Overview
My field of expertise is in high performance computational mathematics, under the umbrella of the broader, multi-disciplinary field of Computational Science & Engineering (CSE), a.k.a. Scientific Computing (SC). My research aims, experience, and contributions so far are in the advancement of the state-of-the-art solution strategies for three main challenges CSE as a discipline has to address, which are key for its success and wide applicability.
The ever-increasing demand for accuracy (e.g., the need for increasingly complex and flexible geometry representations, the efficient resolution of multiple time and space scales, or the discrete conservation of continuum balances) in real-world application problems, and the widespread adoption of explicit hardware parallelism (e.g., multi-core CPUs and many-core accelerators) as the approach to sustain an exponential increase in computational power (as Moore's law dictated), calls for breakthrough inventions in advanced discretization methods (e.g., embedded methods on general polytopal meshes) and scalable solution methods (e.g., hybrid multiscale domain decomposition solvers).
To this end, I have specialized in the design of advanced, application-tailored, Finite Element (FE) discretizations and fast and scalable solution methods for the numerical approximation of PDEs, and their parallel message-passing implementation for the efficient exploitation of current petascale distributed memory supercomputers.
The design and development of flexible, extensible, sustainable, fast and scalable, generic and broadly-applicable FE discretization software packages is a daunting task in itself in which I have developed expertise. This requires a deep understanding of the numerical methods at hand and innovative ideas from the mathematical software abstraction point of view. These endeavours also help in mitigating the gap between breakthrough advances in numerical algorithms and HPSC tools and its generalized adoption by application problem domain experts, e.g., in industry and government research agencies.
To this end, I have specialized in 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.
The steep improvements in data acquisition systems and storage capacity has resulted in an explosion of data from (possibly indirect) experimental observations, which have to be assimilated (under real-time constraints in some cases) for enhanced model predictions and reliability, using, e.g., Artificial Neural Networks (ANNs), PDE-constrained inverse problem solvers, Machine Learning (ML) and optimization techniques. A prototypical mission-critical application problem in which this is needed is in the data assimilation of meteorology station measurements for Numerical Weather Prediction (NWP) models, but there are many more, such as, e.g., bushfire transport and dynamics prediction from satellite infrared data, or the analysis of cardiac electrophysiology from MRI images.
To this end, I have started several research endeavours on exploring the synergy of ANNs and the numerical discretization of forward and inverse PDE problems using FE techniques with application to the problems enumerated above.