1. Y. Efendiev, Hardness of the elastic medium when a solid is turned in it , V-Mosk-Mekh (6),   pp. 76-78 (1994) 
  2.  A. Yu. Beliaev and Y. Efendiev, Homogenization of the Stokes equations with random potential,   Math. Notes, v59 (3-4),   pp. 361-372 (1996) 
  3. Y. Efendiev, T. Hou, X. Wu, Convergence of a nonconformal multiscale finite element method,  SIAM in J. Num. Anal. 37, 888-910 (2000) 
  4.  Y. Efendiev and X.H. Wu, Multiscale finite element methods for the problems with highly oscillatory coefficients,    Numerische  Math., vol.90(3), 2002 
  5.  Y. Efendiev and M. Luskin, Stability of microstructures for some martensitic transformations, Mathematical and Computer Modelling, v.34 (2001), pp. 1289-1305 
  6. Y. Efendiev and M. R. Zachariah,  A model for two component aerosol coagulation and phase separation: A method for changing the growth of nanoparticles,  Chemical Engineering Science. 56, 5763 ( 2001) 
  7.  Y. Efendiev, L. Durlofsky, and S. Lee, Modeling of subgrid effects in coarse-scale simulations of transport in heterogeneous porous media,  Water Resources Research, 36(8),2000, 2031-2041
  8.  Efendiev and L. Durlofsky, Numerical Modeling of Subgrid Heterogeneity in Two Phase Flow Simulations,  Water. Resour. Res.,  38(8), 1128, 2002
  9. Y. Efendiev and M.R. Zachariah, Hybrid Monte-Carlo method for simulation of two-component aerosol coagulation and phase segregation,  J. Colloid and Interface Science 249(1),  30-43 (2002)
  10. Y. Efendiev, H. Struchtrup, M. Luskin, M. R. Zachariah, A hybrid sectional-moment model for coagulation and phase segregation inbinary liquid nanodroplets,  J. Nanoparticle Research 4, 61-72 (2002)
  11. Y. Efendiev and M. Zachariah,  Hierarchical hybrid Monte-Carlo method for simulation of two-component aerosol nucleation, coagulation and phase segregation,  J. Aerosol Sci.  34 (2003),  169-188
  12. X.H. Wu, Y. Efendiev, T. Hou, Analysis of upscaling absolute permeability,   Discrete and Continuous Dynamical Systems - Series B, Vol. 2(2), 2002, pp. 185-204
  13. Y. Efendiev and L. Durlofsky,  A generalized convection-diffusion model for subgrid transport in porous media,  SIAM MMS, vol.1(3), pp.504-526
  14.  Y. Efendiev and A. Pankov, Numerical homogenization of monotone operators,  SIAM MMS, vol.2 (1), pp.,62-79, 2004
  15. Y. Efendiev and A. Pankov, Numerical homogenization of nonlinear random parabolic operators,   SIAM MMS 2(2), 2004, pp.237-268
  16. Y. Efendiev and L. Durlofsky, Accurate subgrid models for two phase flow in heterogeneous reservoirs,  SPE Journal, 9,  219-226 , 2004
  17. Y. Efendiev and A. Pankov, Numerical homogenization and correctors for random nonlinear elliptic equations, SIAM J. Applied Math., 65 (1),  43-68
  18. Y. Efendiev, "Mathematical Modeling and Simulation of multi-component aerosol coagulation", Journal of Computational and Applied Mathematics, vol. 23, 2-3, pp. 401-423, 2004
  19. Y. Efendiev, A. Datta-Gupta, I. Osako, and B. Mallick, Multiscale data integration using coarse-scale models,  Advances in Water Resources, 28 (3), pp. 3-3-314, 2004
  20. V. Ginting, R. Ewing, Y. Efendiev and  R. Lazarov, Upscaled Modeling in Multiphase Flow Applications,  Journal of Computational and Applied Mathematics. vol. 23, 2-3, pp.213-233,  2004 
  21. Y. Efendiev, T. Hou and V. Ginting, Multiscale finite element methods for nonlinear partial differential equations,  Comm. Math. Sci., 2(4), 2004
  22. Y. Efendiev and A. Pankov,  On homogenization of  almost periodic nonlinear parabolic operators,  International Journal of Evolution Equations, volume 1 (3), 2005
  23. Y. Efendiev and B. Popov,   "On homogenization of nonlinear hyperbolic equations", to appear in  Communications on Pure and Applied Analysis,  4(2), 2005, pp. 295-309
