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A new approach to grid generation. (English) Zbl 0794.65085
Summary: An entirely new approach to numerical grid generation, the deformation method, is presented. Each point of an existing grid is moved, in an inter-related manner, to a new position according to a system of \(n\) ordinary differential equations (\(n\) = spacial dimension). The resulting grid has prescribed mesh sizes.

MSC:
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
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[1] DOI: 10.1016/0021-9991(66)90001-5 · Zbl 0254.65069 · doi:10.1016/0021-9991(66)90001-5
[2] A. S. Dvinsky, Adaptive Grid Generation from Harmonic Maps on Riemannian Manifolds, preprint (1990) · Zbl 0733.65074
[3] Anderson D. A., Applied Math. and Computation 35 (1990)
[4] G. G. Liao, On the variational approach to grid generation (to appear in Numerical Methods for P.D.E.s) (1991)
[5] DOI: 10.1090/S0002-9947-1965-0182927-5 · doi:10.1090/S0002-9947-1965-0182927-5
[6] Banyaga A., Enseignement Math 20 (1974)
[7] Dacorogna B., Ann. Inst. H. Poincare, Analyse Non Lineaire 7 (1990)
[8] DOI: 10.1016/0021-9991(74)90114-4 · Zbl 0283.76011 · doi:10.1016/0021-9991(74)90114-4
[9] Brackbill J., J. Comput. Phys 46 (1982)
[10] Thompson J. F., Numerical Grid Generation (1985) · Zbl 0598.65086
[11] S. S. Sritharan, Mathematical aspects of harmonic grid generation, preprint (1990)
[12] Smith P. W., Complex Variables 10 (1988)
[13] Liao G. G., SIAM 8 (1991)
[14] Steinberg S., Numerical Methods for P.D.E.’s 2 (1985)
[15] Castillo J., Applied Mathematics and Computation 2 (1988)
[16] Lewy H., Comm. in P.D.E.’s 2 (1977)
[17] Peter Li, Annals of Mathematics 125 (1987)
[18] Peter Li, J. Differential Geometry 29 (1989)
[19] G. Liao and J. Su, A direct method in Dacorogna-Moser’s approach of grid generation problems, preprint (1991) · Zbl 0803.65114
[20] G. Liao and J. Su, Grid generation via deformation, preprint (1991) · Zbl 0766.58057
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