Domain decomposition methods and scientific computing applications
Bollettino dell'Unione Matematica Italiana (2005)
- Volume: 8-B, Issue: 1, page 21-54
- ISSN: 0392-4041
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topPavarino, Luca F.. "Domain decomposition methods and scientific computing applications." Bollettino dell'Unione Matematica Italiana 8-B.1 (2005): 21-54. <http://eudml.org/doc/194945>.
@article{Pavarino2005,
abstract = {This paper reviews the basic mathematical ideas and convergence analysis of domain decomposition methods. These are parallel and scalable iterative methods for the efficient numerical solution of partial differential equations. Two examples are then presented showing the application of domain decomposition methods to large-scale numerical simulations in computational mechanics and electrocardiology.},
author = {Pavarino, Luca F.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {21-54},
publisher = {Unione Matematica Italiana},
title = {Domain decomposition methods and scientific computing applications},
url = {http://eudml.org/doc/194945},
volume = {8-B},
year = {2005},
}
TY - JOUR
AU - Pavarino, Luca F.
TI - Domain decomposition methods and scientific computing applications
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/2//
PB - Unione Matematica Italiana
VL - 8-B
IS - 1
SP - 21
EP - 54
AB - This paper reviews the basic mathematical ideas and convergence analysis of domain decomposition methods. These are parallel and scalable iterative methods for the efficient numerical solution of partial differential equations. Two examples are then presented showing the application of domain decomposition methods to large-scale numerical simulations in computational mechanics and electrocardiology.
LA - eng
UR - http://eudml.org/doc/194945
ER -
References
top- Special issue on Mapping and control of complex cardiac arrhythmias. Chaos12 (3), 2002.
- Special issue on From excitable media to virtual cardiac tissue. Chaos Solit. Frac.13 (8), 2002.
- Special issue on Biomedical and bioengineering computing. Comput. Visual. Sci.4 (4), 2003.
- AKCELIK, V. et al., High resolution forward and inverse earthquake modeling on terascale computers. In Proceedings of SC2003 (Supercomputing Conference 2003), ACM/IEEE, 2003.
- ASCHER, O. M. - RUUTH, S. J. - WETTON, B. T. R., Implicit-explicit methods for timedependent partial differential equations, SIAM J. Numer. Anal., 32 (3) (1995), 797-823. Zbl0841.65081MR1335656
- BABUŠKA, I., Über Schwarzsche Algorithmen in partiellen Differentialgleichungen der mathematischen Physik, ZAMM, 37 (7/8) (1957), 243-245. Zbl0078.30302MR99492
- BALAY, S. - BUSCHELMAN, K. - GROPP, W. D. - KAUSHIK, D. - CURFMAN MCINNES, L. - SMITH, B. F., PETSc home page, http://www.mcs.anl.gov/petsc, 2001.
- BALAY, S. - GROPP, W. D. - CURFMAN MCINNES, L. - SMITH, B. F., PETSc users manual, Technical Report ANL-95/11 - Revision 2.1.0, Argonne National Laboratory, 2001.
- BERNARDI, C. - MADAY, Y., Spectral Methods, in Handbook of Numerical Analysis, Volume V: Techniques of Scientific Computing (Part 2), North-Holland, 1997, 209-485. MR1470226
- BHARDWAJ, M. - DAY, D. - FARHAT, C. - LEISONNE, M. - PIERSON, K. - RIXEN, D., Application of the FETI method to ASCI problems - scalability results on 1000 processors and discussion of highly heterogeneous problems, Int. J. Numer. Meth. Eng., 47 (1-3) (2000), 513-535. Zbl0970.74069
- BREZZI, F. - FORTIN, M., Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, 15. Springer, New York, 1991. Zbl0788.73002MR1115205
- CANUTO, C. - HUSSAINI, M. Y. - QUARTERONI, A. - ZANG, T. A., Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin, 1988. Zbl0717.76004MR917480
- CHAN, T. F. - MATHEW, T. P., Domain Decomposition Methods, Acta Numerica, (1994) 61-143. Zbl0809.65112MR1288096
- COLLI FRANZONE, P. - PAVARINO, L. F., A parallel solver for reaction-diffusion systems in computational electrocardiology, IMATI-CNR Tech. Rep. 9-PV, 2003, To appear in Math. Mod. Meth. Appl. Sci. Zbl1068.92024MR2069498
- COLLI FRANZONE, P. - SAVARÉ, G., Degenerate evolution systems modeling the cardiac electric field at micro and macroscopic level. In A. Lorenzi and B. Ruf, Editors, Evolution equations, Semigroups and Functional Analysis, 49-78, Birkhauser, 2002. Zbl1036.35087MR1944157
- DRYJA, M. - SMITH, B. F. - WIDLUND, O. B., Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions, SIAM J. Numer. Anal., 31 (1994), 1662-1694. Zbl0818.65114MR1302680
- DRYJA, M. - WIDLUND, O. B., Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems, Comm. Pure Appl. Math., 48 (1995), 121-155. Zbl0824.65106MR1319698
- FARHAT, C. - ROUX, F.-X., Implicit parallel processing in structural mechanics, Comput. Mech. Adv., 2 (1) (1994), 1-124. Zbl0805.73062MR1280753
- GARFINKEL, A. - KIM, Y.-H. - VOROSHILOVSKY, O. - QU, Z. - KIL, J. R. - LEE, M.-H. - KARAGUEUZIAN, H. S. - WEISS, J. N. - CHEN, P.-S., Preventing ventricular fibrillation by flattening cardiac restitution, Proc. Nat. Acad. Sci. USA, 97 (11) (2000), 6061-6066.
