Methods of adaptive harmonic grid generation

S. A. Ivanenko ; G. P. Prokopov

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 37 (1997) no. 6, pp. 643-662

Bibliographie

[1] Bakhvalov N. S., “K optimizatsii metodov resheniya kraevykh zadach pri nalichii pogranichnogo sloya”, Zh. vychisl. matem. i matem. fiz., 9:4 (1969), 841–859 | Zbl

[2] Belikov V. V., Vychislitelnyi kompleks “TRIANA” – generator setok treugolnykh konechnykh elementov v proizvolnykh ploskikh oblastyakh, P007705. GosFAP SSSR, 1984 | Zbl

[3] Belinskii P. P., Godunov S. K., Ivanov Yu. B., Yanenko I. K., “Primenenie odnogo klassa kvazikonformnykh otobrazhenii dlya postroeniya raznostnykh setok v oblastyakh s krivolineinymi granitsami”, Zh. vychisl. matem. i matem. fiz., 15:6 (1975), 1499–1511 | MR

[4] Vnukov E. A., “Sposob postroeniya ortogonalnykh koordinat, osnovannykh na ispolzovanii konformnykh otobrazhenii”, Uch. zap. TsAGI, 18:5 (1987), 94–98

[5] Vyshinskii V. V., Kravchenko S. A., Sorokin A. M., “K voprosu vybora setok pri reshenii aerodinamicheskikh zadach”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1994, no. 1, 58–67

[6] Godunov S. K., Prokopov G. P., “O raschetakh konformnykh otobrazhenii i postroenii raznostnykh setok”, Zh. vychisl. matem. i matem. fiz., 7:5 (1967), 1031–1059 | MR | Zbl

[7] Godunov S. K., Prokopov G. P., “Ob ispolzovanii podvizhnykh setok v gazodinamicheskikh raschetakh”, Zh. vychisl. matem. i matem. fiz., 12:2 (1972), 429–440 | MR | Zbl

[8] Godunov S. K., Zabrodin A. V., Ivanov M. Ya. i dr., Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976 | MR | Zbl

[9] Godunov S. K., Gordienko I. M., Chumakov G. A., “Kvaziizometricheskaya parametrizatsiya krivolineinogo chetyrekhugolnika i metrika postoyannoi krivizny”, Vychisl. metody i modeli prikl. matem., In-t matem. SO RAN, Novosibirsk, 1994, 3–19 | MR | Zbl

[10] Degtyarev L. M., Ivanova T. S., “Metod adaptivnykh setok v odnomernykh nestatsionarnykh zadachakh konvektsii- diffuzii”, Differents. ur-niya, 29:7 (1993), 1179–1192 | MR | Zbl

[11] Delone B. N., “O pustom share”, Izv. AN SSSR. Fiz. Zemli, 7:6 (1934), 793–800

[12] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya, Nauka, M., 1986 | MR

[13] Ivanenko S. A., Postroenie krivolineinykh setok i ikh ispolzovanie v metode konechnykh elementov dlya resheniya uravnenii melkoi vody, VTs AN SSSR, M., 1985 | MR

[14] Ivanenko S. A., Charakhchyan A. A., “Algoritm postroeniya krivolineinykh setok iz vypuklykh chetyrekhugolnikov”, Dokl. AN SSSR, 295:2 (1987), 280–283 | Zbl

[15] Ivanenko S. A., Charakhchyan A. A., “Krivolineinye setki iz vypuklykh chetyrekhugolnikov”, Zh. vychisl. matem. i matem. fiz., 28:4 (1988), 503–514 | MR

[16] Ivanenko S. A., “Postroenie nevyrozhdennykh setok”, Zh. vychisl. matem. i matem. fiz., 28:10 (1988), 1498–1506 | MR

[17] Ivanenko S. A., Raschet techenii v vodoemakh na krivolineinykh setkakh, VTs AN SSSR, M., 1991

[18] Ivanenko S. A., “Adaptivnye setki i setki na poverkhnostyakh”, Zh. vychisl. matem. i matem. fiz., 33:9 (1993), 1333–1351 | MR | Zbl

