Publications of Marcus Sarkis

61. Clemens Pechstein, Marcus Sarkis and Robert Scheichl, New theoretical coefficient robustness results for FETI-DP. 2011. Submitted.

60. Etereldes Goncalves and Marcus Sarkis. Robust parameter-free multilevel methods for Neumann boundary control problems. 2011. Submitted.

59. Jung-Han Kimn and Marcus Sarkis. Shifted Laplacian RAS solvers for the Helmholtz equation. 2011. Submitted.

58. Juan Galvis and Marcus Sarkis. Regularity results for the ordinary product stochastic pressure equation. 2011. Submitted.

57. Maksymilian Dryja and Marcus Sarkis. FETI-DP method for DG discretization of elliptic problems with discontinuous coefficients. 2010, In review.

56. Maksymilian Dryja, Juan Galvis and Marcus Sarkis. Neumann-Neumann methods for a DG discretization of elliptic problems with discontinuous coefficients on geometrically nonconforming substructures . Numerical Methods for Partial Differential Equations, 2011. To appear.

55. Juan Galvis and Marcus Sarkis. FETI-DP for Stokes-Mortar-Darcy Systems. In Domain Decomposition Methods in Science and Engineering XIX, Huang, Y.; Kornhuber, R.; Widlund, O.; Xu, J. (Eds.), Volume 78 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2011, pp.221-228. File.pdf . Bibtex

54. Maksymilian Dryja and Marcus Sarkis. Boundary Layer Technical Tools for FETI-DP Methods to Heterogeneous Coefficients. In Domain Decomposition Methods in Science and Engineering XIX, Huang, Y.; Kornhuber, R.; Widlund, O.; Xu, J. (Eds.), Volume 78 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2011, pp.205-212. File.pdf . Bibtex

53. Maksymilian Dryja, Juan Galvis and Marcus Sarkis. N-N Solvers for a DG Discretization for Geometrically Nonconforming Substructures and Discontinuous Coefficients. In Domain Decomposition Methods in Science and Engineering XIX, Huang, Y.; Kornhuber, R.; Widlund, O.; Xu, J. (Eds.), Volume 78 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2011, pp.27-38. File.pdf . Bibtex

52. Maksymilian Dryja and Marcus Sarkis. Additive average {S}chwarz methods for discretization of elliptic problems with highly discontinuous coefficients. Computational Methods in Applied Mathematics, Vol 10 (2), pp. 164-176, 2010. File.pdf . Bibtex

51. Tarek B. Mathew, Marcus Sarkis and Christian Schaerer. Analysis of block parareal preconditioners for parabolic control problems. SIAM J. Sci. Comput., 32 (3), pp. 1180-1200, 2010. File.pdf . Bibtex

50. Juan Galvis and Marcus Sarkis. FETI and BDD methods for mortar coupling of Stokes-Mortar-Darcy Systems. Commun. Appl. Math. Comput. Sci., Vol. 5(1), pp. 1-30, 2010. File.pdf . Bibtex

49. Juan Galvis and Marcus Sarkis. Approximating infinity-dimensional stochastic Darcy's equations without uniform ellipticity. SIAM J. Numer. Anal. Vol., 47(5), pp. 3624-3651, 2009. File.pdf . Bibtex

48. Tarek P. Mathew, Marcus Sarkis and Christian E. Schaerer. Block diagonal parareal preconditioner for parabolic optimal control problems. In Domain Decomposition Methods in Science and Engineering XVII, Ulrich Langer et al. (eds.), vol. 60 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2008, pp 409-416. File.pdf . Bibtex

47. Maksymilian Dryja, Juan Galvis and Marcus Sarkis. Balancing domain decomposition methods for discontinuous Galerkin discretization. In Domain Decomposition Methods in Science and Engineering XVII, Ulrich Langer et al. (eds.), vol. 60 of Lecture Notes in Computational Science and Engineering,Springer-Verlag, 2008, pp 271-278. File.pdf . Bibtex

46. Etereldes Gon{\c{c}}alves, Tarek P. Mathew, Marcus Sarkis and Christian E. Schaerer. A Robust preconditioner for the Hessian system in elliptic optimal control problems. In Domain Decomposition Methods in Science and Engineering XVII, Ulrich Langer et al. (eds.), vol. 60 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2008, pp. 527-534.. File.pdf . Bibtex

