- Numerical methods for partial differential equations (PDEs)
- Model order reduction techniques
- Reduced basis methods for nonlinear parametrized PDEs
- Optimal control, Inverse problems
What is "Reduced Basis Method"?Reduced Basis Method (RBM) is a new technique developed by A. Patera and Y. Maday to solve parametric PDEs very efficiently. Today RBM is considered one of the most effective Model Order Reduction (MOR) techniques available to solve parametric PDEs in different disciplines including controls, optimization, fluid dynamics, structural dynamics, circuit design , etc.
The core of RBM is about reducing the size of the model in the most efficient possible way. Doing that, it is now possible for us to solve huge parametric PDEs with thousands of degrees of freedom on small computers and even smartphones. To see a rather good profile for RBM see here. To see practical applications of the newly developed RBM, visit here, here.