{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:05:30Z","timestamp":1758823530515},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,6,26]],"date-time":"2012-06-26T00:00:00Z","timestamp":1340668800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2013,4]]},"DOI":"10.1007\/s10915-012-9619-2","type":"journal-article","created":{"date-parts":[[2012,6,25]],"date-time":"2012-06-25T08:25:07Z","timestamp":1340612707000},"page":"1-15","source":"Crossref","is-referenced-by-count":15,"title":["A Multigrid Method on Non-Graded Adaptive Octree and Quadtree Cartesian Grids"],"prefix":"10.1007","volume":"55","author":[{"given":"Maxime","family":"Theillard","sequence":"first","affiliation":[]},{"given":"Chris H.","family":"Rycroft","sequence":"additional","affiliation":[]},{"given":"Fr\u00e9d\u00e9ric","family":"Gibou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,6,26]]},"reference":[{"issue":"1","key":"9619_CR1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s10915-006-9122-8","volume":"31","author":"H. Chen","year":"2007","unstructured":"Chen, H., Min, C., Gibou, F.: A supra-convergent finite difference scheme for the Poisson and heat equations on irregular domains and non-graded adaptive Cartesian grids. J. Sci. Comput. 31(1), 19\u201360 (2007). doi: 10.1007\/s10915-006-9122-8","journal-title":"J. Sci. Comput."},{"key":"9619_CR2","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1016\/0021-9991(84)90073-1","volume":"53","author":"M. Berger","year":"1984","unstructured":"Berger, M., Oliger, J.: Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys. 53, 484\u2013512 (1984). doi: 10.1016\/0021-9991(84)90073-1","journal-title":"J. Comput. Phys."},{"key":"9619_CR3","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1016\/S0021-9991(03)00298-5","volume":"190","author":"S. Popinet","year":"2003","unstructured":"Popinet, S.: Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190, 572\u2013600 (2003). doi: 10.1016\/S0021-9991(03)00298-5","journal-title":"J. Comput. Phys."},{"key":"9619_CR4","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.jcp.2006.01.046","volume":"218","author":"C. Min","year":"2006","unstructured":"Min, C., Gibou, F., Ceniceros, H.: A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids. J. Comput. Phys. 218, 123\u2013140 (2006). doi: 10.1016\/j.jcp.2006.01.046","journal-title":"J. Comput. Phys."},{"issue":"16","key":"9619_CR5","doi-asserted-by":"crossref","first-page":"5803","DOI":"10.1016\/j.jcp.2009.04.044","volume":"228","author":"H. Chen","year":"2009","unstructured":"Chen, H., Min, C., Gibou, F.: A numerical scheme for the Stefan problem on adaptive Cartesian grids with supralinear convergence rate. J. Comput. Phys. 228(16), 5803\u20135818 (2009). doi: 10.1016\/j.jcp.2009.04.044","journal-title":"J. Comput. Phys."},{"key":"9619_CR6","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1016\/j.jcp.2006.07.019","volume":"219","author":"C. Min","year":"2006","unstructured":"Min, C., Gibou, F.: A second order accurate projection method for the incompressible Navier\u2013Stokes equation on non-graded adaptive grids. J. Comput. Phys. 219, 912\u2013929 (2006). doi: 10.1016\/j.jcp.2006.07.019","journal-title":"J. Comput. Phys."},{"key":"9619_CR7","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/j.jcp.2006.11.034","volume":"225","author":"C. Min","year":"2007","unstructured":"Min, C., Gibou, F.: A second order accurate level set method on non-graded adaptive Cartesian grids. J.\u00a0Comput. Phys. 225, 300\u2013321 (2007). doi: 10.1016\/j.jcp.2006.11.034","journal-title":"J.\u00a0Comput. Phys."},{"key":"9619_CR8","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1090\/S0025-5718-1977-0431719-X","volume":"31","author":"A. Brandt","year":"1977","unstructured":"Brandt, A.: Multi-level adaptive solutions to boundary-value problems. Math. Comput. 31, 333\u2013390 (1977). doi: 10.1090\/S0025-5718-1977-0431719-X","journal-title":"Math. Comput."