Numerical analysis and computational mathematics, modeling and numerical analysis of multiscale partial differential equations, numerical methods for atomistic simulation, numerical methods for stiff and stochastic differential equations.
Design and analysis of numerical algorithms for partial differential equations, numerical methods for problems with discrete mathematical structure, numerical techniques to improve the integration between numerical simulation and geometric modelling, applications from elasticity to electromagnetism.
High-order and spectral methods for PDEs, Numerical analysis for time-dependent PDEs, Reduced order methods, Computational wave problems, Machine learning in scientific applications, High performance and parallel computing, Computational science and engineering.
Numerical linear algebra and high-performance computing, low-rank matrix and tensor techniques, computational differential geometry, eigenvalue problems, high-performance computing, and model reduction.
My general research interests concern nonlinear mechanics and mathematics, with emphases on i) parameter continuation, bifurcation and stability exchange results, ii) variational principles.
Development of reliable numerical simulations of complex models appearing in physics, engineering and life science applications, such as fluid-structure interaction in hemodynamics, heart electromechanics, flows in porous media, etc.
Numerical Analysis of PDEs, parallel computing, reduced order modeling. Applications to the simulaiton of the Cardio-vascular system.