A. H. Mohy and N. J. Higham, Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators, SIAM Journal on Scientific Computing, vol.33, issue.2, pp.488-511, 2011.
DOI : 10.1137/100788860

D. N. Arnold, R. S. Falk, and R. Winther, Finite element exterior calculus, homological techniques, and applications, Acta Numerica, vol.15, issue.1, pp.1-155, 2006.
DOI : 10.1017/S0962492906210018

M. Azencot, F. Ben-chen, M. Chazal, and . Ovsjansikov, An Operator Approach to Tangent Vector Field Processing, Computer Graphics Forum, vol.22, issue.1, pp.73-82, 2013.
DOI : 10.1111/cgf.12174

URL : https://hal.archives-ouvertes.fr/hal-00923607

G. K. Batchelor, An Introduction to Fluid Dynamics, 2000.
DOI : 10.1017/CBO9780511800955

M. Ben-chen, A. Butscher, J. Solomon, and L. Guibas, On Discrete Killing Vector Fields and Patterns on Surfaces, Proceedings of the EU- ROGRAPHICS Symposium on Geometric Processing (SGP'10, pp.1701-1711, 2010.
DOI : 10.1111/j.1467-8659.2010.01779.x

D. Bommes, M. Campen, H. Ebke, P. Alliez, and L. Kobbelt, Integer-grid maps for reliable quad meshing, ACM Transactions on Graphics, vol.32, issue.4, 2013.
DOI : 10.1145/2461912.2462014

URL : https://hal.archives-ouvertes.fr/hal-00862648

D. Bommes, H. Zimmer, and L. Kobbelt, Mixed-integer quadrangulation, ACM Trans. Graph, vol.28, p.77, 2009.

M. Campen, D. Bommes, and L. Kobbelt, Dual loops meshing, ACM Transactions on Graphics, vol.31, issue.4, p.31, 2012.
DOI : 10.1145/2185520.2185606

K. Crane, M. Desbrun, and P. Schroder, Trivial Connections on Discrete Surfaces, Computer Graphics Forum, vol.25, issue.4, pp.1525-1533, 2010.
DOI : 10.1111/j.1467-8659.2010.01761.x

J. R. Dormand and P. J. Prince, A family of embedded Runge-Kutta formulae, Journal of Computational and Applied Mathematics, vol.6, issue.1, pp.19-26, 1980.
DOI : 10.1016/0771-050X(80)90013-3

G. Dziuk and C. M. Elliott, Finite element methods for surface PDEs, Acta Numerica, vol.22, pp.289-396, 2013.
DOI : 10.1017/S0962492913000056

S. Elcott, Y. Tong, E. Kanso, P. Schroder, and M. Desbrun, Stable, circulation-preserving, simplicial fluids, ACM Trans. Graph, vol.26, issue.1, 2007.

M. Fisher, P. Schroder, M. Desbrun, and H. Hoppe, Design of tangent vector fields, ACM Trans. Graph, vol.26, issue.3, 2007.

A. N. Hirani, Discrete exterior calculus, 2003.

F. Kalberer, M. Nieser, and K. Polthier, QuadCover - Surface Parameterization using Branched Coverings, Computer Graphics Forum, vol.26, issue.3, pp.375-384, 2007.
DOI : 10.1145/1183287.1183297

F. Knoppel, K. Crane, U. Pinkall, and P. Schroder, Globally optimal direction fields, ACM Transactions on Graphics, vol.32, issue.4, pp.1-5910, 2013.
DOI : 10.1145/2461912.2462005

I. Kolar, Natural Operations in Differential Geometry, 1993.

Y. Lai, M. Jin, X. Xie, Y. He, J. Palacios et al., Metric-driven RoSy field design and remeshing, IEEE Trans. Visual. Comput. Graph, vol.16, issue.1, pp.95-108, 2010.

L. M. Lui, Y. Wang, and T. F. Chan, Solving PDEs on manifolds with global conformal parameterization, Variational, Geometric, and Level Set Methods in Computer Vision, pp.307-319, 2005.