45. Juan Galvis and Marcus Sarkis. Non-matching mortar discretization analysis for the coupling Stokes-Darcy equations. Electron. Trans. Numer. Anal., Vol.26 (2007) pp.373-380. File.pdf . Bibtex

44. Marcus Sarkis and Henrique Versieux. Convergence analysis for the numerical boundary corrector for elliptic equations with rapidly oscilating coefficients. SIAM J. Numer. Anal., 46(2). 2008, pp. 545-576. File.pdf . Bibtex

43. Christopher Larsen, Casey Richardson and Marcus Sarkis. A level set method for the Mumford-Shah functional and fracture. Technical Report Serie A 581, Instituto de Matematica Pura e Aplicada, Brazil, January 2008. File.pdf . Bibtex

42. Maksymilian Dryja, Juan Galvis and Marcus Sarkis. BDDC methods for discontinuous Galerkin discretization of elliptic problems. Journal of Complexity, Vol. 23 (2007) 715-739. File.pdf . Bibtex

41.. Duilio Conceicao, Paulo Goldfeld and Marcus Sarkis. Robust two-level lower-order preconditioners for a higher-order Stokes discretization with highly discontinuous viscosities. High Performance Computing for Computational Sciences-VECPAR2006, Lecture Notes in Computer Sciences, Volume 4395, 2007, pp. 319-333, Springer. File.pdf . Bibtex

40. Marcus Sarkis and Daniel Szyld. Domain Decomposition for Nonsymmetric and Indefinite Linear Systems. Mesh Partitioning Techniques and Domain Decomposition Methods, Ed. F. Magoules, Saxe-Coburg Publications, 2007, pp. 165--188. book.htm

39. Christian E. Schearer, Tarek Mathew and Marcus Sarkis. Temporal domain decomposition for a linear quadratic optimal control problems. High Performance Computing for Computational Sciences-VECPAR2006, Lecture Notes in Computer Sciences, volume 4395, 2007, pp. 452-465, Springer. File.pdf . Bibtex

38. Leopoldo P. Franca, Saulo P. Oliveira and Marcus Sarkis. Continuous Q1-Q1 Stokes elements stabilized with non-conforming null edge average velocity functions. Mathematical Models and Methods in Applied Sciences (M3AS), vol. 17(3) (2007) pp 439-459. File.pdf . Bibtex

37. Tarek P. Mathew, Marcus Sarkis and Christian E. Schaerer. Analysis of block matrix preconditioners for elliptic optimal control problem. Numerical Linear Algebra with Applications, vol. 14(3) (2007). File.pdf . Bibtex

36. Marcus Sarkis and and Daniel B. Szyld. Optimal left and right additive Schwarz preconditioning for minimal residual methods with Euclidean and energy norms. Computer Methods in Applied Mechanics and Engineering, vol. 196 (2007) pp. 1612-1621. File.pdf . Bibtex

35. Jung-Han Kimn and Marcus Sarkis. Restricted overlapping balancing domain decomposition and restricted coarse problem for the Helmholtz equation. , Computer Methods in Applied Mechanics and Engineering, vol. 196 (2007) pp. 1507-1514. File.pdf . Bibtex

34. Christian E. Schaerer, Marcus Sarkis, Dan Marchesin and Pavel Bedrikovetsky. Permeability hysteresis in gravity counterflow segregation. SIAM J. Appl. Math., vol. 66(2), 2006, pp. 1512-1532. File.pdf . Bibtex

33. Luis Roman and Marcus Sarkis. Stochastic Galerkin method for elliptic SPDEs: A white noise approach. DCDS-B, vol. 6(4), 2006, pp. 941-955. File.pdf . Bibtex

32. Henrique Versieux and Marcus Sarkis. Numerical boundary corrector for elliptic equations. Commun. Numer. Methods in Engrg., vol. 22(7), 2006, pp. 577-589. File.pdf . Bibtex

31. Juan Galvis and and Marcus Sarkis. Balancing domain decomposition methods for mortar coupling Stokes-Darcy system. Domain Decomposition Methods in Science and Engineering XVI, Olof Widlund and David Keyes (eds.), Lecture Notes in Computational Science and Engineering, vol. 55, Springer, 2006, pp. 373-380. File.pdf . Bibtex

30. Henrique Versieux and and Marcus Sarkis. A three-scale finite element method for elliptic equations with rapidly oscillating periodic coefficient. Domain Decomposition Methods in Science and Engineering XVI, Olof Widlund and David Keyes (eds.), Lecture Notes in Computational Science and Engineering, vol. 55, Springer, 2006, pp. 763-770. File.pdf . Bibtex

