In recent decades computation has joined theory and experiment as the third pillar of the scientific method. During this time, simulation complexity has evolved from relatively simplistic calculations involving only a handful of basic equations, to massive models that combine many physical processes. While early simulations could be well-understood using standard mathematical techniques, applied mathematics has unfortunately not kept up with the fast pace of scientific simulation development. Thus, although there now exist incredibly efficient algorithms and elegant theory for many relatively simple models, computational scientists who study highly-realistic systems must typically “solve” their multiphysics models using ad hoc methods with questionable accuracy and stability. My research program aims to bridge this gap between mathematical theory and scientific computing practice, through creating, applying, and disseminating flexible algorithms that may be tuned for modern, multiphysics problems, while still providing mathematical assurances such as accuracy, stability and parallel scalability.

General research interests

• Derivation and implementation of advanced time integration methods and algebraic solvers for complex multiphysics simulations.

• Highly collaborative interdisciplinary science.

• Scalable, highly performant, robust and open-source mathematical software.

Further information

• An up-to-date list of my publications, including DOI links, is provided on the Publications page.

• Links to many of my open-source software projects are provided on the Software page.

Funding support

I am grateful for the generous research support from multiple agencies: