Geodesic
Some parallel iterative methods for solving elliptic equations on tetrahedral grids
Matematičeskoe modelirovanie, Tome 21 (2009) no. 12, pp. 3-20.

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Parallel versions of modified incomplete Cholesky conjugate gradient method with regularized preconditioner are proposed for solving elliptic equations on tetrahedral grids on MIMD parallel computers. The constructed parallel methods use special grid points orderings correlated with domain decomposition. The convergence rates of the proposed parallel methods are examined both theoretically and numerically by analyzing a number of model problems. The comparison of convergence rates of prorosed method and some ather well-known methods is performed. 
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O. Yu. Milyukova; I. V. Popov. Some parallel iterative methods for solving elliptic equations on tetrahedral grids. Matematičeskoe modelirovanie, Tome 21 (2009) no. 12, pp. 3-20. http://geodesic.mathdoc.fr/item/MM_2009_21_12_a0/

[1] Popov I. V., “Novyi podkhod k postroeniyu tetraedralnykh setok”, Fundamentalnye zadachi matematicheskoi fiziki i modelirovaniya tekhnicheskikh i tekhnologicheskikh sistem, 10, M., 2007, 128–133

[2] Popov I. V., Polyuakov S. V., Karamzin Yu. N., “High Accuracy Difference Schemes on Unstructured Triangle Grids”, Numerical Methods and Applications, 5th int. conf. NMA 2002, Revised Papers, eds. I. Divov, I. Lirkov, S. Margenov, Z. Zlatev, Springer, Berlin, 2003 | MR

[3] Meijerink J. A., van der Vorst H. A., “An Iterative Solution Method for Linear Systems, of which the Coefficient Matrix is a Symmetric M-matrix”, Math. Comp., 31:137 (1977), 148–162 | DOI | MR | Zbl

[4] Kershaw D., “The Incomplete Choleski-Conjugate Gradient Method for the Iterative Solution of Systems of Linear Equations”, J. Comp. Phys., 26 (1978), 43–65 | DOI | MR | Zbl

[5] Ortega Dzh., Vvedenie v parallelnye i vektornye metody resheniya lineinykh sistem, Mir, M., 1991 | MR

[6] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR

[7] Gustafsson I., “A Class of First Order Factorization Methods”, BIT, 18 (1978), 142–156 | DOI | MR | Zbl

[8] Milyukova O. Yu., “Nekotorye parallelnye iteratsionnye metody s faktorizovannymi matritsami predobuslovlivaniya dlya resheniya ellipticheskikh uravnenii na treugolnykh setkakh”, Zhurn. vychisl. matem. i matem. fiz., 46:7 (2006), 1096–1112 | MR

[9] Milyukova O. Yu., “Novye parallelnye iteratsionnye metody s faktorizovannymi matritsami predobuslovlivaniya dlya resheniya ellipticheskikh uravnenii na treugolnykh setkakh”, Matem. model., 19:9 (2007), 27–48 | MR | Zbl

[10] Milyukova O. Yu., Parallelnye iteratsionnye metody s faktorizovannymi matritsami predobuslovlivaniya dlya resheniya ellipticheskikh uravnenii, Dissertatsiya na soisk. uchenoi stepeni doktora fiz.-mat. nauk, Moskva, 2004

[11] Dzhordzh A., Lyu Dzh., Chislennoe reshenie bolshikh razrezhennykh sistem uravnenii, Mir, M., 1984 | MR

[12] Hendrickson B., Leland R., “A multilevel algorithm for partitioning graphs”, Supercom-puting' 95 Proc., San Diego, CA, 1995

[13] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989, 614 pp. | MR