Ph.D in Mathematics, September 1998, Courant Institute of Mathematical Sciences, New York University
Thesis: Simulations of the Flow Past an Array of Circular Cylinders as a Test of the Immersed Boundary Method.
Thesis Advisor: Charles S. Peskin
M.S in Applied Math., NTHU, Taiwan
B.S in Applied Math., NCHU, Taiwan

Numerical methods for PDEs
Computational fluid mechanics

2007/08-- Chair, Department of Applied Mathematics, National Chiao Tung University
2007/08-- Director, Institute of Mathematical Modeling and Scientific Computing, National Chiao Tung University
2005/08-- Professor, Department of Applied Mathematics, National Chiao Tung University
2002/08-- 2005/07, Associate Professor, Department of Applied Mathematics, National Chiao Tung University
1999/08-- 2002/07, Assistant Professor, Department of Mathematics, National Chung Cheng University
1998/08-- 1999/07, Research Associate, Duke University

Kurt O. Friedrichs Prize for an outstanding dissertation in Mathematics, 1999
Dean's Special Recognition Award, 2003
National Science Council Outstanding Research Award, 2003-2005
National Chiao Tung University Academic Research Award, 2005

Advances in Applied Mathematics and Mechanics, 2009 -

• Fluid dynamics, Analysis and Numerics (invited speaker), Duke University, USA, June 28-30, 2010
• IAS Seminar Series on Soft Matter (SMSS'09, invited speaker, one hour talk), Hong Kong University of Science and Technology, May 25-26, 2009
• ECM2009 invited workshop, The Interface Problem and Its Applications (invited speaker, 30 mins talk), The Hong Kong Polytechnic University May 27-29, 2009
• Meiji University Global COE Program, Kick-off Forum (Guest speaker), Japan, March 2-8, 2009
• The 3rd International Conference on Scientific Computing and Partial Differential Equations (plenary speaker, 45 mins talk), Hong Kong Baptist University, December 8-13, 2008
• Analytical & Computational Fluid Dynamics (plenary speaker, two 50 mins talks), Chung-Ang University, Seoul, Korea, June 24-25, 2008
• The Fifth Conference on Frontiers in Applied and Computational Mathematics (invited speaker, 30 mins talk), New Jersey Institute of Technology, USA, May 19-21, 2008
• The 6th International Congress on Industrial and Applied Mathematics (ICIAM07), mini-symposium- Interface Methods and Applications in Multi-phase problems (invited speaker, 30 mins talk), ETH Zurich, Switzerland, 2007/07
• Workshop on Moving Interface Problems and Applications in Fluid Dynamics (invited speaker, 50 mins talk), Institute for Mathematical Sciences, short term visiting member, NUS, Singapore, 2007/02
• Workshop of NIMS on Scientific Computation and Numerical Computation for Interdisciplinary Mission (invited speaker, 50 mins talk), Daejon and Seoul, Korea, 2006/08

Publications

(A) Refereed Papers:

