The Numerical Mathematics Group

The Numerical Mathematics Group is a research group at King Abdullah University of Science and Technology (KAUST) headed by Professor David Ketcheson. We conduct research in the areas of partial differential equations and numerical methods, with particular areas of focus, including:

• Analysis and design of time discretization methods
• Structure-preserving discretizations
• Nonlinear waves, including shock waves, dispersive waves, and interactions between them
• Numerical software development

Some of the exciting developments that have come from our work in recent years are:

• Relaxation-based integrators: efficient explicit structure-preserving time discretizations for both conservative and dissipative systems
• Discovery of surprising behaviors of nonlinear waves in the presence of periodic structures
• A method for approximation of arbitrary PDEs by first-order hyperbolic systems

What's new:

• Preprint on Solitary wave formation in the compressible Euler equations
• Preprints on Homogenized equations for isentropic gas in a pipe with periodically-varying cross-section
• "Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation" accepted to Nonlinearity

Please see the open positions page for more information.