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

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

Numerical methods for PDEs
Computational fluid mechanics

2007/08-- Chair, Department of Applied Mathematics, 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

Publications

(A) Refereed Papers:

• Immersed Boundary Method
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. 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).
4. M.-C. Lai, Y.-H. Tseng and H. Huang, An immersed boundary method for interfacial flows with insoluble surfactant, Journal of Computational Physics, in revision.
• Immersed Interface Method
1. 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).
2. 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).
3. 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).
4. 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).
5. 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).
6. K. Ito, Z. Li and M.-C. Lai, An augmented method for the Navier-Stokes equations on irregular domains, submitted for publication.
• Boundary Integral Method
1. 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).
2. 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).
• Fast Poisson Solver in non-Cartesian Coordinates
1. 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).
2. 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).
3. 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).
4. M.-C. Lai, A simple compact fourth-order Poisson solver on polar geometry , Journal of Computational Physics, vol 182, 337-345, (2002).
5. 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).
6. M.-C. Lai, Fast Poisson solver in a three-dimensional ellipsoid , Contemporary Mathematics , AMS, vol 329, 203-208, (2003).
7. 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).
8. 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).
9. 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).
• Navier-Stokes Solver in non-Cartesian Coordinates
1. 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).
2. 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).
• Rayleigh-Bernard Convection
1. 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).
• Bose-Einstein Condensation
1. 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).

(B) Conference Papers:

• 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.
• 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.
• 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.
• 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.
• 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.

mclai@math.nctu.edu.tw