  24. Y. Efendiev and A. Pankov,  Homogenization of nonlinear random parabolic operators,   Advances in  Differential Equations, vol. 10,Number 11, 2005, pp., 1235-1260
  25. Y. Efendiev and A. Pankov, "Meyers type estimates for nonlinear elliptic equations and their applications", Discrete and Continuous Dynamical Systems - B, vol. 6, number 3, 2006, pp. 481-492
  26.  Efendiev, A. Datta-Gupta, V. Ginting, X. Ma and B. Mallick, An efficient two-stage Markov chain Monte Carlo methods  for dynamic data integration, Water Resources  Research , 41, W12423, doi:=10.1029/2004WR003764
  27.  J. Eberhard, Y. Efendiev, R. Ewing, A. Cunningham, Coupled cellular models for biofilm growth and hydrodynamic flow in a pipe, International Journal of Multiscale Engineering,    vol. 3, issue 4, 2005, pp. 499-516
  28. Y. Efendiev, T. Hou, and W. Luo, "Preconditioning of MCMC simulations using coarse-scale models", SIAM. Sci. Comp. 28(2), pp. 776-803
  29.  Y. Efendiev, V. Ginting, T. Hou and R. Ewing, "Accurate multiscale finite element methods for two-phase flow simulations",  J. Comp. Physics, 220 (1), pp. 155-174, 2006
  30.  P. Dostert, Y. Efendiev, T. Hou and W. Luo, Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification, Journal of Computational Physics, 217(1), pp.123-142
  31.  L. Durlofsky, Y. Efendiev, V. Ginting, An adaptive local-global multiscale finite volume element method for two-phase flow simulations, Advances in Water Resources, 30 (2007) pp.576-588
  32.  J. Santos, Y. Efendiev,  L. Guarracino,     Hydraulic Conductivity estimation in variable saturated soils using the adjoint method,  Computer Methods in Applied Mechanics and Engineering, 196  (2006), no. 1-3, 161--179
  33.   J. Aarnes and Y. Efendiev,  An adaptive multiscale method for simulation of fluid flow in heterogeneous porous media,   SIAM MMS, Vol.5 (30), pp. 918-939
  34. Y. Efendiev, L. Jiang, and A.  Pankov, Individual homogenization of nonlinear parabolic operators, Applicable Analysis Vol. 85, No. 12, 2006, 1433-1457
  35.  Y. Efendiev and T. Hou,  Multiscale finite element methods for porous media flows and their applications, Applied Numerical Mathematics, 57 (2007), pp. 577-596
  36. C. Douglas, Y. Efendiev, R. Ewing, V. Ginting, R. Lazarov, Dynamic data driven simulations in stochastic environments, Computing, 77 (2006), no.4, pp. 321-333.
  37. Y. Efendiev and A. Pankov,  Meyers type estimates for approximate solutions of nonlinear parabolic equations and their applications, Journal of Numerical Mathematics, Volume 13, Number 2 / June, 2005, pp. 105-118
  38.  L. Jiang, Y. Efendiev,  V. Ginting, Multiscale methods for parabolic equations with continuum spatial scales. Discrete Contin. Dyn. Syst. Ser. B 8 (2007), no. 4, 833--859
  39. J. E. Aarnes, V. L. Hauge, and Y. Efendiev. Coarsening of three-dimensional structured and unstructured grids for subsurface flow. Advances in Water Resources, Vol. 30, Issue 11, November 2007, pp. 2177-2193. DOI: 10.1016/j.advwatres.2007.04.007
  40.  J.E. Aarnes and Y. Efendiev. Mixed multiscale finite element for stochastic porous media flows.  SIAM Sci. Comp., Volume 30, Issue 5, pp. 2319-2339, 2008. DOI: 10.1137/07070108X.
  41.  J. E. Aarnes, Y. Efendiev, and L. Jiang. Mixed multiscale finite element methods using limited global information. Multiscale Modelling and Simulation, Volume 7, Issue 2, pp. 655-676, 2008. DOI: 10.1137/07068848
  42. J.E. Aarnes and Y. Efendiev. A multiscale method for modeling transport in porous media on unstructured corner-point grids. Journal of Algorithms and Computational Technology, Volume 2, Number 2, pp. 299-318, 2008. DOI: 10.1260/17483010878464661
  43. Ma, X., Al-Harbi, M., Datta-Gupta, A. and Efendiev, Y. “A Multistage Sampling Approach to Quantifying Uncertainty During History Matching Geological Models,” SPE Journal, 13(10) (March, 2008), 77-87.