- GOLDFELD, P. - PAVARINO, L. F. - WIDLUND, O. B., Balancing Neumann-Neumann Preconditioners for Mixed Approximations of Heterogeneous Problems in Linear Elasticity, Numer. Math., 95 (2) (2003), 283-324. Zbl1169.65346MR2001079
- I. HERRERA - D. KEYES - O. WIDLUND - R. YATES, Editors, Proceedings of the Fourteenth International Conference on Domain Decomposition Methods, UNAM, Mexico City, 2003. Zbl1103.65004MR2093729
- KEENER, J. - SNEYD, J., Mathematical Physiology, Springer-Verlag, 1998. Zblpre05242554MR1673204
- KEYES, D. E., Terascale implicit methods for partial differential equations. In X. Feng and T. P. Schulze, Editors, Recent Advances in Numerical Methods for Partial Differential Equations and Applications, Contemporary Mathematics, 306, AMS (2002), 29-84. Zbl1018.65121MR1940622
- R. KORNHUBER - R. H. W. HOPPE - D. E. KEYES - J. PERIAUX - O. PIRONNEAU - J. XU, Editors, Proceedings of the Fifteenth International Conference on Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering, Springer, to appear, 2004. Zbl1067.65050
- LE TALLEC, P., Domain decomposition methods in computational mechanics, Comput. Mech. Adv., 1 (2) (1994), 121-220. Zbl0802.73079MR1263805
- LIONS, P.-L., On the Schwarz alternating method. I. In First International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Glowinski et al., Editors, pp. 1-42, SIAM, Philadelphia, 1988. Zbl0658.65090MR972510
- LUO, C. - RUDY, Y., A model of the ventricular cardiac action potential: depolarization, repolarization, and their interaction, Circ. Res., 68 (6) (1991), 1501-1526.
- MANDEL, J. - BREZINA, M., Balancing domain decomposition for problems with large jumps in coefficients, Math. Comp., 65 (1996), 1387-1401. Zbl0853.65129MR1351204
- MOORE, P. K., An adaptive finite element method for parabolic differential systems: some algorithmic considerations in solving in three space dimensions, SIAM J. Sci. Comput., 21 (4) (2000), 1567-1586. Zbl0969.65090MR1756044
- PAVARINO, L. F. - WIDLUND, O. B., A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions, SIAM J. Numer. Anal., 33 (4) (1996), 1303-1335. Zbl0856.41007MR1403547
- PAVARINO, L. F., Neumann-Neumann algorithms for spectral elements in three dimensions, RAIRO M²AN, 31 (1997), pp. 471-493. Zbl0881.65121MR1457457
- L. F. PAVARINO - A. TOSELLI, Editors, Recent Developments in Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering, vol. 23, Springer-Verlag, 2002. Zbl0989.00043MR1962677
- PAVARINO, L. F. - WIDLUND, O. B., Iterative substructuring methods for spectral element discretizations of elliptic systems. II: Mixed methods for linear elasticity and Stokes flow, SIAM J. Numer. Anal., 37 (2000), 375-402. Zbl0951.65123MR1740774
- PAVARINO, L. F. - WIDLUND, O. B., Balancing Neumann-Neumann methods for incompressible Stokes equations, Comm. Pure Appl. Math., 55 (3) (2002), 302-335. Zbl1024.76025MR1866366
- QUARTERONI, A. - VALLI, A., Numerical Approximation of Partial Differential Equations, Springer-Verlag, Berlin, 1994. Zbl1151.65339MR1299729
- QUARTERONI, A. - VALLI, A., Domain Decomposition Methods for Partial Differential Equations, Oxford Science Publications, 1999. Zbl0931.65118MR1857663
- SCHWARZ, H. A., Gesammelte Mathematische Abhandlungen, volume 2, pp. 133-143, Springer, 1890.
- SMITH, B. F. - BJøRSTAD, P. - GROPP, W. D., Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, 1996. Zbl0857.65126MR1410757
- SOBOLEV, S. L., Lalgorithme de Schwarz dans la théorie de lelasticité, Compt. Rend. Acad. Sci. URSS, IV (XIII 6) (1936), 243-246. Zbl0015.40503
- TOSELLI, A. - WIDLUND, O. B., Domain Decomposition Methods: Algorithms and Theory, Springer-Verlag, 2004. Zbl1069.65138
- TUFO, H. M. - FISCHER, P. F., Fast parallel direct solvers for coarse grid problems, J. Paral. Distr. Comput., 61 (2) (2001), 151-177. Zbl0972.68191
- WINFREE, A. T., Electrical turbulence in three-dimensional heart muscle, Science, 266 (5187) (1994), 1003-1006.
- YU, H., A local space-time adaptive scheme in solving two-dimensional parabolic problems based on domain decomposition methods, SIAM J. Sci. Comput., 23 (1) (2001), 304-322. Zbl0990.65108MR1860916
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