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Dr. Chuan Li

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Dr. Chuan Li

Office: UNA 115
Phone: (610)-436-1081
Fax: (610)-738-0578
E-mail: cli@wcupa.edu

Dr. Chuan Li

Dr. Chuan Li

Contact Information

Office: UNA 115
Phone: (610)-436-1081
Fax: (610)-738-0578
E-mail Dr. Chuan Li

Education

About Dr. Chuan Li

Teaching

  • Spring 2017
    • MAT325 Computational Mathematics (one section)
    • MAT343 Differential Equations (two sections)
  • Fall 2016
    • MAT113 Algebra & Functions (one section)
    • MAT343 Differential Equations (two sections)
    • MAT554 Scientific Computing (one section)
  • Spring 2016
    • MAT107 Algebra & Functions (one section)
    • MAT108 Brief Calculus (one section)
    • MAT343 Differential Equations (two sections)
  • Fall 2015
    • MAT107 Algebra & Functions (two sections)
    • MAT343 Differential Equations (two sections)
  • Courses taught
  • WeBWorK, an online homework system

Professional Experiment

Research Interests

  • Scientific (parallel) Computing
  • Mathematical Biology:
    • Numerical methods for solving 3D parabolic interface problems with general jump conditions and complex geometries
    • Calculating electrastatic potential and energies of sysmtems comprised of biological marcromolecules and their assemblages
    • Calculating action potentials in the heart, cardiac physiology
  • Numerical methods for solving Ordinary and Partial Differential Equations
  • Google Scholar Profile

Ongoing Research Projects

Development of a Matched Interface and Boundary (MIB) method for solving interface problems with complex interfaces

Grant: This project is now supported by the Research in Mathematics and Sciencs (RIMS) Award, College of Mathematics and Sciences, WCU, 2017-2018.

Involved Students: Cameron Campbell (undergraduate), Stacy Porten-Willson (undergraduate)
Collaborator: Prof. Shan Zhao, Professor of Mathematics, Department of Mathematics, University of Alabama Zhihan Wei, PhD candidate, Department of Mathematics, University of Alabama

Description: This work aims to overcome the difficulties of previous matched Alternate Direction Implicit (ADI) method for solving parabolic equations with complex interfaces. In general parabolic interface problems, the discontinuities of a function and its flux across an interface are mathematically described by spatial-and-temporal-dependent jump conditions on the interface. Without appropriately addressing such conditions, the central difference spatial approximation is known to be inaccurate in the classical ADI schemes. This motivates the development of a matched ADI method, in which the central difference is locally corrected according to essentially one-dimensional (1D) jump conditions. Based on the Douglas ADI (D-ADI) method, this newly developed matched D-ADI method is unconditionally stable and restores the second order of accuracy in space for geometries with simple interfaces. In order to make the developed ADI method work for geometries with complex interfaces, a formal temporal discretization is formulated to avoid extra perturbations of the original matched ADI framework. Second, approximations to tangential derivatives are substantially improved in the tensor product decomposition of 2D or 3D jump conditions so that the essential 1D jump conditions become more stable.

Recent Activities:

  • EPeDal Meeting April 1, 2017 at Kutztown University Congratulations to Cameron and Stacy for presenting their first research talk in this event.
  • All Science Poster Day Fall 2016 Congratulations to Cameron and Stacy for winning the 2nd place of undergraduate student poster presentations in this event.
  • Research Day October 2016 Cameron and Stacy presented their work, along with other Math students, in the poster display at a recent West Chester University Research Day.

 Development of Schemes for Parallel Computing of the Electrostatics in Biological Systems: Implementation in DelPhi

Grant: This project is now supported by a NIH grant "New Generation DelPhi: large systems and beyond electrostatics" (NIH grant #: 5R01GM093937-07), 2017-2018.

