Journal Papers (boldface name means the corresponding author):

  1. J. Tian, M. Cai, Z. Luo, Y. You, and G. Chen, A 3D OpenFOAM based Finite Volume solver for incompressible Oldroyd-B model with infinity relaxation time. Commun. Nonlinear Sci. Numer. Simul. 78 (2019), 104876, 18 pp.
  2. L. Zhang, M. Cai and M. Mu, A multirate approach for fluid-structure interaction computation with decoupled methods, Commun. Comput. Phys., (accepted).
  3. G. Zhang and M. Cai, Normal mode analysis of 3D incompressible viscous fluid flow models, Appl. Anal. doi.
  4. Y. Zeng, M. Cai and F. Wang, An H(div)-conforming finite element method for Biot’s consolidation model, East Asian J. Appl. Math. , Vol. 9, No. 3, 2019, pp. 558-579. doi.
  5. M. Cai and G. Zhang, Comparisons of some iterative algorithms for Biot equations, (a special issue "Differential Equations, Almost Periodicity, and Almost Automorphy”, dedicated to the memory of Prof. V.V. Zhikov.). Int. J. Evol. Equ., Vol. 10, No. 3-4, 2017, pp. 267–282. doi.
  6. M. Cai, P. Huang, and M. Mu, Some multilevel decoupled algorithms for a mixed Navier-Stokes/Darcy model. Adv. Comput. Math. 44 (2018), no. 1, 115–145. doi.
  7. F. Qin, J. Chen, Z. Li and M. Cai. A Cartesian grid nonconforming immersed finite element method for planar elasticity interface problems. Comput. Math. Appl., 73, no.3, 2017, pp. 404-418. doi.
  8. P. Huang, J. Chen and M. Cai. A mortar method using nonconforming and mixed finite elements for the coupled Stokes-Darcy model. Adv. Appl. Math. Mech., 9(3), 2017, pp. 596-620. doi
  9. M. Cai and L. Pavarino, Hybrid and multiplicative overlapping Schwarz algorithms with standard coarse space for mixed linear elasticity and Stokes problems. Commun. Comput. Phys., 20(4), 2016, pp. 989-1015.doi
  10. P. Huang, M. Cai and F. Wang, A Newton type linearization based two grid method for coupling fluid flow with porous media flow，Appl. Numer. Math., 106, 2016, pp. 182-198. doi.
  11. M. Cai, L. Pavarino and O. Widlund, Overlapping Schwarz methods with a standard coarse space for almost incompressible linear elasticity. SIAM J. Sci. Comput., 37(2), pp. A811-A831.doi
  12. M. Cai, Analysis of some projection method based preconditioners for models of incompressible flow, Appl. Numer. Math., 90, 2015, pp. 77-90.doi
  13. M. Cai, A. Nonaka, B. Griffith, J. Bell and A. Donev, Efficient variable-coefficient finite volume Stokes solvers, Commmun. Comput. Phys., 16 no. 5, 2014, pp. 1263-1297.doi
  14. H. Liu, M. Cai, C. Yang, D. Tang, J. Zheng, R. Bach, M. Kural, K. Billiar, D. Muccigrosso, D. Lu, D. Tang, IVUS-based computational modeling and planar biaxial artery material properties for human coronary plaque vulnerability assessment, (Mol Cell Biomech. 2012 Mar;9(1) pp.77-93.) doi
  15. P. Huang, J. Chen and M. Cai, A mixed and nonconforming FEM with nonmatching meshes for a coupled Stokes-Darcy model, (J. Sci. Comput. 53 (2012), no. 2, pp. 377–394.) doi
  16. M. Kural, M. Cai, D. Tang, T. Gwyther, J. Zheng and K. Billiar, Planar biaxial characterization of diseased humen coronary and carotid arteries for computational modeling, J. of Biomechanics, Vol. 45, Iss. 5, pp. 790–798 doi
  17. M. Cai and M. Mu, A multilevel decoupled method for a mixed Stokes/Darcy model, (J. Comput. Appl. Math., 236 (2012), no. 9, pp. 2452–2465.) doi
  18. M. Cai, M. Mu and J. Xu, Numerical solution to a mixed Navier-Stokes/Darcy model by the two-grid approach, SIAM J. Numer. Anal., Vol. 47 (2009), pp. 3325-3338. doi (Top 20 Most Read Articles, Oct. 2009 - Jan. 2010)
  19. M. Cai, M. Mu and J. Xu, Preconditioning techniques for a mixed Stokes/Darcy model in porous media applications, J. Comput. Appl. Math., Vol. 233 (2009), pp. 346-355. doi
  20. M. Cai, X. Jin and Y. Wei, A generalization of T. Chan's preconditioner, Lin. Alg. Appl., Vol. 407 (2005), pp. 11-18. doi
  21. M. Cai and X. Jin, BCCB preconditioners for solving linear systems from delay differential equations, Comput. Math. Appl. Vol. 50 (2005), pp. 281-288. doi
  22. M. Cai and X. Jin, A note on T. Chan's precondtioner, Lin. Alg. Appl., Vol. 376 (2004), pp. 283-290. doi

Book Chapters:

  1. M. Cai, Decoupled algorithms for the coupled surface/subsurface flow interaction problems, E-Book Series Progress in Computational Physics (PiCP), Volume 2. doi

Thesis Works:

  1. Modeling and numerical simulation for the coupling of surface flow with subsurface flow, M. Cai, Ph. D. thesis. doi
  2. Some properties of T. Chan's preconditioner and applications in numerical differential equations, M. Cai, Master thesis. doi

Selected Conference Papers, Tech. Reports, Proceedings, and Posters:

  1. M. Cai, C. Yang, M. H. Kural, R. Bach, D. Muccigrosso, D. Yang, J. Zheng, C. L. Billiar and D. Tang, Intravascular ultrasound (IVUS)-based computational modeling and planar biaxial artery material properties for human coronary plaque vulnerability assessment, conference paper, International Conference on Computational and Experimental Engineering and Sciences. ICCES, vol.19, no.4, pp.97-104, 2011. doi
  2. M. Cai, C. Yang, P. Yu, B. Nguyen, M. Tao, C. K. Ozaki and D. Tang, Intimal hyperplasia and total vessel thickness correlate positively with flow shear stress in a murine vein graft model with advanced focal stenosis, ATVB 2011 Poster.
  3. M. Cai and S. Turek, Numerical studies of time dependent Ginzburg-Landau model by FEM with moving grid deformation, (Tech. Report. Techn. Univ., Fak. fur Mathematik, 2010.)