{"a12ad03be0f1f7b5ccab6d8f4bf95a1fgdmcbain":{"DOI":"","ISBN":"","ISSN":"","URL":"","abstract":"In many physical problems, a key aspect is the motion of a propagating front separating two components. As fundamental as this may be, the development of a numerical algorithm to accurately track the moving front is difﬁcult. In this report, we describe some previous theoretical and numerical work. We begin with two examples to motivate the problem, followed by some analytical results. These theoretical results are then used as a foundation for two different types of numerical schemes. Finally, we describe the application of one of these schemes to our work in combustion.","annote":"","author":[{"family":"Sethian","given":"J. A."}],"citation-label":"citeulike:4211537","collection-editor":[{"family":"Concus","given":"P."},{"family":"Finn","given":"R."}],"collection-title":"","container-author":[{"family":"Concus","given":"P."},{"family":"Finn","given":"R."}],"container-title":"Variational Methods for Free Surface Interfaces, Proceedings of the Sept, 1985 Vallambrosa Conference","documents":[],"edition":"","editor":[{"family":"Concus","given":"P."},{"family":"Finn","given":"R."}],"event-date":{"date-parts":[["1987"]],"literal":"1987"},"event-place":"New York","id":"a12ad03be0f1f7b5ccab6d8f4bf95a1fgdmcbain","interhash":"304729668c5f2e87f237eb5ffce22262","intrahash":"a12ad03be0f1f7b5ccab6d8f4bf95a1f","issue":"","issued":{"date-parts":[["1987"]],"literal":"1987"},"keyword":"76m25-other-numerical-methods-in-fluid-mechanics 53a05-surfaces-in-euclidean-space 35l65-hyperbolic-conservation-laws 35k55-nonlinear-pde-of-parabolic-type","misc":{"citeulike-attachment-1":"sethian_87_numerical_33454.pdf; /pdf/user/gdmcbain/article/4211537/33454/sethian_87_numerical_33454.pdf; 96a0ceda7ed7bc5ddbfd14eb424980bc36034e34","citeulike-article-id":"4211537","file":"sethian_87_numerical_33454.pdf","comment":"(private-note)Cited by Adalsteinsson \\& Sethian (1995a) `Thus, the derivative of the Hamilton--Jacobi equation with parabolic right-hand-side for the changing height phi is a viscous hyperbolic conservation law for the propagating slope u (see \\~{})'.","priority":"2","posted-at":"2009-03-23 22:38:27"},"note":"","number":"","page":"","page-first":"","publisher":"Springer","publisher-place":"New York","status":"","title":"Numerical Methods for Propagating Fronts","type":"paper-conference","username":"gdmcbain","version":"","volume":""},"fcbe8389a475aa10dcb54f9764fed45dgdmcbain":{"DOI":"","ISBN":"","ISSN":"","URL":"http://math.berkeley.edu/\\~sethian/2006/Publications/Book/2006/book\\_1999.html","abstract":"This is a new book on level set methods and Fast Marching Methods, which are numerical techniques for analyzing and computing interface motion in a host of settings. The numerical techniques can be used to track three-dimensional complex fronts that can develop sharp corners and change topology as they evolve. The text includes applications from physics, chemistry, fluid mechanics, combustion, image processing, material science, seismology, fabrication of microelectronic components, computer vision and control theory. The book is intended for mathematicians, applied scientists, practicing engineers, computer graphic artists, and anyone interested in the evolution of boundaries and interfaces.The book is written on an introductory level. As a prerequisite, it is suggested that the reader be acquainted with some beginning programming, vector calculus, and some very basic aspects of scientific computing. The text is an equal blend of theory, implementations, and applications areas, including detailed descriptions of the appropriate numerical schemes.","annote":"","author":[{"family":"Sethian","given":"J. A."