Involved Students: Xiaojuan Cathy Yu (graduate)
Collaborator: Prof. Emil Alexov, Professor of Physics, Department of Physics and Astronomy, Clemson University Dr. Zhe Jia, Postdoctoral Researcher, Department of Physics and Astronomy, Clemson University

Description: Nowadays calculating the electrostatic potential and corresponding energies has become a standard computational approach for studying biomolecules and nano-objects immersed in water and salt phase. One most recognized math model in the area of molecular biology is the Poisson-Boltzmann Equation (PBE), for which no analytical solutions are available for irregular-shaped molecules and proteins, and the distribution of the potential can only be found numerically. However, no existing sequential PBE solver is ready to be utilized to solve PBE for large macromolecules and macromolecular complexes due to high computational time and memory requirements. In order to make the calculations feasible for large macromolecules and complexes, a set of computing schemes was introduced to parallelize the processes of molecular surface construction, numerical Successive Over Relaxation (SOR) iteration, and energy calculations. The parallelization schemes are implemented in the popular software DelPhi and results in speedup of several folds. As a demonstration of the efficiency and capability of this methodology, the electrostatic potential, and electric field distributions are calculated for several large macromolecules and complexes to illustrate their complex topology, which cannot be obtained by modeling the super-complex components alone.

Recent Activities:

  • EPeDal Meeting April 1, 2017 at Kutztown University Congratulations to Cathy for presenting her first research talk in this event.

Parallel Computing the Minimized Molecular Surface (MMS) of macromolecules and large complexes

Involved Students: Ryan Moser (undergraduate)
Collaborator: Prof. Shan Zhao, Professor of Mathematics, Department of Mathematics, University of Alabama

Description: This project is computationally oriented. Modeling biomolecular surface is a challenging task due to complicated molecular structures. The resulting surface has great impact on the accuracy of all biomolecular structures and interactions related studies and analysis. Conventional molecular surface (MS) models are lack of physical justification and usually admit geometrical singularities. In the contrast, a recently derived minimal molecular surface (MMS) model delivers minimized surface area and surface free energy, which occur naturally when a less polar macromolecule is immersed in a polar aquatic environment. A fast alternating direction implicit (ADI) algorithm has been developed to solve the governing differential equation for MMS generation. However, the computational cost of the sequential code is still prohibitively expensive when solving ultra large protein systems, such as large protein complexes consisting of one million atoms. In this project, we propose to introduce new parallel computing techniques to significantly improve the performance of the sequential program. A parallel computing software package, which is able to effectively model molecular surface for extremely large macromolecules and complexes, will be developed using the Message Passing Interface (MPI) library. Upon completion, the MMS program will be released as a free software package for academic and research purposes. Funds are requested to disseminate the research findings and showcase the software product to related research societies.

Recent Activities:

  • All Science Poster Day Fall 2016 Ryan presented his work in the poster display at a recent West Chester University All Science Day.

Recent Grant Supporters

  • 2017-2018, PI, Development of a New Matched Alternating Direction Implicit (ADI) Method for Solving Parabolic Interface Problems, Research in Mathematics and Sciencs (RIMS) Award, College of Mathematics and Sciences, WCU, $6,496.
  • 2017-2018, PI, Subcontract of Prof. Emil Alexov's NIH grant "New Generation DelPhi: large systems and beyond electrostatics" (NIH grant #: 5R01GM093937-07) for developing in DelPhi parallel computing algorithms and numerical methods for solving time-dependent differential equations with numerous applications in molecular biology, $54,857.
  • 2015-2017, Co-PI (PI: Dr. Baoling Ma from Millersville University), A mathematical model for the interactions between Plasmodium falciparum malaria parasite and host immune response (MU ID#: M01039795), Millersville University Student Grants for Research and Creative Activity, $365.

Computational Sciences and Applied Mathematics Seminar

Contribute Talks:

  • Chuan Li, The extended parareal algorithm for time-and-space parallel computing of the cable equation, Nov. 10, 2016.
  • Chuan Li, Parallel computing of solving Poisson-Boltzmann equation and calculating corresponding electrostatics for large macromolecules and complexes, Oct 27, 2016