[19] Ivanenko S. A., “Adaptivnye krivolineinye setki v metode konechnykh elementov”, Zh. vychisl. matem. i matem. fiz., 35:9 (1995), 1334–1355 | MR | Zbl

[20] Ivanenko S. A., “Primenenie adaptivno-garmonicheskikh setok dlya chislennogo resheniya zadach s pogranichnymi i vnutrennimi sloyami”, Zh. vychisl. matem. i matem. fiz., 35:10 (1995), 1494–1517 | MR | Zbl

[21] Liseikin V. D., “Tekhnologiya konstruirovaniya trekhmernykh setok dlya zadach aerogidrodinamiki (obzor)”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1991, no. 3, 31–45

[22] Liseikin V. D., “O konstruirovanii regulyarnykh setok na $n$-mernykh poverkhnostyakh”, Zh. vychisl. matem. i matem. fiz., 31:11 (1991), 1670–1683 | MR

[23] Liseikin V. D., “Obzor metodov postroeniya strukturnykh adaptivnykh setok”, Zh. vychisl. matem. i matem. fiz., 36:1 (1996), 3–41 | MR

[24] Mikhalin V. A., “Modifikatsiya parabolicheskogo generatora setok”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1995, no. 1–2, 91–94

[25] Prokopov G. P., Postroenie ortogonalnykh raznostnykh setok posredstvom rascheta konformnykh otobrazhenii, Preprint No 45, IPMatem. AN SSSR, M., 1970

[26] Prokopov G. P., O raschete raznostnykh setok, blizkikh k ortogonalnym, v oblastyakh s krivolineinymi granitsami, Preprint No 17, IPMatem. AN SSSR, M., 1974

[27] Prokopov G. P., “Nekotorye obschie voprosy konstruirovaniya algoritmov postroeniya raznostnykh setok”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1988, no. 1, 3–13 | MR

[28] Prokopov G. P., “Ob organizatsii sravneniya algoritmov i programm postroeniya regulyarnykh dvumernykh raznostnykh setok”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1989, no. 3, 98–108

[29] Prokopov G. P., “Postroenie raznostnykh setok putem optimizatsii parametrov interpolyatsionnykh formul”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1990, no. 1, 7–16

[30] Prokopov G. P., “Konstruirovanie testovykh zadach dlya postroeniya dvumernykh regulyarnykh setok”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1993, no. 1, 7–12

[31] Prokopov G. P., “Avtomatizatsiya podgotovki i kontrolya dannykh dlya rascheta blochno-regulyarnykh setok”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1994, no. 1, 36–44

[32] Rabinovich B. I., Tyurin Yu. V., “Ob odnom chislennom metode konformnogo otobrazheniya”, Dokl. AN SSSR, 272:3 (1983), 532–535 | MR | Zbl

[33] Rabinovich B. I., Tyurin Yu. V., “Rekurrentnyi chislennyi metod konformnogo otobrazheniya dvusvyaznykh oblastei na krugovoe koltso”, Dokl. AN SSSR, 272:4 (1983), 795–798 | MR | Zbl

[34] Rasskazova V. V., Sofronov I. D., “Nekotorye voprosy chislennogo resheniya trekhmernykh zadach mekhaniki sploshnoi sredy”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1987, no. 1, 76–87

[35] Saraev V. A., “Postroenie regulyarnykh chetyrekhugolnykh setok v oblastyakh s krivolineinymi granitsami po tochkam vlozhennykh drug v druga krivolineinykh chetyrekhugolnikov”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1985, no. 3, 25–38

[36] Sakhabutdinov Zh. M., Petrov G. A., Maigurova S. V., “Postroenie i optimizatsiya trekhmernykh krivolineinykh setok”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1989, no. 1, 9–18

[37] Semenov A. Yu., “Marshevyi metod postroeniya ortogonalnykh setok na ploskosti i poverkhnostyakh”, Zh. vychisl. matem. i matem. fiz., 35:11 (1995), 1689–1704 | MR | Zbl

