A fully implicit, nonlinear adaptive grid strategy

Journal of Computational Physics

Volumn 212, Issue 2, 2006, Pages 703-717

  Chacon L ^a   Lapenta, G ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Beltrami equation; Fully implicit methods; Grid generation; Harmonic maps; Moving mesh; Multigrid; Newton Krylov

Indexed keywords

MESH GENERATION;

ADAPTIVE GRIDS; BELTRAMI; BELTRAMI EQUATION; FULLY IMPLICIT METHODS; GRID GENERATION; HARMONIC MAP; MOVING MESH; MULTIGRIDS; NEWTON-KRYLOV; NON-LINEAR SOLVER;

NONLINEAR EQUATIONS;

EID: 29144530996     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.07.023     Document Type: Article

References (48)

1. J.U. Brackbill J.S. Saltzman Adaptive zoning for singular problems in 2 dimensions J. Comput. Phys. 46 3 1982 342-368
2. A.E. Giannakopoulos A.J. Engel Directional control in grid generation J. Comput. Phys. 74 1988 422-439
3. A.S. Dvinsky Adaptive grid generation from Harmonic maps J. Comput. Phys. 95 1991 450-476
4. J.U. Brackbill An adaptive grid with directional control J. Comput. Phys. 108 1993 38-50
5. M.J. Baines Moving Finite Elements 1994 Oxford University Press Oxford
6. W. Huang Y. Ren R.D. Russell Moving mesh partial differential equations (MMPDES) based on the equidistribution principle SIAM J. Numer. Anal. 31 3 1994 709-730
7. P. Knupp Mesh generation using vector fields J. Comput. Phys. 119 1995 142-148
8. S. Li L. Petzold Moving mesh methods with upwinding schemes for time dependent PDEs J. Comput. Phys. 131 1997 368-377
9. W. Cao W. Huang R.D. Russell An r-adaptive finite element method based upon moving mesh PDEs J. Comput. Phys. 149 1999 221-244
10. W. Cao W. Huang R.D. Russell A study of monitor functions for two-dimensional adaptive grid generation SIAM J. Sci. Comput. 20 6 1999 1978-1994
11. R. Li T. Tang P. Zhang Moving mesh methods in multiple dimensions based on Harmonic maps J. Comput. Phys. 170 2001 562-588
12. W. Huang Variational mesh adaptation: Isotropy and equidistribution J. Comput. Phys. 174 2001 903-924
13. H. Tang Solution of the shallow water equations using an adaptive moving mesh method Int. J. Numer. Meth. Fluids 44 2004 789-810
14. V.D. Liseikin Grid Generation Methods 1999 Springer Berlin, New York
15. P. Knupp S. Steinberg Fundationals of Grid Generation 1994 CRC Press Boca Raton, FL
16. J.F. Thompson Z.A. Warsi C.W. Mastin Numerical Grid Generation: Foundations and Applications 1985 North-Holland New York
17. J.E. Castillo Mathematics Aspects of Numerical Grid Generation 1991 SIAM Philadelphia, PA
18. D.A. Knoll L. Chacón L. Margolin V.A. Mousseau On balanced approximations for the time integration of multiple time scale systems J. Comput. Phys. 185 2003 583-611
19. V.D. Liseikin A Computational Differential Geometry Approach to Grid Generation 2003 Springer Berlin, New York
20. R.M. Spitaleri V. Regolo Multiblock multigrid grid generation algorithms: Overcoming multigrid anisotropy Appl. Math. Comput. 84 1997 246-267
21. R.M. Spitaleri V. Micacchi A multiblock multigrid generation method for complex simulations Math. Comput. Simulat. 46 1998 1-12
22. R.M. Spitaleri Full-Fas multigrid grid generation algorithms Appl. Numer. Math. 32 2000 483-494
23. W.M. Tscharnuter K.-H. Winkler A method for computing selfgravitating gas flows with radiation Comput. Phys. Commun. 18 1979 171-199
24. K.-H.A. Winkler M.L. Normand M.J. Newmann Adaptive mesh techniques for fronts in star formation Physics D 12D 1-3 1984 408-425
25. E.A. Dorfi L.O. Drury Simple adaptive grids for 1-D initial value problems J. Comput. Phys. 69 1987 175-195
26. M. Gehmeyr D. Mihalas Adaptive grid radiation hydrodynamics with TITAN Physics D 77 1994 320-341
27. C.T. Kelley Iterative Methods for Linear and Nonlinear Equations 1995 SIAM Philadelphia
28. R. Dembo S. Eisenstat R. Steihaug Inexact Newton methods J. Numer. Anal. 19 1982 400
29. L. Chacón D.A. Knoll A 2D high-β Hall MHD implicit nonlinear solver J. Comput. Phys. 188 2 2003 573-592
30. G. Liao A study of regularity problem of Harmonic maps Pacific J. Math. 131 1988 291-302
31. G. Liao N. Smale Harmonic maps with nontrivial higher-dimensional singularities Lecture Notes in Pure and Applied Mathematics vol. 144 1993 Dekker New York 79-89
32. J. Eells J.H. Sampson Harmonic mappings of Riemannian manifolds Am. J. Math. 86 1 1964 109-160
33. R. Hamilton Harmonic maps of manifolds with boundary Lecture Notes in Mathematics vol. 471 1975 Springer New York
34. R. Schoen S.T. Yau On univalent harmonic maps between surfaces Invent. Math. 44 1978 265-278
35. P. Wesseling An Introduction to Multigrid Methods 1992 Wiley Chichester
36. D.A. Knoll W.J. Rider A multigrid preconditioned Newton-Krylov method SIAM J. Sci. Comput. 21 2 1999 691-710
37. W.J. Rider D.A. Knoll G.L. Olson A multigrid Newton-Krylov method for multimaterial equilibrium radiation diffusion J. Comput. Phys. 152 1 1999 164-191
38. D.A. Knoll G. Lapenta J.U. Brackbill A multilevel iterative field solver for implicit, kinetic, plasma simulation J. Comput. Phys. 149 1999 377-388
39. L. Chacón D.A. Knoll J.M. Finn Implicit, nonlinear reduced resistive MHD nonlinear solver J. Comput. Phys. 178 1 2002 15-36
40. A.R. Curtis M.J.D. Powell J.K. Reid On the estimation of sparse Jacobian matrices J. Inst. Math. Appl. 13 1974 117-119
41. T.F. Coleman J.J. Moré Estimation of sparse Jacobian matrices and graph coloring problems SIAM J. Numer. Anal. 20 1983 187-209
42. M. Ainsworth J.T. Oden A Posteriori Error Estimation in Finite Element Analysis 2000 Wiley New York
43. G. Lapenta Variational grid adaptation based on the minimization of local truncation error: Time independent problems J. Comput. Phys. 193 2004 159
44. G. Lapenta A recipe to detect the origin of error in discretization schemes Int. J. Numer. Meth. Engng. 59 2004 2065
45. A. Winslow Numerical solution of the quasi-linear poisson equation in a nonuniform triangle mesh J. Comput. Phys. 1 1967 149
46. S.I. Braginskii Transport processes in a plasma in: M.A. Leontovich (Ed.) Reviews of Plasma Physics vol. 1 1965 Consultants Bureau New York 205-311
47. H.R. Strauss D.W. Longcope An adaptive finite element method for magnetohydrodynamics J. Comput. Phys. 147 2 1998 318-336
48. S. Balay, K. Buschelman, V. Eijkhout, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, B.F. Smith, H. Zhang, PETSc users manual, Technical Report ANL-95/11 - Revision 2.1.5, Argonne National Laboratory, 2004.