In the past decade, large-scale computing has become a prevalent means of discovery and of 'getting things done' in almost all areas of research and technology. The research area of Numerical Analysis and Scientific Computing is playing a central role in this evolution, developing numerical methods for advanced simulation in a variety of fields which include the physical sciences, engineering, the life sciences, and information technology.
Traditional areas of strength in Scientific Computing research in the department include numerical methods for PDEs and numerical linear algebra. Research is also conducted in other areas of Scientific Computing, such as numerical methods for ODEs, inverse problems and numerical optimization. Research in Scientific Computing involves a variety of methods and techniques, ranging from the development and mathematical analysis of numerical algorithms to advanced implementations on parallel supercomputers and GPUs. There are frequent research interactions and joint graduate courses in the Scientific Computing field with Waterloo's School of Computer Science, Department of Combinatorics and Optimization, and Centre for Computational Mathematics. Large-scale computing infrastructure is provided by SHARCNET and Compute Canada.
The regular faculty whose primary research area is Scientific Computing are:
- Hans De Sterck (numerical linear algebra, multigrid, finite volume methods for hyperbolic conservation laws, large-scale applications in information technology (tensors, graphs, networks) and in space physics)
- David Del Rey Fernández (development and analysis of mathematically rigorous methods for partial differential equations, continuous/discontinuous Galerkin methods, finite-difference methods, mesh adaptation, machine learning for high performance computing acceleration)
- Lilia Krivodonova (discontinuous Galerkin methods, error estimation and adaptive methods, finite element methods, musical acoustics, hyperbolic conservation laws, GPU computing)
- Sander Rhebergen (discontinuous Galerkin finite element methods, space-time finite element methods for deforming domain problems, higher-order accurate finite element methods, preconditioners, fluid dynamics, aerodynamics, magma/mantle dynamics, two-phase flows)
- Giang Tran (sparse modeling and sparse optimization methods, data science, image processing and medical imaging, compressed sensing)