Overview
My field of expertise is in reduced order modeling, within the broader, multidisciplinary domain of scientific computing. The applications I typically work on involve parameterized partial differential equations (PDEs), which describe a wide variety of physical phenomena – from wildfire propagation to cardiac electrophysiology. My research objectives, experience, and contributions focus on advancing state-of-the-art strategies to address two key challenges that scientific computing must overcome to achieve broader impact and applicability.
The ever-growing demand for accurately and efficiently solving parameterized PDEs in real-world scenarios calls for innovative progress in low-dimensional solvers, particularly leveraging the increasing availability of hardware-level parallelism.
To this end, I have specialized in the development of advanced reduced order models, incorporating cutting-edge techniques from low-rank tensor representations, localized manifold techniques, and message-passing interfaces harnessing the power of modern distributed-memory supercomputers.
The design and development of flexible, extensible, fast, generic and broadly applicable reduced order model software packages is a complex and relatively underexplored task – one in which I have built substantial expertise. This work demands both a deep understanding of the underlying numerical methods and a forward-thinking approach to mathematical software abstraction. These efforts also play a key role in narrowing the gap between cutting-edge advances in numerical algorithms and their widespread adoption by domain experts in applied fields such as 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 parameterized , encompassing both the implementation of efficient full-order discretizations and the construction of high-performance reduced order solvers.