[38] Sidorov A. F., “Ob odnom algoritme rascheta optimalnykh raznostnykh setok”, Tr. Matem. in-ta AN SSSR, 74, M., 1966, 147–151 | MR | Zbl

[39] Sidorov A. F., “Algoritmy rascheta optimalnykh krivolineinykh raznostnykh setok”, Chisl. metody resheniya zadach perenosa, Minsk, 1979, 56–59

[40] Sidorov A. F., Shabashova T. M., “Ob odnom metode rascheta optimalnykh raznostnykh setok dlya mnogomernykh oblastei”, Chisl. metody mekhan. sploshnoi sredy, 12, no. 5, ITPM SO AN SSSR, Novosibirsk, 1981, 106–124

[41] Sidorov A. F., Ushakova O. V., “Ob odnom algoritme postroeniya optimalnykh adaptiruyuschikhsya setok i ego prilozheniyakh”, Chisl. metody mekhan. sploshnoi sredy, 16, no. 5, ITPM SO AN SSSR, Novosibirsk, 1985, 101–115 | MR

[42] Sofronov I. D., Rasskazova V. V., Nesterenko L. V., “Neregulyarnye setki v metodakh rascheta nestatsionarnykh zadach gazovoi dinamiki”, Vopr. matem. modelirovaniya, vychisl. matem. i informatiki, Arzamas-16: Min. RF Atomnoi energii, M., 1994, 131–183

[43] Tolstykh A. I., Kompaktnye raznostnye skhemy i ikh primenenie v zadachakh aerogidrodinamiki, Nauka, M., 1990 | MR

[44] Tikhonov A. N., Gorbunov A. D., “Otsenki pogreshnosti metoda tipa Runge–Kutta i vybor optimalnykh setok”, Zh. vychisl. matem. i matem. fiz., 4:2 (1964), 232–241 | MR | Zbl

[45] Uskov V. M., “Postroenie setok iz nevyrozhdennykh chetyrekhugolnikov s ispolzovaniem kriteriya Delone”, Vopr. atomnoi nauki i tekhn. Matem. modelirovanie fiz. protsessov, 1994, no. 2, 12–16

[46] Ushakova O. V., “Primenenie optimalnykh adaptiruyuschikhsya setok dlya resheniya zadach s pogransloyami”, Modelirovanie v mekhan., 3(20), no. 6, Novosibirsk, 1989, 141–145 | MR | Zbl

[47] Ushakova O. V., “Teoriya suschestvovaniya i edinstvennosti resheniya kraevoi zadachi postroeniya odnomernykh optimalnykh adaptiruyuschikhsya setok”, Modelirovanie v mekhan., 3(20), no. 2, Novosibirsk, 1989, 134–141 | MR | Zbl

[48] Ushakova O. V., “Iteratsionnaya protsedura rascheta dvumernykh adaptivnykh setok”, Priblizhennye metody issledovaniya nelineinykh zadach mekhan. sploshnykh sred, Sverdlovsk, 1992, 58–65 | Zbl

[49] Ushakova O. V., “LADA – ekonomichnyi algoritm i programma postroeniya dvumernykh krivolineinykh optimalnykh setok v odnosvyaznykh oblastyakh geometricheski slozhnoi formy”, Vopr. atomnoi nauki i tekhniki, Matem. modelirovanie fiz. protsessov, 1994, no. 3, 47–56

[50] Khairullina O. B., “Metod rascheta blochnykh optimalnykh setok v dvumernykh mnogosvyaznykh oblastyakh”, Vopr. atomnoi nauki i tekhniki, Matem. modelirovanie fiz. protsessov, 1992, no. 1, 62–66

[51] Khairullina O. B., “Postroenie blochno-regulyarnykh optimalnykh setok”, Vopr. atomnoi nauki i tekhniki, Matem. modelirovanie fiz. protsessov, 1994, no. 1, 19–25