},{"key":"9619_CR9","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719505","volume-title":"A Multigrid Tutorial","author":"W. Briggs","year":"2000","unstructured":"Briggs, W., Henson, V.E., McCormick, S.: A Multigrid Tutorial, 2nd edn. SIAM, Philadelphia (2000). ISBN 0-89871-462-1","ISBN":"http:\/\/id.crossref.org\/isbn\/0898714621","edition":"2"},{"issue":"3","key":"9619_CR10","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1137\/090747774","volume":"32","author":"R.S. Sampath","year":"2010","unstructured":"Sampath, R.S., Biros, G.: A parallel geometric multigrid method for finite elements on octree meshes. SIAM J. Sci. Comput. 32(3), 1361\u20131392 (2010). doi: 10.1137\/090747774","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"9619_CR11","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1016\/j.jcp.2006.10.012","volume":"223","author":"E. Haber","year":"2007","unstructured":"Haber, E., Heldmann, S.: An octree multigrid method for quasi-static Maxwell\u2019s equations with highly discontinuous coefficients. J. Comput. Phys. 223(2), 783\u2013796 (2007). doi: 10.1016\/j.jcp.2006.10.012","journal-title":"J. Comput. Phys."},{"key":"9619_CR12","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S. Osher","year":"1988","unstructured":"Osher, S., Sethian, J.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton\u2013Jacobi formulations. J. Comput. Phys. 79, 12\u201349 (1988). doi: 10.1016\/0021-9991(88)90002-2","journal-title":"J. Comput. Phys."},{"key":"9619_CR13","volume-title":"Level Set Methods and Dynamic Implicit Surfaces","author":"S. Osher","year":"2002","unstructured":"Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York (2002)"},{"key":"9619_CR14","volume-title":"Level Set Methods and Fast Marching Methods","author":"J. Sethian","year":"1999","unstructured":"Sethian, J.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)"},{"key":"9619_CR15","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1006\/jcph.1999.6259","volume":"152","author":"J. Strain","year":"1999","unstructured":"Strain, J.: Fast tree-based redistancing for level set computations. J. Comput. Phys. 152, 664\u2013686 (1999). doi: 10.1006\/jcph.1999.6259","journal-title":"J. Comput. Phys."},{"key":"9619_CR16","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.jcp.2004.04.019","volume":"200","author":"C. Min","year":"2004","unstructured":"Min, C.: Local level set method in high dimension and codimension. J. Comput. Phys. 200, 368\u2013382 (2004). doi: 10.1016\/j.jcp.2004.04.019","journal-title":"J. Comput. Phys."},{"key":"9619_CR17","volume-title":"Applications of Spatial Data Structures: Computer Graphics, Image Processing and GIS","author":"H. Samet","year":"1990","unstructured":"Samet, H.: Applications of Spatial Data Structures: Computer Graphics, Image Processing and GIS. Addison-Wesley, New York (1990)"},{"key":"9619_CR18","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971446","volume-title":"Applied Numerical Linear Algebra","author":"J.W. Demmel","year":"1997","unstructured":"Demmel, J.W.: Applied Numerical Linear Algebra. SIAM, Philadelphia (1997)"},{"key":"9619_CR19","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1017\/S0962492900002385","volume":"2","author":"H. Yserentant","year":"1993","unstructured":"Yserentant, H.: Old and new convergence proofs for multigrid methods. Acta Numer. 2, 285\u2013326 (1993). doi: 10.1017\/S0962492900002385","journal-title":"Acta Numer."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-012-9619-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-012-9619-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-012-9619-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T04:45:40Z","timestamp":1559450740000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-012-9619-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,26]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,4]]}},"alternative-id":["9619"],"URL":"https:\/\/doi.org\/10.1007\/s10915-012-9619-2","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,26]]}}}