A grid redistribution method for singular problems

Journal of Computational Physics

Volumn 228, Issue 7, 2009, Pages 2354-2365

  Ditkowski, Adi ^a   Gavish, Nir ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Grid generation; Iterative grid redistribution (IGR); Nonlinear Schr dinger (NLS); Singular problems

Indexed keywords

BOUNDARY LAYERS; NUMERICAL METHODS;

ADAPTIVE-GRID METHOD; BOUNDARY BLOW-UP SOLUTIONS; BOUNDARY-LAYER SOLUTION; GRID GENERATION; ITERATIVE GRID REDISTRIBUTION; LOCALISED; NONLINEAR SCHRÖDINGE; PHYSICAL PHENOMENA; SINGULAR BEHAVIOR; SINGULAR PROBLEM;

ITERATIVE METHODS;

EID: 60149097709     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.11.035     Document Type: Article

References (22)

1. Beckett G., Mackenzie J.A., Ramage A., and Sloan D.M. On the numerical solution of one-dimensional pdes using adaptive methods based on equidistribution. J. Comput. Phys. 167 (2001) 372-392
2. Berger M.J., and Collela P. Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82 (1989) 64-84
3. De Boor C. Good Approximation by Splines with Variable Knots II (Springer Lecture Notes Series 363) (1973), Springer-Verlag, Berlin
4. Budd C.J., Chen S., and Russell R.D. New self-similar solutions of the nonlinear Schrödinger equation with moving mesh computations. J. Comput. Phys. 152 (1999) 756
5. Budd C.J., Huang W., and Russell R.D. Moving mesh methods for problems with blow-up. SIAM J. Sci. Comput. 17 (1996) 305
6. Ceniceros H.D., and Hou T.Y. An efficient dynamically adaptive mesh for potentially singular solutions. J. Comput. Phys. 172 (2001) 609639
7. Fibich G., and Gavish N. Theory of singular vortex solutions of the nonlinear Schrödinger equation. Physica D (2008)
8. Fibich G., Gavish N., and Wang X.P. New singular solutions of the nonlinear Schrödinger equation. Physica D 211 (2005) 193-220
9. Fibich G., Gavish N., and Wang X.P. Singular ring solutions of critical and supercritical nonlinear Schrödinger equations. Physica D 231 (2007) 55-86
10. Fibich G., Ren W., and Wang X.P. Numerical simulations of self focusing of ultrafast laser pulses. Phys. Rev. E 67 (2003) 056603
11. Huang W., Ren Y., and Russell R.D. Moving mesh methods based on moving mesh partial differential equations. SIAM J. Comput. Phys. 113 (1994) 279-290
12. Kosmatov N.E., Shvets V.F., and Zakharov V.E. Computer simulation of wave collapses in the nonlinear Schrödinger equation. Physica D 52 (1991) 16-35
13. McLaughlin D.W., Papanicolaou G.C., Sulem C., and Sulem P.L. Focusing singularity of the cubic Schrödinger equation. Phys. Rev. A 34 (1986) 1200-1210
14. 2 supercritical nonlinear Schrödinger equation. Duke Math. J. 134 2 (2006) 199-258
15. Ren W., and Wang X.P. An iterative grid redistribution method for singular problems in multiple dimensions. J. Comput. Phys. 159 (2000) 246-273
16. M Sanz-Serna J., and Christie I. A simple adaptive technique for nonlinear wave problems. J. Comput. Phys. 128 (1996) 274-288
17. Saucez P., Vande Wouwer A., and Schiesser W.E. Some observations on a static spatial remeshing method based on equidistribution principles. J. Comput. Phys. 128 (1996) 274-288
18. Saucez P., Vande Wouwer A., and Schiesser W.E. An adaptive method of lines solution of the Korteweg-de Vries equation. Comput. Math. Appl. 35 (1998) 13-25
19. Sulem C., and Sulem P.L. The Nonlinear Schrödinger Equation (1999), Springer, New York
20. van Dam A., and Zegeling P.A. A robust moving mesh finite volume method applied to 1D hyperbolic conservation laws from magnetohydrodynamics. J. Comput. Phys. 216 (2006) 526-546
21. Wang D., and Wang X.P. A three-dimensional adaptive method based on the iterative grid redistribution. J. Comput. Phys. 199 (2004) 423-436
22. X.P. Wang, Personal communications.