My field of expertise is High Performance Scientific Computing. Within this field, I have particularly specialized in: (1) the design of advanced, application-tailored, finite element discretizations and fast and scalable solution methods for the numerical approximation of Partial Differential Equations (PDEs), and their parallel message-passing implementation for the efficient exploitation of current petascale distributed memory supercomputers; (2) the development of innovative mathematical software design patterns for the numerical approximation of PDEs, the implementation of these in open source scientific software packages, and the application of these advances in the solution of real-world challenges in collaboration with application-problem specialists, and/or private sector companies, (3) the development of Scientific Machine Learning innovative approaches for the data-driven, physics-constrained numerical solution of inverse PDE problems. I am leading the development of the so-called in Gridap.jl Julia ecosystem of packages for the numerical solution of PDEs on supercomputers.
Keywords
Computational Science and Engineering. High Performance Scientific Computing. Partial Differential Equations. Finite Elements. Parallel Preconditioning for Large Scale PDEs. Scalable Preconditioning. Scientific Machine Learning. Artificial Neural Networks for PDEs. Open Source Scientific Software. GPU computing.
Current research topics
- Exploiting the synergy among Artificial Neural Networks and the numerical solution of PDEs.
- Scientific Machine Learning approches for large-scale inverse problems.
- Physics-informed Neural Networks with application to prediction of bushfire dynamics.
- Hybridizable finite element methods for general polytopal meshes (HDG, HHO, VEM, etc.).
- Scalable preconditioning for these schemes (h/p geometric multigrid approaches, hybrid multiscale domain decomposition, etc.).
- Numerical methods for geophysical flows with application to Numerical Weather Prediction.
Research students
I am always looking for highly motivated and talented research students at different academic levels (undergraduate, PhB, Honours, Masters, and PhD/MPhil). These include individual research projects for ANU students enrolled in COMP3770/4550/8603/8604/8800/SCNC2101.
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