  44.   Efendiev, Y., Datta-Gupta, A., Ma Xilian and Mallick, B, “Modified MCMC for Dynamic Data Integration Using Streamline Models,” Mathematical Geology, 2007.
  45.  P. Dostert, Y. Efendiev, and T. Hou, Multiscale finite elemenet methods for stochastic porous media flow equations and application to uncertainty quantification,   Comput. Methods Appl. Mech. Engrg. 197 (2008), no. 43-44, 3445–3455
  46. Das, N. N., B. P. Mohanty, and Y. Efendiev, Characterization of Saturated Hydraulic Conductivity in an Agricultural Field Using Karhunen-Loeve Expansion and MCMC, Water Resour. Res., under revision. 
  47. Efendiev, Y.; Hou, T.; Strinopoulos, T. Multiscale simulations of porous media flows in flow-based coordinate system. Comput. Geosci. 12 (2008), no. 3, 257–272.
  48. L. Jiang, Y. Efendiev, V. Ginting, Analysis of global multiscale finite element methods for wave equations with continuum spatial scales, Applied Numerical Mathematics, 60 (2010), 862--876
  49.  Das, N. N., B. P. Mohanty, and Y. Efendiev, A New Multiscale Data Assimilation Algorithm to Downscale Satellite-Based Soil Moisture Data, Water Resour. Res., Submitted.
  50.  Y. Efendiev, A. Datta-Gupta, X. Ma, B. Mallick, An Efficient Two-Stage Markov Chain Monte Carlo Method for Dynamic Data Integration, Water Resources Research, 41, W12423, 10.1029/2004WR003764, Dec. 2005.    
  51. Y. Efendiev,  L. Jiang,  and I. Mishev,  Mixed Multiscale Finite Element Methods Using Approximate Global Information Based on Partial Upscaling, Comp. Geo.14 (2010), 319--341
  52. Ewing, Richard; Efendiev, Yalchin; Ginting, Victor; Wang, Hong Upscaling of transport equations for multiphase and multicomponent flows. Domain decomposition methods in science and engineering XVII, 193–200, Lect. Notes Comput. Sci. Eng., 60, Springer, Berlin, 2008
  53. E. Chung and Y. Efendiev, Some multiscale methods for elliptic equations in high-contrast heterogeneous media, SIAM MMS , 8, 2010, pp. 1126-1153
  54. P. Popov, Y. Efendiev, Y. Gorb, Multiscale Modeling and Simulation of Fuid Flows in Highly Deformable Porous Media, Proceeding of 7-th Conference on Large-Scale Scientific Computing, Sozopol, Bulgaria, Eds. Lirkov, I., and Margenov, S., and Wasniewski, J., pp. 148-156, 2010
  55.  Mondal, A.; Efendiev, Y.; Mallick, B.; and Datta-Gupta, A. Bayesian Uncertainty Quantification for Flows in Heterogeneous Porous Media Using Reversible Jump Markov Chain Monte Carlo Methods, Advances in Water Resources, 33(3), pg., 241-256
  56. Y. Efendiev, J. Galvis, R. Lazarov, S. Margenov and J. Ren, Multiscale domain decomposition preconditioners for anisotropic high-contrast problemsEfendiev, Yalchin; Xiu, Dongbin Preface [Special issue—Mathematical and computational aspects of multi-scale problems]. J. Algorithms Comput. Technol. 2 (2008), no. 2, i, 65-06
  57.  P. Popov, G. Qin, L. Bi, Y. Efendiev, Z. Kang, and J. Li, Multiphysics and Multiscale Methods for Modeling Fluid Flow Through Naturally Fractured Carbonate Karst Reservoirs, SPE Reservoir Evaluation & Engineering, 12(2):218--231, 2009.
  58.  P. Popov, Y. Efendiev, G. Qin, Multiscale Modeling and Simulations of Flows in Naturally Fractured Karst Reservoirs , Communications in Computational Physics, 6: 162-184, 2009.
  59.  P. Popov, Y. Efendiev, Y. Gorb, Multiscale finite element methods for  fluid-structure interaction problem, submitted to SIAM MMS
  60.  Y. Efendiev, J. Galvis,  and Wu, X.  Multiscale finite element methods for high-contrast problems using local spectral basis functions, Journal of Computational Physics doi:10.1016/j.jcp.2010.09.026