[52] Khairullina O. B., “Uskorenie skhodimosti iteratsionnogo protsessa pri postroenii blochno-regulyarnykh setok”, Vopr. atomnoi nauki i tekhniki, Matem. modelirovanie fiz. protsessov, 1995, no. 1–2, 54–59

[53] Charakhchyan A. A., “Pochti konservativnye raznostnye skhemy dlya uravnenii gazovoi dinamiki”, Zh. vychisl. matem. i matem. fiz., 33:11 (1993), 1681–1692 | MR

[54] Shabashova T. I., “Ob odnom ekonomichnom sposobe postroeniya optimalnykh raznostnykh setok”, Chisl. metody mekhan. sploshnoi sredy, 14, no. 5, ITPM SO AN SSSR, Novosibirsk, 1983, 139–157 | MR

[55] Shabashova T. I., “O postroenii optimalnykh krivolineinykh koordinatnykh setok v trekhmernykh oblastyakh”, Chisl. metody mekhan. sploshnoi sredy, 17, no. 1, ITPM SO AN SSSR, Novosibirsk, 1986, 144–155

[56] Shevelev Yu. D., Prostranstvennye zadachi vychislitelnoi aerogidrodinamiki, Nauka, M., 1986 | Zbl

[57] Yanenko N. N., Danaev N. T., Liseikin V. D., “O variatsionnom metode postroeniya setok”, Chisl. metody mekhan. sploshnoi sredy, 8, no. 4, Novosibirsk, 1977, 157–163 | MR

[58] Anderson D. A., Ray M. M., “The use of solution adaptive grids in solving partial differential equations”, Appl. Math. and Comput., 10–11 (1982), 317–338 | DOI | MR | Zbl

[59] Anderson D. A., “Grid cell volume control with an adaptive grid generator”, Appl. Math. and Comput., 35:3 (1990), 209–217 | DOI | Zbl

[60] Arcilla A. S., Hauser J., Eiseman P. R., Thompson J. F., “Numerical grid generation in computational fluid dynamics and related fields”, Proc. Third Internat. Conf. Barcelona, Spain, 3–7 June, 1991 (North-Holland, N.Y. etc.) | MR

[61] Arina R., Tarditi S., “Orthogonal block structured surface grids”, Numer. Methods for Fluid Dynamics 4, Proc. Conf. Held at Reading Univ. United Kingdom, April 1992, Clarendon Press, Oxford, 1993, 293–300 | Zbl

[62] Babuska I., Rheinbold W. C., “A-posteriory error estimates for the finite element method”, Internat. J. Numer. Meth. Engng., 12 (1978), 1597–1615 | DOI | Zbl

[63] Babuska I., Miller A., “The post-processing approach in the finite element method. Part 1: Calculation of displacements, stresses, and other higher derivatives of the displacements”, Internat. J. Numer. Meth. Engng., 20 (1984), 1085–1109 ; “Part 2: The calculation stress intencity factors”, 1111–1129 | DOI | Zbl | Zbl

[64] Berger M. G., Oliger J., “Adaptive mesh refinement for hyperbolic partial differential equations”, J. Comput. Phys., 53:3 (1984), 484–512 | DOI | MR | Zbl

[65] Blacker T. D., “Paving: a new approach to automated quadrilateral mesh generation”, Internat. J. Numer. Meth. Engng., 32 (1991), 811–847 | DOI | Zbl

[66] De Boor C., “Good approximation by splines with variable knots. II”, Conf. Numer. Solution of Differential Equations, Lect. Notes in Math., 363, Springer, Berlin, 1973, 12–20 | MR

[67] Brackbill J. U., Saltzman J. S., “Adaptive zoning for singular problems in two dimensions”, J. Comput. Phys., 46:3 (1982), 342–368 | DOI | MR | Zbl

[68] Brackbill J. U., “An adaptive grid with directional control”, J. Comput. Phys., 108:1 (1993), 38–50 | DOI | MR | Zbl

[69] Diaz A. R., Kikuchi N., Taylor J. E., “A method of grid optimization for finite element method”, Comput. Meth. Appl. Mech. Engng., 41 (1983), 29–45 | DOI | MR | Zbl