M. Meyer, M. Desbrun, P. Schroder, and A. H. Baar, Discrete Differential-Geometry Operators for Triangulated 2-Manifolds, Proceedings of the VisMath Conference (VisMath'02, pp.35-57, 2002.
DOI : 10.1007/978-3-662-05105-4_2

C. Moler and C. Van-loan, Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later, SIAM Review, vol.45, issue.1, pp.3-49, 2003.
DOI : 10.1137/S00361445024180

. Morita, Geometry of Differential Forms, p.13, 2001.

A. Myles, N. Pietroni, and D. Zorin, Robust field-aligned global parameterization, ACM Trans. Graph, vol.33, issue.4, 2014.

A. Myles and D. Zorin, Controlled-distortion constrained global parametrization, ACM Transactions on Graphics, vol.32, issue.4, pp.1-10514, 2013.
DOI : 10.1145/2461912.2461970

P. K. Newton, N-Vortex Problem: Analytical Techniques, Applied Mechanics Reviews, vol.55, issue.1, 2001.
DOI : 10.1115/1.1445334

I. Nitschke, A. Voigt, and J. Wensch, A finite element approach to incompressible two-phase flow on manifolds, Journal of Fluid Mechanics, vol.4, p.418, 2012.
DOI : 10.1098/rspa.1998.0273

D. Panozzo, E. Puppo, M. Tarini, and O. Sorkine-hornung, Frame fields, ACM Transactions on Graphics, vol.33, issue.4, 2014.
DOI : 10.1145/2601097.2601179

P. Petersen, Riemannian Geometry, 2006.

K. Polthier, Computational aspects of discrete minimal surfaces, Global Theory Minim. Surf, vol.2, pp.65-111, 2005.

K. Polthier and E. Preuss, Identifying Vector Field Singularities Using a Discrete Hodge Decomposition, Visual. Math, vol.3, pp.113-134, 2003.
DOI : 10.1007/978-3-662-05105-4_6

K. Polthier and M. Schmies, Straightest geodesics on polyhedral surfaces, ACM SIGGRAPH 2006 Courses on , SIGGRAPH '06, pp.135-150, 1998.
DOI : 10.1145/1185657.1185664

H. Pottmann, Q. Huang, B. Deng, A. Schiftner, M. Kilian et al., Geodesic patterns, ACM Trans. Graph, vol.29, issue.3, 2010.

N. Ray and D. Sokolov, Tracing cross-free polylines oriented by a n-symmetry direction field on triangulated surfaces, 2013.

P. G. Saffman, Vortex Dynamics, 1992.

L. Shi and Y. Yu, Inviscid and incompressible fluid simulation on triangle meshes, Computer Animation and Virtual Worlds, vol.15, issue.34, pp.3-4, 2004.
DOI : 10.1002/cav.19

J. Stam, Stable fluids, Proceedings of the 26th annual conference on Computer graphics and interactive techniques , SIGGRAPH '99, pp.121-128, 1999.
DOI : 10.1145/311535.311548

A. Szymczak and E. Zhang, Robust Morse Decompositions of Piecewise Constant Vector Fields, IEEE Transactions on Visualization and Computer Graphics, vol.18, issue.6, pp.938-951, 2012.
DOI : 10.1109/TVCG.2011.88

M. Wardetzky, Discrete differential operators on polyhedral surfaces ? Convergence and approximation, 2006.

M. Wardetzky, S. Mathur, F. Kalberer, and E. Grinspun, Discrete Laplace operators, ACM SIGGRAPH ASIA 2008 courses on, SIGGRAPH Asia '08, pp.33-37, 2007.
DOI : 10.1145/1508044.1508063

E. Zhang, K. Mischaikow, and G. Turk, Vector field design on surfaces, ACM Transactions on Graphics, vol.25, issue.4, pp.1294-1326, 2006.
DOI : 10.1145/1183287.1183290