  61.  L. Bi,  G. Qin, P. Popov, Y. Efendiev, M. Espedal, An Efficient Upscaling Process Based on a Unified Fine-scale Multi-Physics Model for Flow Simulation in Naturally Fracture Carbonate Karst Reservoirs, 
  62. Achi Brandt, Yalchin Efendiev and Oleg Iliev, Numerical Upscaling for Flow Problems: Theory and Applications. Abstracts from the mini-workshop held March 1–7, 2009. Oberwolfach Reports. Vol. 6, no. 1. Oberwolfach Rep. 6 (2009), no. 1, 681–723,
  63. Y. Efendiev and J. Galvis,  Enriching coarse spaces with local multiscale basis functions for high-contrast flow problems. Robust domain decomposition preconditioners and multiscale finite element methods, DD19 Proceeding, 2009
  64.  Y.  Efendiev, J. Galvis, and P. Vassilievski, Spectral element agglomerate algebraic multigrid methods for elliptic problems with high-contrast coefficients, DD19 Proceeding, 2009.
  65.  J. Galvis and Y. Efendiev, Domain decomposition  preconditioners for multiscale flows in high-contrast media:, SIAM MMS, Volume 8, Issue 4, pp. 1461-1483 (2010)
  66.  S. Akella, Y. Efendiev,  and A. Datta-Gupta, Ensemble Kalman Filter with Coarse-scale Constraints,  International Journal for Uncertainty Quantification, Issue 1 (1), 2010, pp. 49-76
  67.  J. Galvis and Y. Efendiev, Domain decomposition  preconditioners for multiscale flows in high-contrast media: Reduced dimension coarse spaces, SIAM MMS, Volume 8, Issue 5, pp. 1621-1644 (2010)
  68. E. Chung, Y. Efendiev, R. Gibson, An energy-conserving discontinuous multiscale finite element method for wave equation in heterogeneous media, Advances in Adaptive Data Analysis, 3(2011), pp. 251-268
  69. Y. Efendiev and L. Truskinovsky, Thermalization of a driven bi-stable FPU chain,  Continuum Mech. Thermodyn. (2010), 22:679-698
  70. Y. Efendiev and J. Galvis, Coarse-Grid Multiscale Model Reduction Techniques for Flows in HeterogeneousMedia and Applications, Numerical Analysis of Multiscale Problems, Eds: I.G. Graham, T.Y.-Hou, O. Lakkis and R. Scheichl, Springer LNCSE 83, September 2011, ISBN 978-3-642-22060-9
  71. Y. Efendiev, J. Galvis, S. Ki Kang and R. Lazarov, Robust multiscale domain decomposition method for nonlinear flows in highly heterogeneous media. Numerical Mathematics: Theory , Methods and Applications. To appear.
  72. Y. Efendiev, J. Galvis, R. Lazarov and J. Willems, Robust Solvers for Symmetric Positive Definite Operators and Weighted Poincare´ Inequalities. Large-Scale Scientific Computing: 8th International Conference, LSSC 2011, Sozopol, Bulgaria
  73. V. Calo, Y. Efendiev, and J. Galvis A note on variational multiscale methods for high-contrast heterogeneous flows with rough source terms. Advances in Water Resources, 34 (9), September 2011, pp. 1177-1185.
  74. D. Brown, P. Popov, Y. Efendiev, On homogenization of stokes flow in slowly varying media with applications to fluid–structure interaction, GEM- Internation Journal on Geomathematics, to appear
  75. Y. Efendiev, J. Galvis and E. Gildin, Local-global multiscale model reduction for flows in highly heterogeneous media, submitted
  76. Y. Efendiev, J. Galvis, R. Lazarov and J. Willems, Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms, ESAIM: Mathematical Modelling and Numerical Analysis September 2012 46 : pp 1175-1199
  77. Y. Efendiev, J. Galvis and F. Thomines, A systematic coarse-scale model reduction technique for parameter-dependent flows in highly heterogeneous media and its applications (RB-MsFEM), submitted
  78. J. Wei, A. Mondal, A. Datta-Gupta, Y. Efendiev, B. Mallick, Bayesian inversion for channelized reservoirs via reduced dimensional parameterization, submitted to International Journal of Uncertainty Quantification
  79. D. Brown, Y. Efendiev, V.H. Hoang, An Efficient Hierarchical Multiscale Finite Element Method for Stokes Equations in Slowly Varying Media. Submitted