29. Jung-Han Kimn and Marcus Sarkis. OBDD: overlapping balancing domain decomposition methods and generalizations to Helmholtz equations. Domain Decomposition Methods in Science and Engineering XVI, Olof Widlund and David Keyes (eds.), Lecture Notes in Computational Science and Engineering, vol. 55, Springer, 2006, pp. 317-324. File.pdf . Bibtex

28. Marcus Sarkis and and Daniel B. Szyld. A Proposal for a dynamically adapted inexact additive Schwarz preconditioner. Domain Decomposition Methods in Science and Engineering XVI>, Olof Widlund and David Keyes (eds.), Lecture Notes in Computational Science and Engineering, vol. 55, Springer, 2006, pp. 333-337. File.pdf . Bibtex

27. Xiao-Chuan Cai, Maksymilian Dryja and Marcus Sarkis. Restricted additive Schwarz preconditioner with harmonic overlap for symmetric positive definite linear systems. SIAM J. Numer. Anal., 41(4), 2003, pp. 1209-1231. File.pdf. Bibtex

26. Marcus Sarkis and Xuemin Tu. Singular function mortar finite element methods. Comput. Methods. Appl. Math., 3(1), 2003, pp. 202-218. File.pdf. Bibtex

25. Marcus Sarkis. Domain decomposition methods: Schwarz methods. Applied mathematics and scientific computing (Dubrovnik, 2001), Kluwer/Plenum, New York, 2003, pp. 3--29. Bibtex

24. Xuemin Tu and Marcus Sarkis. Singular function enhanced mortar finite element methods. Domain decomposition methods in science and engineering, Natl. Auton. Univ. Mex., Mexico, 2003, pp. 475--482. Bibtex

23. Marcus Sarkis. Partition of unity coarse spaces: enhanced versions, discontinuous coefficients and applications to elasticity. Domain decomposition methods in science and engineering, Natl. Auton. Univ. Mex., Mexico, 2003, pp. 149-158. File.pdf . Bibtex

22. Xiao-Chuan Cai, Maksymilian Dryja and Marcus Sarkis. RASHO: A restricted additive Schwarz preconditioner with harmonic overlap. Domain decomposition methods in science and engineering (Lyon, 2000), Theory Eng. Appl. Comput. Methods, Internat. Center Numer. Methods Eng. (CIMNE), Barcelona, 2002, pp. 337-344. File.pdf . Bibtex

21. Marcus Sarkis. A coarse space for elasticity: partition of unity rigid body motions coarse space. Applied Mathematics and Scientific Computing (Dubrovnik, 2001), Kluwer/Plenum, New York, 2003, pp 261-273. File.pdf . Bibtex

20. Marcus Sarkis. Partition of unity coarse spaces and Schwarz methods with harmonic overlap. Lect. Notes Comput. Sci. Eng. (Zurich, 2001), Springer-Verlag, Vol. 23, 2002, pp. 75-92. File.pdf . Bibtex

19. Marcus Sarkis. Partition of unity coarse spaces. Contemp. Math. (Holyoke, 2001), Vol. 295, Amer. Math. Soc., Providence, RI, 2002, pp. 445-456. File.pdf . Bibtex

18. Michel Lesoinne, Marcus Sarkis, Ulrich Hetmaniu and Charbel Farhat. A linearized method for the frequency analysis of three-dimensional fluid/structure interaction problems in all flow regimes. Computer Methods in Applied Mechanics and Engineering, vol. 190, 2001, pp. 3121-3146. File.pdf . Bibtex

17. Marcus Sarkis and Bruno Koobus. A scaled and minimum overlap restricted additive Schwarz method with application on aerodynamics. Computer Methods in Applied Mechanics and Engineering, vol. 184, 2000, pp. 391-400. File.pdf . Bibtex

16. Xiao-Chuan Cai, Tarek Mathew and Marcus Sarkis. Maximum norm analysis of overlapping non-matching grid discretizations of elliptic equations. SIAM J. Numer. Anal., 37 (5), 2000, pp. 1709-1728. File.pdf . Bibtex

15. Xiao-Chuan Cai and Marcus Sarkis. A restricted additive Schwarz preconditioner for general sparse linear systems. SIAM J. Sci. Comput., 21 (2), 1999, pp. 792-797. File.pdf . Bibtex

