Ming-Chih Lai, Professor
My CV
Education:
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
Prizes and Awards:
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
Research Interests:
Numerical methods for PDEs
Computational fluid mechanics
Positions:
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
- 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).
- 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).
- 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).
- 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
- 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).
- 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).
- 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).
- 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).
- 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).
- 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
- 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).
- 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
- 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).
- 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).
- 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).
- M.-C. Lai, A simple compact fourth-order Poisson
solver on polar geometry , Journal of Computational Physics,
vol 182, 337-345, (2002).
- 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).
- M.-C. Lai, Fast Poisson solver in a three-dimensional
ellipsoid , Contemporary Mathematics , AMS, vol 329, 203-208,
(2003).
- 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).
- 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).
- 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
- 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).
- 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
- 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
- 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.