[70] Dvinsky A. S., “Adaptive grid generation from harmonic maps on Riemanian manifolds”, J. Comput. Phys., 95:3 (1991), 450–476 | DOI | MR | Zbl

[71] Dwyer H. A., “Grid adaption for problems in fluid dynamics”, AIAA Journal, 22 (1984), 1705–1712 ; Duaier X. A., “Adaptatsiya setok dlya zadach gidrodinamiki”, Aerokosmich. tekhn., 1985, no. 8, 172–181 | DOI | Zbl

[72] Eells J., Sampson J. H., “Harmonic mappings of Riemanian manifolds”, Amer. J. Math., 86:1 (1964), 109–160 | DOI | MR | Zbl

[73] Eells J. E., Lemaire L., “Another report on harmonic maps”, Bull. London Math. Soc., 20:86 (1988), 387–524 | MR

[74] Eiseman P. R., “Adaptive grid generation”, Comput. Methods in Appl. Mech. and Engng., 64 (1987), 321–376 | DOI | MR | Zbl

[75] Frey W. H., Field D. H., “Mesh relaxation: a new technique for improving triangulations”, Internat. J. Numer. Meth. Engng., 31 (1991), 1121–1133 | DOI | MR | Zbl

[76] Fuller F. B., “Harmonic mappings”, Proc. Nat. Acad. Sci., 40 (1954), 987–991 | DOI | MR | Zbl

[77] Golias N. A., Tsiboukis T. O., “An approach to refining three-dimensional tetrahedral meshes based on Delauney transformations”, Internat. J. Numer. Meth. Engng., 37 (1994), 793–812 | DOI | MR | Zbl

[78] Hamilton R., Harmonic maps of manifolds with boundary, Lect. Notes in Math., 471, 1975, 165 pp. | MR | Zbl

[79] Jaquotte O.-P., “A mechanical model for a new grid generation method in computational fluid dynamics”, Comput. Math. and Appl. Mech. Engng., 66 (1980), 323–338 | DOI | MR

[80] Jordan S. A., Spaulding M. L., “A fast algorithm for grid generation”, J. Comput. Phys., 104 (1993), 118–128 | DOI | Zbl

[81] Jost J., Schoen R., “On the existence of harmonic diffeomorphisms between surfaces”, Invent. Math., 66:2 (1982), 353–359 | DOI | MR | Zbl

[82] Carcaillet R., Kennon S. R., Dulikravich G. S., “Optimization of three-dimensionai computational grids”, J. Aircraft., 5 (1986), 415–421 ; Karkailet P., Kennon S. R., Dulikravich G. S., “Optimizatsiya trekhmernykh setok”, Aerokosmich. tekhn., 1987, no. 1, 99–106 | DOI

[83] Kennon S. R., Dulikravich G. S., “Generation of computational grids using optimization”, AIAA J., 24:7 (1986), 1069–1073 ; Kennon S. R., Dulikravich G. S., “Postroenie setok s pomoschyu optimizatsionnogo metoda”, Aerokosmich. tekhn., 1987, no. 1, 107–112 | DOI | Zbl

[84] Kennon S. R., Anderson D. A., “Unstructured grid adaption for non-convex domains”, Proc. Conf. Numer. Grid Generation in Comput. Fluid Mech., Pineridge Press, London: U.K., Swansea U.K., 1988, 599–609

[85] Khamayseh A., Mastin C. W., “Surface grid generation based on elliptic PDE models”, Appl. Math. Comput., 65:1–3 (1994), 253–264 | DOI | MR | Zbl

[86] Kreis R. I., Thames F. C., Hassan H. A., “Application of a variational method for generating adaptive grids”, AIAA Journal, 3 (1986), 404–410 ; Kreis R. I., Teimz F. K., Khasan Kh. A., “Postroenie adaptiruyuschikhsya setok s pomoschyu variatsionnogo metoda Brekbilla–Zaltsmana”, Aerokosmich. tekhn., 1987, no. 1, 83–90 | DOI | MR | Zbl