1. M.-C. Lai and C. S. Peskin, An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, Journal of Computational Physics, 160, 705-719 (2000).
2. M.-C. Lai and Z. Li, A remark on jump conditions for the three-dimensional Navier-Stokes equations involving an immersed moving membrane , Applied Mathematics Letters 14, vol 2 , 149-154, (2001).
3. J. T. Beale and M.-C. Lai, A method for computing nearly singular integrals , SIAM J. on Numerical Analysis, vol 38, No 6, 1902-1925, (2001).
4. M.-C. Lai, A note on finite difference discretizations for Poisson equation on a disk , Numerical Methods for Partial Differential Equations, vol 17, issue 3, 199-203, (2001).
5. Z. Li and M.-C. Lai, The immersed interface method for the Navier-Stokes equations with singular forces , Journal of Computational Physics, vol 171, No 2, 822-842, (2001).
6. M.-C. Lai and W.-C. Wang, Fast direct solvers for Poisson equation on 2D polar and spherical geometries , Numerical Methods for Partial Differential Equations vol 18, 56-68, (2002).
7. M.-C. Lai, W.-W. Lin and W. Wang, A fast spectral/difference method without pole conditions for Poisson-type equations in cylindrical and spherical geometries , IMA J. of Numerical Analysis, vol 22, No 4, 537-548, (2002).
8. M.-C. Lai, A simple compact fourth-order Poisson solver on polar geometry , Journal of Computational Physics, vol 182, 337-345, (2002).
9. M.-C. Lai, Fast Poisson solver in a three-dimensional ellipsoid , Contemporary Mathematics , AMS, vol 329, 203-208, (2003).
10. Z. Li, W.-C. Wang, I.-L. Chern and M.-C. Lai, New formulations for interface problems in polar coordinates, SIAM J. on Scientific Computing, vol 25, No 1, 224-245, (2003).
11. K.-H. Chiam, M.-C. Lai and H. S. Greenside, Efficient algorithm on a nonstaggered mesh for simulating Rayleigh-Benard convection in a box , Physical Review E , 68, 026705, (2003).
12. M.-C. Lai, Fourth-order finite difference scheme for the incompressible Navier-Stokes equations in a disk , International Journal for Numerical Methods in Fluids , vol. 42, 909-922, (2003).
13. M.-C. Lai, Fast direct solver for Poisson equation in a 2D elliptical domain, Numerical Methods for Partial Differential Equations , vol 20, 72-81, (2004).
14. M.-C. Lai, C.-Y. Huang and T.-S. Lin, A simple Dufort-Frankel type scheme for the Gross-Pitaevskii equation of Bose-Einstein condensates on different geometries , Numerical Methods for Partial Differential Equations , vol 20, No 4, 624-638, (2004).
15. M.-C. Lai and Y.-H. Tseng, A fast iterative solver for the variable coefficient diffusion equation on a disk , Journal of Computational Physics, vol 208, 196-205, (2005).
16. M.-C. Lai and H.-C. Liu, Fast direct solver for the biharmonic equation on a disk and its application to incompressible flows, Applied Mathematics and Computation, vol 164, 679-695, (2005).
17. M.-C. Lai, Z. Li and X. Lin, Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain, Journal of Computational and Applied Mathematics , vol 191, 106-125, (2006).
18. J. Huang, M.-C. Lai and Y. Xiang, An integral equation method for epitaxial step flow growth simulations , Journal of Computational Physics, vol 216, 724-743, (2006).
19. S.-W. Su, M.-C. Lai and C.-A. Lin, An immersed boundary technique for simulating complex flows with rigid boundary, Computers and Fluids , vol 36, 313-324, (2007).
20. Z. Li, K. Ito and M.-C. Lai, An augmented approach for Stokes equations with discontinuous viscosity and singular forces , Computers and Fluids , vol 36, 622-635, (2007).
21. M.-C. Lai and J.-M Tseng, A formally fourth-order accurate compact scheme for 3D Poisson equation in cylindrical coordinates , Journal of Computational and Applied Mathematics, vol 201, 175-181, (2007).
22. M.-C. Lai, C.-T. Wu and Y.-H. Tseng, An efficient semi-coarsening multigrid method for variable diffusion problems in cylindrical coordinates , Applied Numerical Mathematics, vol 57, 801-810, (2007).
23. M.-C Lai and H.-C. Tseng, A simple implementation of the immersed interface methods for Stokes flows with singular forces , Computers and Fluids , vol 37, 99-106, (2008).
24. M.-C. Lai, Y.-H. Tseng and H. Huang, An immersed boundary method for interfacial flows with insoluble surfactant, Journal of Computational Physics, 227, 7279-7293, (2008).
25. H. Huang, M.-C. Lai and H.-C. Tseng, A parametric derivation of the surfactant transport equation along a deforming fluid interface, Frontiers of Applied and Computational Mathematics , ed. by D. Blackmore, A. Bose and P. Petropoulos, pp. 198--205, (2008).
26. K. Ito, M.-C. Lai and Z. Li A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains, Journal of Computational Physics, 228, 2616-2628 (2009).
27. M.-C. Lai, C.-W. Hsu and H. Huang, A front-tracking method for motion by mean curvature with surfactant, Advances in Applied Mathematics and Mechanics, Vol 1, No 2, 288-300 (2009).
28. Z. Li, M.-C. Lai, G. He and H. Zhao, An augmented method for free boundary problems with moving contact lines, submitted for publication.
29. Y. Kim, M.-C. Lai and C. S. Peskin, Numerical simulations of two-dimensional foam by the immersed boundary method, submitted for publication.

(B) Conference Papers:

1. M.-C. Lai, Jump conditions for the two-dimensional Navier-Stokes equations involving an immersed moving elastic boundary, Proceedings of Third Sino-Philippine Symposium in Analysis, Matimyas Matematika, 2000, special issue, 104-110.
2. M.-C. Lai, K.-H. Chiam, M. C. Cross, and H. S. Greenside, Simulating complex dynamics in intermediate and large-aspect-ratio convection systems, 18th symposium on Energy Engineering Sciences, Argonne National Laboratory, May 15-16, 2000.
3. M.-C. Lai, Two simple fast direct solvers without pole condition for Poisson equation on a disk, Proceedings of the 9th differential equations conference, National Cheng Kung University, 2001.
4. M.-C. Lai, A new implementation technique for solving Poisson problem in 2D infinite domain, Proceedings of the 13th differential equations conference , National Chung Cheng University, 2005.
5. M.-C. Lai, H.-C. Tseng, Z. Li, A simple immersed interface method for the Stokes flow with singular forces , Proceedings of the National Institute for Mathematical Sciences, NIMS workshop for Scientific Computation, Korea, 2006.

(C) Dissertation:

• M.-C. Lai, Simulations of the flow past an array of circular cylinders as a test of the immersed boundary method, Ph.D thesis, Courant Institute of Mathematical Sciences, New York University, 1998/09. This work won 1999 Kurt O. Friedrichs Prize for an outstanding dissertation in Mathematics at Courant Institute.