Level Set Equations on Surfaces via the Closest Point Method
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Bertalmío, M., Cheng, L.-T., Osher, S., Sapiro, G.: Variational problems and partial differential equations on implicit surfaces. J. Comput. Phys. 174(2), 759–780 (2001)
Cheng, L.-T., Tsai, R.: Redistancing by flow of the time dependent Eikonal equation (2008). Under review
Cheng, L.-T., Burchard, P., Merriman, B., Osher, S.: Motion of curves constrained on surfaces using a level-set approach. J. Comput. Phys. 175(2), 604–644 (2002)
Crandall, M.G., Lions, P.-L.: Two approximations of solutions of Hamilton–Jacobi equations. Math. Comput. 43(167), 1–19 (1984)
Fedkiw, R.P., Aslam, T., Merriman, B., Osher, S.: A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152(2), 457–492 (1999)
Greer, J.B.: An improvement of a recent Eulerian method for solving PDEs on general geometries. J. Sci. Comput. 29(3), 321–352 (2006)
Jiang, G.-S., Peng, D.: Weighted ENO schemes for Hamilton–Jacobi equations. SIAM J. Sci. Comput. 21(6), 2126–2143 (2000)
Jiang, G.-S., Shu, C.-W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126(1), 202–228 (1996)
Liu, X.-D., Osher, S., Chan, T.: Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115(1), 200–212 (1994)
Merriman, B., Ruuth, S.J.: Diffusion generated motion of curves on surfaces. J. Comput. Phys. 225(2), 2267–2282 (2007)
Merriman, B., Ruuth, S.J.: Embedding methods for the numerical solution of PDEs on manifolds. In preparation
Mitchell, I.: A toolbox of level set methods. Technical Report TR-2004-09, University of British Columbia Department of Computer Science, July 2004. http://www.cs.ubc.ca/~mitchell/ToolboxLS/Papers/Toolbox/toolboxLS-1.0.pdf
Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Applied Mathematical Sciences, vol. 153. Springer, New York (2003)
Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988)
Osher, S., Shu, C.-W.: High-order essentially nonoscillatory schemes for Hamilton–Jacobi equations. SIAM J. Numer. Anal. 28(4), 907–922 (1991)
Russo, G., Smereka, P.: A remark on computing distance functions. J. Comput. Phys. 163(1), 51–67 (2000)
Ruuth, S.J., Merriman, B.: A simple embedding method for solving partial differential equations on surfaces. J. Comput. Phys. 227(3), 1943–1961 (2008)
Saboret, L., Attene, M., Alliez, P.: “Laurent’s Hand”, the AIM@SHAPE shape repository (2007). http://shapes.aimatshape.net
Sebastian, K., Shu, C.-W.: Multidomain WENO finite difference method with interpolation at subdomain interfaces. J. Sci. Comput. 19(1–3), 405–438 (2003)
Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge Monographs on Applied and Computational Mathematics, vol. 3, 2nd edn. Cambridge University Press, Cambridge (1999)
Shu, C.-W.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Technical Report NASA CR-97-206253 ICASE Report No. 97-65, Institute for Computer Applications in Science and Engineering, November 1997
Shu, C.-W., Osher, S.: Efficient implementation of essentially nonoscillatory shock-capturing schemes. J. Comput. Phys. 77(2), 439–471 (1988)
Wikipedia contributors: Klein bottle. Wikipedia, the free encyclopedia, http://en.wikipedia.org/w/index.php?title=Klein_bottle&oldid=133679151 (2007). Accessed 29 May 2007