Regularizationof the barrier variational method of grid generation

Computational Mathematics and Mathematical Physics

Volumn 39, Issue 9, 1999, Pages 1426-1440

  Garanzha, V A ^a   Kaporin, I E ^a  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142108773     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. Brackbill, J.U. and Saltzman, J.S., Adaptive Zoning for Singular Problems in Two Dimensions, J. Comput. Phys., 1982, vol. 46, no. 3, pp. 342-368.
2. Gilbarg, D. and Trudinger, N.S., Elliptic Partial Differential Equations of Second Order, Berlin: Springer-Verlag, 1983, 2nd ed. Translated under the title Ellipticheskie differentsial'nye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Moscow: Nauka, 1989.
3. Godunov, S.K. and Prokopov, G.P., On Calculations of Conformal Mappings and Grid Generation, Zh. Vychisl. Mat. Mat. Fiz., 1967, vol. 7, no. 6, pp. 902-914.
4. Belinskii, P.P., Godunov, S.K., Ivanov, Yu.B., and Yanenko, I.K., Application of a Class of Quasi-Conformal Mappings in Grid Generation in Domains with Curved Boundaries, Zh. Vychisl. Mat. Mat. Fiz., 1975, vol. 15, no. 6, pp. 1499-1511.
5. Dvinsky, A.S., Adaptive Grid Generation from Harmonic Maps on Riemannian Manifolds, J. Comput. Phys., 1991, vol. 95, p. 450.
6. Liseikin,V.D., Constructing Regular Grids on N-Dimensional Surfaces, Zh. Vychisl. Mat. Mat. Fiz., 1991, vol. 31, no. 11, pp. 1670-1683.
7. Ivanenko, S.A. and Charakhch'yan, A.A., Curvilinear Grids of Convex Quadrangles, Zh. Vychisl. Mat. Mat. Fiz., 1988, vol. 28, no. 10, pp. 1498-1506.
8. Winslow, A.M., Numerical Solution of the Quasilinear Poisson Equation in a Non-Uniform Triangle Mesh, J. Comput. Phys., 1967, vol. 1, no. 2, pp. 149-172.
9. Charakhch'yan, A.A. and Ivanenko, S.A., A Variational Form of the Winslow Grid Generator, J. Comput. Phys., 1997. vol. 136, pp. 385-398.
10. Strang, G. and Fix, G., An Analysis of the Finite Element Method, Englewood Cliffs: Prentice-Hall, 1973. Translated under the title Teoriya metoda konechnykh elementov, Moscow: Mir, 1977.
11. Garanzha, V.A., Kaporin, I.E., and Konshin, V.N., Reliable Flow Solver Based on the High Order Control Volume Padé-type Differences, Sixteenth International Conference on Numerical Methods in Fluid Dynamics: Proceedings of the Conference Held in Arcachon, France, 6-10 July, 1998, Bruneau, C.-H., Ed., Berlin: Springer-Verlag, 1998. pp. 278-283.
12. Garanzha, V.A. and Kaporin, I.E., Variational Generation of Grids Around Arbitrary Trajectory Wells in Reservoir Simulation, Numerical Grid Generation in Computational Field Simulations: Proc. of the 6th Int. Conf., Held at the Univ. of Greenwich, July 6-July 9, 1998, Cross, M. et al., Eds., Mississippi State (Miss.): NSF Engineering Research Center for Computational Field Simulation, 1998, pp. 1001-1010.
13. Kaporin, I.E., Second Order Incomplete Cholesky Preconditionings for the CG Method, Iterative Solution Methods for the Elasticity Equations As Arising in Mechanics and Biomechanics IMMB'98, Axelsson, O., Meytcheva, M., and Polman, B., Eds., Nijmegen: Katholieke Univ. Nijmegen, 1998, pp. 47-49.
14. Ajiz, M.A. and Jennings, A., A Robust Incomplete Choleski-Conjugate Gradient Algorithm, Int. J. Numer. Methods Eng., 1984, vol. 20, pp. 949-966.
15. Saad, Y. and Schultz, M., GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM J. Sci. Statist. Comput., 1986, vol. 7, pp. 856-869.
16. Papadrakakis, M. and Yakoumidakis, M., On the Preconditioned Conjugate Gradient Method for Solving Ax -λBx = 0, Int. J. Numer. Methods Eng., 1987, vol. 24, pp. 1355-1366.
17. Vasil'ev, F.P., Metody resheniya ekstremal'nykh zadach (Solution Methods for Extremum Value Problems), Moscow: Nauka, 1981.