}],"citation-label":"citeulike:4212453","collection-editor":[],"collection-title":"Cambridge Monograph on Applied and Computational Mathematics","container-author":[],"container-title":"","documents":[],"edition":"Second","editor":[],"event-date":{"date-parts":[["1999"]],"literal":"1999"},"event-place":"","id":"fcbe8389a475aa10dcb54f9764fed45dgdmcbain","interhash":"cc0764d256f082d31410d665f6ffbd6a","intrahash":"fcbe8389a475aa10dcb54f9764fed45d","issue":"","issued":{"date-parts":[["1999"]],"literal":"1999"},"keyword":"76m25-other-numerical-methods-in-fluid-mechanics 53a05-surfaces-in-euclidean-space 35l65-hyperbolic-conservation-laws 35k55-nonlinear-pde-of-parabolic-type","misc":{"citeulike-article-id":"4212453","citeulike-linkout-0":"http://math.berkeley.edu/\\~{}sethian/2006/Publications/Book/2006/book\\_1999.html","priority":"2","posted-at":"2009-03-24 02:56:40"},"note":"","number":"","page":"","page-first":"","publisher":"Cambridge Univeristy Press","publisher-place":"","status":"","title":"Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science","type":"book","username":"gdmcbain","version":"","volume":""},"1213083ddc0a21a4a58a5507bd12e79egdmcbain":{"DOI":"","ISBN":"","ISSN":"","URL":"http://projecteuclid.org/euclid.jdg/1214444092","abstract":"","annote":"","author":[{"family":"Sethian","given":"J. A."}],"citation-label":"citeulike:4212475","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Journal of Differential Geometry","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["1990"]],"literal":"1990"},"event-place":"","id":"1213083ddc0a21a4a58a5507bd12e79egdmcbain","interhash":"b5eaee0858238b3c1ab58c08675b64f0","intrahash":"1213083ddc0a21a4a58a5507bd12e79e","issue":"","issued":{"date-parts":[["1990"]],"literal":"1990"},"keyword":"76m25-other-numerical-methods-in-fluid-mechanics 53a05-surfaces-in-euclidean-space 35l65-hyperbolic-conservation-laws 35k55-nonlinear-pde-of-parabolic-type","misc":{"citeulike-attachment-1":"sethian_90_numerical_33545.pdf; /pdf/user/gdmcbain/article/4212475/33545/sethian_90_numerical_33545.pdf; d601af5a86f250a076cdf12346a8a7a50d820e84","citeulike-article-id":"4212475","file":"sethian_90_numerical_33545.pdf","citeulike-linkout-0":"http://projecteuclid.org/euclid.jdg/1214444092","priority":"2","posted-at":"2009-03-24 03:08:48"},"note":"","number":"","number-of-pages":"30","page":"131--161","page-first":"131","publisher":"","publisher-place":"","status":"","title":"Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws","type":"book","username":"gdmcbain","version":"","volume":"31"},"4d16df7601341b7e42c1db63cb2b3a18gdmcbain":{"DOI":"","ISBN":"","ISSN":"","URL":"http://math.berkeley.edu/\\~sethian/2006/Publications/Book/2006/book\\_1999.html","abstract":"","annote":"","author":[{"family":"Sethian","given":"J. A."}],"citation-label":"citeulike:4281061","collection-editor":[],"collection-title":"Cambridge Monographs on Applied and Computational Mathematics","container-author":[],"container-title":"","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["1996"]],"literal":"1996"},"event-place":"","id":"4d16df7601341b7e42c1db63cb2b3a18gdmcbain","interhash":"2589911d7fb151c417c62bf65b7bb5b4","intrahash":"4d16df7601341b7e42c1db63cb2b3a18","issue":"","issued":{"date-parts":[["1996"]],"literal":"1996"},"keyword":"76m25-other-numerical-methods-in-fluid-mechanics 53a05-surfaces-in-euclidean-space 35l65-hyperbolic-conservation-laws 35k55-nonlinear-pde-of-parabolic-type","misc":{"citeulike-article-id":"4281061","citeulike-linkout-0":"http://math.berkeley.edu/\\~{}sethian/2006/Publications/Book/2006/book\\_1999.html","comment":"(private-note)Holdings: pers. (rec'd from Amazon-Alibris 2009-04-07)","priority":"2","posted-at":"2009-04-07 07:38:08"},"note":"","number":"","page":"","page-first":"","publisher":"Cambridge Univeristy Press","publisher-place":"","status":"","title":"Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Materials Science","type":"book","username":"gdmcbain","version":"","volume":""}}