Large scale computer simulation. Numerical methods for partial differential equations: finite difference methods; finite element methods – conforming and nonconforming elements; mixed finite element methods; discontinuous Galerkin methods.
High performance computer architectures and algorithms. Methods and algorithms based on Fast Fourier Transform. Parallel methods and algorithms: algorithms and software tools for domain partitioning; algorithms and software tools for block splitting of sparse matrices.
- Computational linear algebra. Iterative methods for sparse matrices. High performance preconditioning methods and algorithms: multilevel methods; domain decomposition methods; block-factorization methods.
- Applications in science, engineering and ecology. Computer and supercomputer simulation: mass and head transfer; electrostatics; magnetostatics; flows in porous media; biomedical applications; modeling of Li-ion batteries; transport of pollutants; microstructure of composite materials, etc.