Li-Tien Cheng

Department of Mathematics
University of California, San Diego
9500 Gilman Dr
La Jolla, CA 92093-0112

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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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.
  Download (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:

• Summer 2014
  • Beijing
• Winter 2015
  • Math 270B

Colloquium:

• Department Colloquium Website 2010--2011

Other:

• Pictures of China

Related Links:

Scientific Computation Group

Department of Mathematics

Infopath

The UC Office of the President

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