","DOI":"10.1137\/130947179","volume":"36","author":"S Deparis","year":"2014","unstructured":"Deparis, S., Forti, D., Quarteroni, A.: A rescaled localized radial basis function interpolation on non-cartesian and nonconforming grids. SIAM J. Sci. Comput. 36, A2745\u2013A2762 (2014)","journal-title":"SIAM J. Sci. Comput."},{"key":"431_CR14","doi-asserted-by":"crossref","DOI":"10.1201\/b14581","volume-title":"Real-Time Collision Detection (The Morgan Kaufmann Series in Interactive 3D Technology)","author":"C Ericson","year":"2004","unstructured":"Ericson, C.: Real-Time Collision Detection (The Morgan Kaufmann Series in Interactive 3D Technology). Morgan Kaufmann Publishers Inc., San Francisco (2004)"},{"key":"431_CR15","volume-title":"Kernel-Based Approximation Methods Using Matlab, Interdisciplinary Mathematical Sciences","author":"G Fasshauer","year":"2015","unstructured":"Fasshauer, G., McCourt, M.: Kernel-Based Approximation Methods Using Matlab, Interdisciplinary Mathematical Sciences, vol. 19. World Scientific, Singapore (2015)"},{"key":"431_CR16","doi-asserted-by":"crossref","DOI":"10.1142\/6437","volume-title":"Meshfree Approximation Methods with Matlab, Interdisciplinary Mathematical Sciences","author":"GE Fasshauer","year":"2007","unstructured":"Fasshauer, G.E.: Meshfree Approximation Methods with Matlab, Interdisciplinary Mathematical Sciences, vol. 6. World Scientific, Singapore (2007)"},{"key":"431_CR17","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1186\/1756-0500-4-21","volume":"4","author":"GE Fasshauer","year":"2011","unstructured":"Fasshauer, G.E.: Positive definite kernels: past, present and future. Dolomites Res. Notes Approx. 4, 21\u201363 (2011)","journal-title":"Dolomites Res. Notes Approx."},{"key":"431_CR18","unstructured":"Fernando, R.: GPU Gems: Programming Techniques. Tips and Tricks for Real-Time Graphics, Pearson Higher Education (2004)"},{"key":"431_CR19","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611974041","volume-title":"A Primer on Radial Basis Functions with Applications to the Geosciences","author":"B Fornberg","year":"2015","unstructured":"Fornberg, B., Flyer, N.: A Primer on Radial Basis Functions with Applications to the Geosciences. SIAM, Philadelphia (2015)"},{"key":"431_CR20","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1137\/09076756X","volume":"33","author":"B Fornberg","year":"2011","unstructured":"Fornberg, B., Larsson, E., Flyer, N.: Stable computations with Gaussian radial basis functions. SIAM J. Sci. Comput. 33, 869\u2013892 (2011)","journal-title":"SIAM J. Sci. Comput."},{"key":"431_CR21","unstructured":"Forum, M.P.I.: MPI: A Message-Passing Interface Standard Version 3.0 (2012). Chapter author for Collective Communication, Process Topologies, and One Sided Communications"},{"key":"431_CR22","doi-asserted-by":"crossref","first-page":"1089","DOI":"10.1007\/s10915-015-0120-6","volume":"67","author":"A Heryudono","year":"2016","unstructured":"Heryudono, A., Larsson, E., Ramage, A., von Sydow, L.: Preconditioning for radial basis function partition of unity methods. J. Sci. Comput. 67, 1089\u20131109 (2016)","journal-title":"J. Sci. Comput."},{"key":"431_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-17939-1","volume-title":"Spherical Radial Basis Functions, Theory and Applications. SpringerBriefs in Mathematics","author":"S Hubbert","year":"2015","unstructured":"Hubbert, S., Le Gia, Q., Morton, T.: Spherical Radial Basis Functions, Theory and Applications. SpringerBriefs in Mathematics. Springer, London (2015)"},{"key":"431_CR24","doi-asserted-by":"crossref","first-page":"C307","DOI":"10.1137\/15M1008361","volume":"38","author":"R Krause","year":"2016","unstructured":"Krause, R., Zulian, P.: A parallel approach to the variational transfer of discrete fields between arbitrarily distributed finite element meshes. SIAM J. Sci. Comput. 38, C307\u2013C333 (2016)","journal-title":"SIAM J. Sci. Comput."},{"key":"431_CR25","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/S0045-7825(96)01087-0","volume":"139","author":"JM Melenk","year":"1996","unstructured":"Melenk, J.M., Babu\u0161ka, I.: The partition of unity finite element method: basic theory and applications. Comput. Methods. Appl. Mech. Eng. 139, 289\u2013314 (1996)","journal-title":"Comput. Methods. Appl. Mech. Eng."},{"key":"431_CR26","volume-title":"Pthreads Programming","author":"B Nichols","year":"1996","unstructured":"Nichols, B., Buttlar, D., Farrell, J.P.: Pthreads Programming. O\u2019Reilly & Associates Inc, Sebastopol (1996)"},{"issue":"2","key":"431_CR27","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1145\/1365490.1365500","volume":"6","author":"J Nickolls","year":"2008","unstructured":"Nickolls, J., Buck, I., Garland, M., Skadron, K.: Scalable parallel programming with CUDA. Queue 6(2), 40\u201353 (2008)","journal-title":"Queue"},{"key":"431_CR28","doi-asserted-by":"crossref","unstructured":"Novak, E., Wo\u017aniakowski, H.: Tractability of Multivariate Problems Volume 1: Linear Information. No.