The development and utilization of numerical methods of large-scale,
computer-aided analysis. Central are: discretization methods of
partial differential equations based on the combination of Galerkin
weighted residuals and finite element basis functions; computer-implemented
methods of bifurcation theory for nonlinear analysis; iterative
methods for the solution of large, linearized equation sets and
for eigenvalue computations. The recent research directions are
towards the implementation of Krylov-type methods, matrix-free computations
and coarse bifurcation analysis – all adapted to the needs
for efficient computing on parallel processors.
High-performance computing facilities are in house: "Pegasus", a 16 dual node cluster and "Andromeda", a hybrid CPU/GPU cluster.
Part of this research is carried out in collaboration with Prof.
Yannis Kevrekidis at the Department of Chemical and Biomolecular Engineering, Johns Hopkins University, USA