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.
Susanne C. Brenner