Li-Tien Cheng
Address:
Department of Mathematics
University of California, San Diego
9500 Gilman Dr
La Jolla, CA 92093-0112
Office: AP&M 5707
Phone: 858-534-3894
Fax: 858-534-5273
E-mail:
lcheng@math.ucsd.edu
Background
- Professor, UCSD (Ph.D. UCLA 2000, MA/BS UCLA 1996)
Research Interests
- Field:
Mathematics for scientific computing.
- Specialization:
Level set methods, numerical PDE's, image processing.
Published Papers:
Biomolecules
- Interfaces and hydrophobic interactions in receptor-ligand systems: A
level-set
variational implicit solvent approach
Li-Tien Cheng, Zhongming Wang, Piotr Setny, Joachim Dzubiella, Bo Li,
and J. Andrew McCammon
Submitted 2009.
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(type = .pdf, size = 1 MB).
- Dewetting-controlled binding of ligands to hydrophobic pockets
Piotr Setny, Zhongming Wang, Li-Tien Cheng, Bo Li, J. Andrew McCammon,
and Joachim Dzubliella
Submitted 2009.
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(type = .pdf, size = 532 KB).
- Coupling the level-set method with molecular mechanics for variational
implicit
solvation of nonpolar molecules
Li-Tien Cheng, Yang Xie, Joachim Dzubiella, J. Andrew McCammon, Jianwei Che,
and Bo Li
J. Chem. Theory Comput., 5(2), 257-266, 2009.
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(type = .pdf, size = 424 KB).
- Application of the level-set method to the implicit solvation of
nonpolar molecules
Li-Tien Cheng, Joachim Dzubiella, J. Andrew McCammon, and Bo Li
J. Chem. Phys., 127, 084503, 2007.
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(type = .pdf, size = 420 KB).
Visibility
- Visibility Optimizations Using Variational Approaches
Li-Tien Cheng and Yen-Hsi Tsai
Comm. Math. Sci. 3(3):425--451, 2005.
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(type = .pdf, size = 2.9 MB).
- Visibility and its Dynamics in a PDE Based Implicit Framework
Yen-Hsi Tsai, Li-Tien Cheng, Paul Burchard, Stanley Osher, and Guillermo Sapiro
J. Comput. Phys. 199(1):260--290, 2004.
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(type = .pdf, size = 6.8 MB).
High-Frequency Wave Propagation
- An Efficient Level Set Method for Constructing
Wavefronts in Three Space Dimensions
Li-Tien Cheng
J. Comput. Phys., 226(2):2250--2270, 2007.
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(type = .pdf, size = 372 KB).
- Computational High-Frequency Wave Propagation Using the Level
Set Method, with
Applications to the Semi-Classical Limit of
Schrodinger Equations
Li-Tien Cheng, Hailiang Liu, and Stanley Osher
Comm. Math. Sci., 1(3):593--621, 2003.
- Level Set Based Eulerian Method for Multivalued Traveltimes in
Both Isotropic and
Anisotropic Wave Propagations
Li-Tien Cheng, Stanley Osher, and Jianliang Qian
73rd Internat. Mtg, Soc. Expl. Geophys. Expanded Abstracts, 1891--1804,
2003.
- Reflection in a Level Set Framework for Geometric Optics
Li-Tien Cheng, Myungjoo Kang, Stanley Osher, Hyeseon Shim, and Yen-Hsi Tsai
Comput. Model. Eng. Sci., 5(4):347--360, 2004.
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(type = .ps.gz, size = 896 KB).
- A Level Set Based Eulerian Approach for Anisotropic Wave
Propagations
Jianliang Qian, Li-Tien Cheng, and Stanley Osher
Wave Motion, 37(4):365--379, 2003.
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(type = .ps.gz, size = 323 KB).
- Geometric Optics in a Phase Space Based Level Set and Eulerian
Framework,
Stanley Osher, Li-Tien Cheng, Myungjoo Kang, Hyeseon Shim, and Yen-Hsi Tsai,
Submitted to Journal of Computational Physics.
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(type = .ps.gz, size = 958 KB).
Materials Science
- Level Set Simulations of Dislocation-Particle Bypass Mechanisms
Yang Xiang and David Srolovitz and Li-Tien Cheng and Weinan E
Acta Mater., 52(7):1745--1760, 2004.
