Computational fluid dynamics activity

- High order control volume Pade-type approximations schemes for the Navier-Stokes equations in complex geometries with application to 3-D mixing problems;
- Development of well models and application of mixed finite element methods/control volume mixed finite element methods for modelling the non-Darcy gas flows in porous media;
- Development of approximation schemes suitable for highly distorted hexahedral grids

Geometrical optimization activity

- Development of methods for 2-D and 3-D quasi-isometric grid generation;
- Surface grid generation, surface morphings and projections;
- Maximum-norm optimization methods in the construction of the spatial mappings;
- Integration of linear solvers and the solution methods for highly nonlinear variational problems.

Linear iterative solvers activity

- Iterative solvers for large dense complex/real linear systems and for sparse symmetric/unsymmetric and structured/unstructured linear systems;
- Sparse and factorized sparse approximate inverses and incomplete block factorizations in the inverse-free form;
- Robust second-order incomplete Cholesky preconditionings for linear systems with ill-conditioned SPD matrices;
- Highly sparse incomplete QR decompositions;
- Parallel fast Strassen-like matrix-matrix multiplication and inversion algorithms.