Office: UNA 115
|Dr. Chuan Li|
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.
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.
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.