Math Tutorials created by students with Dr. Chuan Li

Publications

  • Zhihan Wei, Chuan Li, Shan Zhao, "A spatially second order alternating direction implicit (ADI) method for three dimensional parabolic interface problems", preprint, 2017
  • Chuan Li, Shan Zhao, "A matched Peaceman-Rachford ADI method for solving parabolic interface problems", Journal of Applied Mathematics and Computation, 299: 28-44, 2017
  • Brandon Campbell, Marharyta Petukh, Emil Alexov, and Chuan Li, "On the electrostatic properties of homodimeric proteins", Journal of Theoretical and Computational Chemistry, 2014
  • Lin Li, Chuan Li, and Emil Alexov, "On the modeling of polar component of solvation energy using smooth Gaussian-based dielectric function", Journal of Theoretical and Computational Chemistry, 2013
  • Chuan Li, Marharyta Petukh, Lin Li, and Emil Alexov, "Continuous development of schemes for parallel computing of the electrostatics in biological systems: Implementation in DelPhi", Journal of computational chemistry, 34, no. 22: 1949-1960, 2013
  • Chuan Li, Lin Li, Marharyta Petukh, and Emil Alexov, "Progress in developing Poisson-Boltzmann equation solvers", Molecular based mathematical biology, 1: 42-62, 2013
  • Lin Li, Chuan Li, Zhe Zhang, and Emil Alexov, "On the dielectric "constant" of proteins: smooth dielectric function for macromolecular modeling and its implementation in Delphi", Journal of chemical theory and computation, 9, no. 4: 2126-2136, 2013
  • Nicholas Smith, Brandon Campbell, Lin Li, Chuan Li, and Emil Alexov, "Protein Nano-Object Integrator (ProNOI) for generating atomic style objects for molecular modeling", BMC structural biology, 12, no. 1: 31, 2012
  • Chuan Li, Lin Li, Jie Zhang, and Emil Alexov, "Highly efficient and exact method for parallelization of grid©\based algorithms and its implementation in DelPhi", Journal of computational chemistry, 33, no. 24: 1960-1966, 2012. [Figure 3 of the manuscript is the cover page of the journal: J Comput Chem. 15;33(24).]
  • Marharyta Petukh, Maxim Zhenirovskyy, Chuan Li, Lin Li, Lin Wang, and Emil Alexov, "Predicting nonspecific ion binding using DelPhi", Biophysical journal, 102, no. 12: 2885-2893, 2012
  • Lin Li, Chuan Li, Subhra Sarkar, Jie Zhang, Shawn Witham, Zhe Zhang, Lin Wang, Nicholas Smith, Marharyta Petukh, and Emil Alexov, "DelPhi: a comprehensive suite for DelPhi software and associated resources", BMC biophysics, 5, no. 1: 9, 2012
  • Nicholas Smith, Shawn Witham, Subhra Sarkar, Jie Zhang, Lin Li, Chuan Li, and Emil Alexov, "DelPhi web server v2: incorporating atomic-style geometrical figures into the computational protocol", Bioinformatics, 28, no. 12: 1655-1657, 2012
  • Chuan Li, Vasilios Alexiades, and Jack W. Buchanan, "Robustness of Action Potentials in Cardiac Myocytes", Proceedings of Dynamic Systems and Applications, 6: 241-247, 2012
  • Chuan Li, "A Time-and-space Parallelized Algorithm for the Cable Equation", PhD dissertation, University of Tennessee, 2011
  • Chuan Li and Vasilios Alexiades, "Comparison of time stepping schemes on the cable equation", Electronic J of Differential Equations, 189-196, 2010
  • Chuan Li and Vasilios Alexiades, "Time stepping for the cable equation, Part 2: Parallel performance", Proceedings of Neural, Parallel & Scientific Computations, 4: 247-251, 2010
  • Chuan Li and Vasilios Alexiades, "Time stepping for the cable equation, Part 1: Serial performance", Proceedings of Neural, Parallel & Scientific Computations, 4: 241-246, 2010

