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Part of my research is devoted to the development of two simulation-based software packages for multi-scale and multi-physics phenomena across disciplines.


*  The rbMIT © MIT Software package implements in Matlab® all the relevant algorithms to solve parametrized partial differential equations by the reduced basis method. The reduced basis method has received considerable interest in the last few years due to its potential advantages over classical numerical methods for real-time or many-query contexts. This method and the related rbMIT software have been used to solve a wide variety of engineering problems including optimal control, shape optimization, inverse problems and stochastic partial differential equations. The rbMIT software and relevant papers can be found from Professor Patera’s research group website www.augustine.mit.edu.

The development of the rbMIT Software package is led by Professor Anothony T. Patera at the Department of Mechanical Engineering, MIT. The rbMIT team including Phuong Huynh, Ngoc-Cuong Nguyen, and Gianluigi Rozza won the Springer CSE prize 2009 for their work on the rbMIT Software which is being used for both CSE research and education.      

*  Professor Jaime Peraire and I are currently developing the Fully Implicit High-Order Hybridizable Discontinuous Galerkin (IHDG) Software package for multi-physic applications modeled by partial differential equations. Numerous results obtained with the IHDG Software feature in a number of our recent (and future) papers including linear and nonlinear convection-diffusion equations, wave equations, incompressible and compressible Navier-Stokes equations, Maxwell’s equations in frequency and time domain, and linear and nonlinear elasticity, and plasticity. Our current development is focused on fluid-structure interaction, computational electromagnetics, and immersed interface problems. This work is in collaboration with Professor Bernardo Cockburn at the Department of Mathematics, UMN.     

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