Scientific Computing and Numerical Analysis

Computational mathematics is a fundamental part of science and engineering. Efficient computational methods are needed to enable and use complex scientific models, as well as drive engineering design. Moreover, raw scientific data requires reliable algorithms to process, analyze, and visualize the data. When combined with high performance computing (HPC), computational mathematics can push scientific fields to new levels.

The scientific computing/numerical analysis research group have interests that cover the following areas:

  • numerical methods for partial differential equations (PDEs), one of the main modeling tools in science and engineering. Some example applications are mechanics (fluid and solid), electromagnetics, optimal design, fracture, liquid crystals, image processing and digital geometry processing.
  • uncertainty quantification (UQ) and stochastic modeling in physical systems. Understanding the effects of randomness in real world applications through approximation and statistical approaches.
  • nonlinear optimization theory, algorithms and applications. Examples include nonlinear optimization software, sparse matrix computing, graph partitioning, inverse Problems in medical imaging, and data science.

Research topics in all these areas range from design and analysis of numerical schemes to iterative methods for the discretized problems and their parallel implementations.


Photo of Susanne C. Brenner

Susanne C. Brenner
SIAM Fellow, AMS Fellow, AAAS Fellow, AWM Fellow
Boyd Professor, PhD The University of Michigan
Research interest: Numerical analysis, finite element methods, multigrid methods, domain decomposition methods
Office: 212 Lockett Hall
Telephone: +1 225 578 1678
Personal Home Page of Susanne C. Brenner

Photo of Li-yeng Sung

Li-yeng Sung
Professor, PhD State University of New York at Stony Brook
Research interest: Partial differential equations, inverse scattering, numerical analysis
Office: 208 Lockett Hall
Telephone: +1 225 578 1598
Personal Home Page of Li-yeng Sung

Photo of Shawn Walker

Shawn Walker
Professor, PhD University of Maryland
Research interest: Finite element methods, liquid crystals, geometric evolution, optimal control of PDEs
Office: 210 Lockett Hall
Office hours: TuTh 1:00pm–2:00pm
Telephone: +1 225 578 1603
Personal Home Page of Shawn Walker

Photo of Xiaoliang Wan

Xiaoliang Wan
Professor, PhD Brown University
Research interest: Stochastic modeling, numerical methods for stochastic PDEs, minimum action method.
Office: 226 Lockett Hall
Office hours: MW 3:00pm–4:30pm
Telephone: +1 225 578 6367
Personal Home Page of Xiaoliang Wan

Photo of Hongchao Zhang

Hongchao Zhang
A. K. and Shirley Barton Professor, PhD University of Florida
Research interest: Nonlinear optimization and its applications, numerical analysis, numerical linear algebra
Office: 220 Lockett Hall
Telephone: +1 225 578 1982
Personal Home Page of Hongchao Zhang