Invited Talks

  • Improvements on a matched interface and boundary (MIB) method for solving parabolic interface problems, SIAM CSS 2016, University of Arkansas at Little Rock, , September 30 – October 2, 2016
  • High-performance parallel computing algorithms for calculating electrostatic potentials and energies for large biological macromolecules and their applications in DelPhi, The Tenth International Conference on Scientific Computing and Applications (ICSCA2016), Toronto, Ontario, June 6-10, 2016
  • Parabolic Interface Problems and Their Applications in Computational Biophysics, joint math colloquium at Millersville University and Franklin & Marshall College, Millersville University, October 1, 2015
  • A matched Alternative Direction Implicit (ADI) method for solving 2D parabolic interface problems, 1st Annual Meeting of SIAM Central States Section, Missouri Unviersity of Science and Technology, April 11-12, 2015
  • Continuous developement of a matched Alternative Direction Implicit (ADI) method for solving parabolic interface problems, SIAM-SEAS 2015, University of Alabama at Birmingham, March 20-22, 2015
  • Poisson-Boltzmann equation, elecctrostatics and parallel computing, Applied Math seminar, Department of Mathematics, University of Alabama, September 19, 2014
  • Parallel computing of calculating electrostatic potential and energies for large macromolecules and complexes,SEARCDE 2013, Univesity of Tennesee, Knoxville, September 21-22, 2013
  • Revealing the role of electrostatics in guiding long-range electron carries, 246th ACS National Meeting, Indianapolis, Indiana, September 8-12, 2013
  • Parallel computing techniques in DelPhi to solve the Poisson-Boltzmann equation and calculate electrostatic energies of biological macromolecules, 9th Mississippi State-UAB Conference on Differential Equations and Computational Simulations, Mississippi State University, October 4-6, 2012
  • Computer parallelization of continum electrostatics: Implementation in DelPhi, Bio-seminar, Clesmon Unviersity, September 25, 2012
  • Parallelized DelPhi: a multi-processor Poisson-Boltzmann solver to calculate electrostatic energies of biological macromolecules, 244th ACS National Meeting & Exposition, Philadelphia, PA, Auguest 19-23, 2012
  • Comparison of parallel algorithms for solving the cable equation, 31st Southeastern-Atlantic Reginal Conference on Differential Equations, Georgia Southern University, September 30- Octomber 1, 2011
  • A time-and-space parallel scheme on the cable equation, Bio-seminor, Clemson University, August 31, 2011
  • Time and space parallelization using the Parareal algorithm, 30th Southeastern-Atlantic Regional Conference on Differential Equations, Virginia Tech, Octomber 1-2, 2010
  • Time stepping for the cable equation, part 2: parallel performance, 4th International Conference on Neural, Parallel & Scientific Computations, Morehouse College, Auguest 11-14, 2010
  • Comparison of time stepping schemes on the cable equation, 8th Differential Equations & Computational Simulations, Mississippi State-UAB Conference, Mississippi State University, May 7-9, 2009
  • Representation of functions and operators in L2[0,1] using multiwavelet bases, 7th Differential Equations & Computational Simulations, Mississippi State-UAB Conference, University of Alabama at Birmingham, Octomber 31 - November 2, 2007

Poster Presentations

  • Multi-level and interleaved (MLIPB) method for parallel computing of the electrostatics and its application, Biophysical Society 57th Annual Meeting, Philadelphia, Pennsylvania Feburary 2-6, 2013
  • New parallelized DelPhi: Fast and efficient Poisson-Boltzmann solver to calculate electrostatics of large supramolecular structures, Biophysical Society 56th Annual Meeting, San Diego, California, February 25-29, 2012
  • Algorithms for solving the nonlinear Poisson-Boltzmann equation in macromolecular electrostatics, Annual research symposium in the Dept. of Physics and Astronomy, Clemson University, Aug 22, 2011

Academic Activities

  • Poster reviewer at Made in Millersville 2016, Millersville University, Millersville, PA, April 21, 2016
  • 2015 Joint Mathematics Meetings (JMM), San Antonio, TX, January 10-13, 2015
  • 10th Mississippi State Conference on Differential Equations and Computational Simulations, Mississippi State University, Starkville, MS, Octomber 23-25, 2014
  • Workshop in the International Conference of High Performance Computing, Networking, Storage and Analysis (SC12), Salt Lake City, Utah, November 10-11, 2012
  • Student internship in Computer Science & Mathematics Division at Oak Ridge National Laboratory (ORNL), Oak Ridge, TN, May-Aug 2006

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