[87] Levy H., “On the non-vanishing of the Jacobian in certain one-to-one mappings”, Bull. Amer. Math. Soc., 42 (1936), 689–692 | DOI | MR

[88] Liseikin V. D., “On some interpretations of a smoothness functional used in constructing regular and adaptive grids”, Russ. J. Numer. Analys. Modelling, 8:6 (1993), 507–518 | DOI | MR | Zbl

[89] Loehner R., Parikh P., “Generation of three-dimensional unstructured girds by the advancing-front method”, Internat. J. Numer. Meth. Fluids, 8:10 (1988), 1135–1149 | DOI | Zbl

[90] Muller K., Muller R. N., “Moving finite elements I”, SIAM J. Numer. Analys., 18:6 (1981), 1019–1032 | DOI | MR

[91] Muller K., “Moving finite elements. II”, SIAM J. Numer. Analys., 18:6 (1981), 1033–1057 | DOI | MR

[92] Nakahashi K., Deiwert G. S., “Three-dimensional adaptive grid method”, AIAA Journal, 6 (1986), 948–954 ; Nakakhasi K., Deiuert D. S., “Novyi metod postroeniya trekhmernykh adaptiruyuschikhsya setok”, Aerokosmich. tekhn., 1987, no. 1, 90–98 | DOI

[93] Oden J. T., Demkowicz L., Strouboulis T., Devlow P., “Adaptive methods for problems in solid and fluid mechanics”, Accuracy Estimates and Adaptive Refinements in Finite Element Comput., John Willey Sons Ltd., London–New York, 1986, 249–280 | MR

[94] Pardhanani A., Carey G. F., “Optimization of computational grids”, Numer. Methods Partial Differential Equations, 4:2 (1988), 95–117 | DOI | MR | Zbl

[95] Pearce D., Optimized grid generation with geometry definition decoupled, AIAA Paper, 1990

[96] Pereyra V., Sewell E. G., “Mesh selection for discrete solutions of boundary value problems in ordinary differential equations”, Numer. Math., 23:3 (1975), 261–268 | DOI | MR | Zbl

[97] Roache P. J., Steinberg S., “A new approach to grid generation using a variational formulation”, Proc. AIAA 7-th CFD Conf. Cincinnati, 1985, 360–370

[98] Russel R. D., Christiansen J., “Adaptive mesh selection strategies for solving boundary value problems”, SIAM J. Numer. Analys., 15:1 (1978), 59–80 | DOI | MR | Zbl

[99] Ryskin G., Leal L. G., “Orthogonal mapping”, J. Comput. Phys., 50:1 (1983), 71–100 | DOI | MR | Zbl

[100] Saltzman J., “Variational methods for generating meshes on surfaces”, J. Comput. Phys., 63 (1986), 1–19 | DOI | MR | Zbl

[101] Samareh-Abolhassani J., Steward J. E., “Surface grid generation in an parameter space”, J. Comput. Phys., 113:1 (1994), 112–121 | DOI | Zbl

[102] Shih M. H., Yu T., Soni B. K., “Interactive grid generation and NURBS applications”, Appl. Math. Comput., 65:1–3 (1994), 279–294 | DOI | MR | Zbl

[103] Shoen R., Yau S. T., “On univalent harmonic maps between surface”, Invent. Math., 44:3 (1978), 265–278 | DOI | MR

[104] Soni B. K., “Elliptic grid generation system: control function revisited – I”, Applied Math. and Comput., 59 (1993), 151–163 | DOI | MR | Zbl

[105] Steinberg S., Roache P., “Anomalies in gird generation in curves”, J. Comput. Phys., 91 (1990), 255–277 | DOI | MR | Zbl

[106] Steinberg S., Roache P., “Variational curve and surface grid generation”, J. Comput. Phys., 100:1 (1992), 163–178 | DOI | MR | Zbl