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(type = .ps.gz, size = 2.6 MB).
- A Level Set Method for Dislocation Dynamics
Yang Xiang and Li-Tien Cheng and David Srolovitz and Weinan E
Acta Mater., 51(18):5499--5518, 2003.
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(type = .ps.gz, size = 328 KB).
- Level Set Method for Thin Film Epitaxial Growth
Susan Chen, Barry Merriman, Myungjoo Kang, Russel Caflisch, Christian Ratsch,
Li-Tien
Cheng, Mark Gyure, Ronald Fedkiw, and Stanley Osher
J. Comput. Phys., 167:475--500, 2001.
Image Processing
- Estimation of 3D Surface Shape and Smooth Radiance from 2D
Images: A Level Set
Approach
Hailin Jin, Anthony Yezzi, Yen-Hsi Tsai, Li-Tien Cheng, and Stefano Soatto
J. Sci. Comput., 19(1--3):267--292, 2003.
- Variational Problems and PDE's on Implicit Surfaces
Marcelo Bertalmio, Guillermo Sapiro, Li-Tien Cheng, and Stanley Osher
Proc. IEEE Workshop on Variational and Level Set Methods in Computer
Vision, 759--780,
2001.
- Variational Problems and Partial Differential Equations on Implicit
Surfaces: The
Framework and Examples in Image Processing and Pattern
Formation
Marcelo Bertalmio, Li-Tien Cheng, Stanley Osher, and Guillermo Sapiro
J. Comput. Phys., 174(2):759--780, 2001.
Numerical PDE's
- Redistancing by Flow of Time Dependent Eikonal Equation
Li-Tien Cheng and Yen-Hsi Tsai
J. Comput. Phys., 227(8):4002--4017, 2008.
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(type = .pdf, size = 168 KB).
- A Level Set Framework for Capturing Multi-Valued Solutions of
Nonlinear First-
Order Equations
Hailiang Liu, Li-Tien Cheng, and Stanley Osher
Accepted by J. Sci. Comput.
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(type = .pdf, size = 407 KB).
- A Second Order Accurate Symmetric Discretization of the Poisson
Equation on
Irregular Domains
Frederic Gibou, Ronald Fedkiw, Li-Tien Cheng, and Myungjoo Kang
J. Comput. Phys., 176(1):205--277, 2002.
- Fast Sweeping Algorithms for a Class of Hamilton-Jacobi
Equations,
Yen-Hsi Tsai, Li-Tien Cheng, Stanley Osher, and Hong-Kai Zhao,
SIAM J. Numer. Anal., 41(2):673--694, 2003.
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(type = .pdf, size = 1.2 MB).
Multi-scale
- The Heterogeneous Multi-Scale Method for Interface Dynamics
Li-Tien Cheng and Weinan E
Contemp. Math., 330:43--53, 2003.
Geometry
- Minimization with the Affine Normal Direction
Hsiao-Bing Cheng, Li-Tien Cheng, and Shing-Tung Yau
Comm. Math. Sci. 3(4):561--574, 2005.
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(type = .pdf, size = 252 KB).
- Construction of Shapes Arising from the Minkowski Problem Using
a Level Set
Approach
Li-Tien Cheng
J. Sci. Comput., 19(1--3):123--138, 2003.
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(type = .pdf, size = 366 KB).
Level Set Method
- Motion of Curves Constrained on Surfaces Using a Level Set
Approach
Li-Tien Cheng, Paul Burchard, Barry Merriman, and Stanley Osher
J. Comput. Phys., 175(2):604--644, 2002.
- Motion of Curves in Three Spatial Dimensions Using a Level Set
Approach
Paul Burchard, Li-Tien Cheng, Barry Merriman, and Stanley Osher
J. Comput. Phys., 170(2):720--741, 2001.
Thesis
- The Level Set Method Applied to Geometrically Based Motion,
Materials Science, and
Image Processing
Li-Tien Cheng
Ph.D. Thesis, UCLA, 2000.
Teaching:
Colloquium:
Other:
Related Links:
Scientific Computation Group
Homepage for the Scientific
Computation Group.
Department of Mathematics Homepage for the UCSD Math Dept.
Infopath UCSD's Campus-Wide Information System.
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UC resources.