BOOK

Efendiev, Yalchin; Hou, Thomas Y. Multiscale finite element methods. Theory and applications. Surveys and Tutorials in the Applied Mathematical Sciences, 4. Springer, New York, 2009. xii+234 pp. ISBN:

PROCEEDING PUBLICATIONS:


1. C. C. Douglas, M. R. Cole, Y. Efendiev, R. Ewing, V. Ginting, G. Jones, C. R. Johnson, R. Lazarov, C. Shannon, and J. Simpson, A note on dynamic data driven application simulation (DDDAS) using virtual telemetry.  Appeared in ICPACE 2003, J. Zou and X. Chi (eds.), Chinese University of Hong Kong, 2003, pp. 193-198.
      
2.  Efendiev, Y., Durlofsky, L.J.: Accurate subgrid models for two phase flow in heterogeneous reservoirs, SPE paper 79680, presented at the SPE Reservoir Simulation Symposium, Houston, Feb. 3-5 (2003)

3.  C. C. Douglas, Y. Efendiev, R. Ewing, R. Lazarov, M. R. Cole, C. R. Johnson, and G. Jones, Virtual telemetry middleware for DDDAS, in Computational Sciences - ICCS 2003, P. M. A. Sllot, D. Abramson, J. J. Dongarra, A. Y. Zomaya, and Yu. E. Gorbachev (eds.), 4 (2003), pp. 279--288

4.  C. C. Douglas, C. Shannon, Y. Efendiev, R. Ewing, V. Ginting, R. Lazarov, M. R. Cole, G.Jones, C. R. Johnson, and J. Simpson,  Telemetry-Driven Application Simulations, Computational Sciences - ICCS 2004
    
5. Craig C. Douglas, Yalchin Efendiev, Richard Ewing, Raytcho Lazarov,  Martin J. Cole, Greg Jones, Chris R. Johnson, Dynamic Data-Driven Application Simulations. Interpolation and Update,  2006 to Springer as a volume of the NATO Security Through Science¡ Series C Environmental Security. The book is  entitled  Air, Water and Soil Quality Modelling for Risk and Impact Assessment.

6.  P. Popov, L. Bi, Y. Efendiev, R. Ewing, G. Qin, J. Li, Multi-physics and Multi-scale methods for modeling fluid flows through naturally fractured vuggy carbonate reservoirs, SPE 105378, 15th SPE Middle East Oil \& Gas Show and Conference, Kingdom of Bahrain, 11-14 March, 2007

7. X. Ma, M. Al-Harbi, A. Datta-Gupta, Y. Efendiev, Multi-stage sampling method for rapid quantification of uncertainty in history matching of geological models, SPE 102476, SPE Annual Conference and Exhibition, San Antonio, 24-27 September 2007

8.  Y. Li,  Y. Efendiev, R. E. Ewing, G.Qin, X.H. Wu, An accurate Multiphase Upscaling for Flow and Transport in Heterogeneous Porous Media,  SPE 105377-PP, 15th SPE Middle East Oil & Gas Show and Conference, Kingdom of Bahrain, 11-14 March, 2007

9. Y. Wu, G. Qin, R. Ewing, Y. Efendiev, Z. Kang, Y. Ren, A Multiple-Continuum Approach for Modeling Multiphase Flow in Naturally Fractured Vuggy Petroleum Reservoirs, SPE 104173, 2006 SPE International Oil \& Gas Conference and Exhibition in China held in Beijing, China, 5-7 December 2006.

10. Efendiev, Yalchin; Hou, Thomas Y. Multiscale computations for flow and transport in heterogeneous media. Quantum transport, 169–248, Lecture Notes in Math., 1946, Springer, Berlin, 2008.