[107] Steger J. L., Chaussee D. S., “Generation of body-fitted coordinates using hyperbolic partial differential equations”, SIAM J. Sci. Statist. Comput., 1 (1980), 431–437 | DOI | MR | Zbl

[108] Strang G., Fix G. J., An analysis of the finite element method, Prentice-Hall Inc., N.J., Englewood Cliffs, 1973 ; Streng G., Fiks Dzh., Teoriya metoda konechnykh elementov, Mir, M., 1977 | MR | Zbl | MR

[109] Takagi T., Miki K., Chen B. C. J., Sha U. T., “Numerical generation of boundary-fitted curvilinear coordinate systems for arbitrary curved surfaces”, J. Comput. Phys., 58 (1985), 67–79 | DOI | Zbl

[110] Thomas P. D., “Composite three dimensional grids generated by elliptic systems”, AIAA Journal, 20:9 (1982), 1195–1202 ; Tomas P. D., “Postroenie sostavnykh trekhmernykh raschetnykh setok na osnove resheniya ellipticheskikh uravnenii”, Aerokosmich. tekhn., 1:4 (1983), 59–67 | DOI | Zbl | MR

[111] Thomas P. D., Middlecoff J. F., “Direct control of the grid point distribution in meshes generation by elliptic equations”, AIAA Journal, 18 (1980), 652–656 | DOI | MR

[112] Thompson J. F., Thames F. C., Mastin C. W., “Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies”, J. Comput. Phys., 15:3 (1974), 299–319 | DOI | Zbl

[113] Numerical grid generation, Appl. Math. and Comput., 10–11, eds. J. F. Thompson, 1982 | MR

[114] Thompson J. F., Warsi Z. U. A., Mastin C. W., “Boundary-fitted coordinate systems for numerical solution of partial differential equations”, J. Comput. Phys., 47:2 (1982), 1–108 | DOI | MR | Zbl

[115] Thompson J. F., “Grid generation techniques in computational fluid dynamics”, AIAA Journal, 22:11 (1984), 1505–1523 ; Tompson D. F., “Metody rascheta setok v vychislitelnoi aerodinamike”, Aerokosm. tekhn., 1985, no. 8, 141–171 | DOI | Zbl

[116] Thompson J. F., Warsi Z. U. A., Mastin C. W., Numerical grid generation, North-Holland, New York etc., 1985 | MR | Zbl

[117] Tu Y., Thompson J. F., “Three-dimensional solution-adaptive grid generation on composite configurations”, AIAA Journal, 29:12 (1991), 2025–2026 | DOI | Zbl

[118] Visbal M., Knight D., “Generation of orthogonal and nearly orthogonal coordinates with grid control near boundaries”, AIAA Journal, 20:3 (1982), 305–306 | DOI | Zbl

[119] Voroni M. G., “Nouvelles applications des parameters continus a la theorie des formes quadratiques”, Z. Reine und Angew., 134 (1908), 198–287 | DOI

[120] Warsi Z. U. A., “Numerical grid generation in arbitrary surfaces through a second-order differential – geometric model”, J. Comput. Phys., 64 (1986), 82–96 | DOI | MR | Zbl

[121] Warsi Z. U. A., Thompson J. F., “Application of variational methods in the fixed and adaptive grid generation”, Comput. Math. and Applic., 19:8/9 (1990), 31–41 | DOI | MR | Zbl

[122] White A. B. Jr., “On selection of equidistributing meshes for two-point boundary-value problems”, SIAM J. Numer. Analys., 16:3 (1979), 472–502 | DOI | MR | Zbl

[123] White A. B. Jr., “On the numerical solution of initial / boundary value problems in one space dimension”, SIAM J. Numer. Analys., 19:4 (1982), 683–697 | DOI | MR | Zbl

[124] Winslow A. M., “Numerical solution of quasilinear Poisson equation in nonuniform triangle mesh”, J. Comput. Phys., 1:2 (1966), 149–172 | DOI | MR | Zbl

[125] Winslow A. M., Adaptive mesh zoning by the equipotential method, UCID-19062, Lawrence Livermore Nat. Lab. Univ. California, 1981