14. Xiao-Chuan Cai, Marius Paraschivoiu and Marcus Sarkis. An explicit multi-model compressible flow formulation based on the full potential equation and the Euler Equations on 3D unstructured meshes. Eleventh International Conference on Domain Decomposition Methods (London, 1998), 1999, pp. 159-177. File.pdf , Bibtex

13. Xiao-Chuan Cai, Maksymilian Dryja and Marcus Sarkis. Overlapping nonmatching grid mortar element methods for elliptic problems. SIAM J. Numer. Anal., 36(2). 1999, pp. 581-606. File.pdf . Bibtex

12. Xiao-Chuan Cai, David Keyes, Marius Paraschivoiu, Marcus Sarkis and David Young. Multi-domain multi-model formulation for compressible flows: Conservative interface coupling and parallel implicit solvers for 3D unstructured applications in 3D flow simulations. Proceedings of the 37th AIAA Aerospace Sciences Meeting and Exhibit , AIAA Paper 99-0784, 1999. File.pdf . Bibtex

11. Xiao-Chuan Cai, Charbel Farhat and Marcus Sarkis. A minimum overlap restricted additive Schwarz preconditioner and applications in 3D flow simulations. Contemp. Math. (Boulder, CO, 1997) , Vol. 218, Amer. Math. Soc., Providence, RI, 1998, pp. 479-485. File.pdf . Bibtex

10. Xiao-Chuan Cai and Marcus Sarkis. Local multiplicative Schwarz algorithms for steady and unsteady convection-diffusion equations. East-West J. Numer. Math. , 6(1), 1998, pp. 27-41. File.pdf . Bibtex

9. Xiao-Chuan Cai, Maksymilian Dryja and Marcus Sarkis. Error analysis of overlapping mortar element methods for elliptic problems. Proceedings of the Third IMACS International Symposium on Iterative Methods in Scientific Computation, Wyoming, IMACS Series in Computational and Applied Mathematics, Vol. 4, 1997, pp. 205-210.

8. Marcus Sarkis. Nonstandard coarse spaces and Schwarz methods for elliptic problems with discontinuous coefficients using non-conforming elements. Numer. Math., 77(3), 1997, pp. 383-406. File.pdf. Bibtex

7. Xiao-Chuan Cai, Charbel Farhat and Marcus Sarkis. Variable degree Schwarz methods for the unsteady compressible flows. Domain Decomposition Methods in Science and Engineering , P. Bjorstad and D. Keyes, John Wiley & Sons, Ltd., pp. 682-689, 1996. File.pdf . Bibtex

6. Xiao-Chuan Cai, Charbel Farhat and Marcus Sarkis. Variable degree Schwarz methods for the implicit solution of unsteady compressible Navier--Stokes equations on two-dimensional unstructured meshes. ICASE Report No. 96-48, NASA Langley Research Center, 1996. File.pdf. Bibtex

5. Xiao-Chuan Cai, Charbel Farhat and Marcus Sarkis. Schwarz methods for the unsteady comppressible Navier-Stokes equations on unstructured meshes. Domain Decomposition Methods in Science and Engineering , R. Glowinski, J. Periaux, Z. Shi and O. Widlund, eds, John Wiley & Sons, Ltd. 1996. . File.pdf . Bibtex

4. Maksymilian Dryja, Marcus Sarkis and Olof Widlund. Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions. Numer. Math., 72(3), 1996, pp. 313-348. File.pdf. Bibtex

3. Marcus Sarkis. Schwarz preconditioners for elliptic problems with discontinuous coefficients using conforming and non-conforming elements. PhD Dissertation, Technical Report 671, Courant Institute, September 1994. File.pdf. Bibtex

2. Marcus Sarkis. Multilevel methods for $P_1$ nonconforming finite elements and discontinuous coefficients in three dimensions. Decomposition Methods in Scientific and Engineering (Univesity Park, PA, 1993), Contemp. Math. , Vol. 180, Amer. Math. Soc., Providence, RI, 1994, pp. 119-124. File.pdf . Bibtex

1. Marcus Sarkis. Two-level Schwarz methods for $P_1$ nonconforming finite elements and discontinuous coefficients. Proceedings of the Sixth Copper Mountain Conference on Multigrid Methods, Number 3224, Part 2, pages 543-566, Hampton VA, 1993. NASA. File.pdf. Bibtex