\u00a06 in EMS Tracts in Mathematics. European Mathematical Society (2008)","DOI":"10.4171\/026"},{"key":"431_CR29","unstructured":"NVIDIA: CUDA Samples (2013)"},{"key":"431_CR30","unstructured":"OpenMP Architecture Review Board: OpenMP Application Program Interface Version 3.0 (2008). http:\/\/www.openmp.org\/mp-documents\/spec30.pdf"},{"key":"431_CR31","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1016\/j.cam.2011.05.021","volume":"236","author":"M Pazouki","year":"2011","unstructured":"Pazouki, M., Schaback, R.: Bases for kernel-based spaces. J. Comput. Appl. Math. 236, 575\u2013588 (2011)","journal-title":"J. Comput. Appl. Math."},{"key":"431_CR32","unstructured":"R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2014)"},{"key":"431_CR33","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.camwa.2016.04.048","volume":"72","author":"J Rashidinia","year":"2016","unstructured":"Rashidinia, J., Fasshauer, G.E., Khasi, M.: A stable method for the evaluation of Gaussian radial basis function solutions of interpolation and collocation problems. Comput. Math. Appl. 72, 178\u2013193 (2016)","journal-title":"Comput. Math. Appl."},{"key":"431_CR34","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1145\/45054.45055","volume":"14","author":"R Renka","year":"1988","unstructured":"Renka, R.: Multivariate interpolation of large sets of scattered data. ACM Trans. Math. Softw. 14, 139\u2013148 (1988)","journal-title":"ACM Trans. Math. Softw."},{"key":"431_CR35","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1023\/A:1018975909870","volume":"11","author":"S Rippa","year":"1999","unstructured":"Rippa, S.: An algorithm for selecting a good value for the parameter $$c$$ c in radial basis function interpolation. Adv. Comput. Math. 11, 193\u2013210 (1999)","journal-title":"Adv. Comput. Math."},{"key":"431_CR36","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/s10915-014-9935-9","volume":"64","author":"A Safdari-Vaighani","year":"2015","unstructured":"Safdari-Vaighani, A., Heryudono, A., Larsson, E.: A radial basis function partition of unity collocation method for convection-diffusion equations arising in financial applications. J. Sci. Comput. 64, 341\u2013367 (2015)","journal-title":"J. Sci. Comput."},{"key":"431_CR37","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF03024331","volume":"19","author":"E Saff","year":"1997","unstructured":"Saff, E., Kuijlaars, A.: Distributing many points on a sphere. Math. Intell. 19, 5\u201311 (1997)","journal-title":"Math. Intell."},{"key":"431_CR38","volume-title":"The Boost C++ Libraries","author":"B Schling","year":"2011","unstructured":"Schling, B.: The Boost C++ Libraries. XML Press, Fort Collins (2011)"},{"key":"431_CR39","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.camwa.2015.11.007","volume":"71","author":"V Shcherbakov","year":"2016","unstructured":"Shcherbakov, V., Larsson, E.: Radial basis function partition of unity methods for pricing vanilla basket options. Comput. Appl. Math. 71, 185\u2013200 (2016)","journal-title":"Comput. Appl. Math."},{"key":"431_CR40","unstructured":"Speck, R., Gibbon, P., Hofmann, M.: Efficiency and scalability of the parallel Barnes-Hut tree code PEPC. In: B.\u00a0Chapman, F.\u00a0Desprez, G.R. Joubert, A.\u00a0Lichnewsky, F.J. Peters, T.\u00a0Priol (eds.) Parallel Computing: From Multicores and GPU\u2019s to Petascale, Advances in Parallel Computing, vol.\u00a019, pp. 35\u201342. IOS Press (2010)"},{"issue":"3","key":"431_CR41","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1109\/MCSE.2010.69","volume":"12","author":"JE Stone","year":"2010","unstructured":"Stone, J.E., Gohara, D., Shi, G.: Opencl: a parallel programming standard for heterogeneous computing systems. IEEE Des. Test 12(3), 66\u201373 (2010). doi: 10.1109\/MCSE.2010.69","journal-title":"IEEE Des. Test"},{"key":"431_CR42","unstructured":"Wendland, H.: Fast evaluation of radial basis functions: methods based on partition of unity. In: C.K. Chui, L.L. Schumaker, J.\u00a0St\u00f6ckler (eds.) Approximation Theory X: Wavelets, Splines, and Applications, pp. 473\u2013483. Vanderbilt University Press (2002)"},{"key":"431_CR43","volume-title":"Scattered Data Approximation, Cambridge Monographs on Applied and Computational Mathematics","author":"H Wendland","year":"2005","unstructured":"Wendland, H.: Scattered Data Approximation, Cambridge Monographs on Applied and Computational Mathematics, vol. 17. Cambridge University Press, Cambridge (2005)"},{"key":"431_CR44","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/10867651.1997.10487471","volume":"2","author":"R Wong","year":"1997","unstructured":"Wong, R., Luk, W., Heng, P.: Sampling with Hammersley and Halton points. J. Graphics Tools 2, 9\u201324 (1997)","journal-title":"J. Graphics Tools"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0431-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0431-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0431-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T06:39:08Z","timestamp":1692772748000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0431-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,21]]},"references-count":44,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["431"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0431-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4,21]]}}}