Research areas

We work on ultra-fast linear O(N) computational cost solvers for numerical simulations of difficult unstable problems.

We employ higher continuity smooth B-spline basis functions for discretization and we design and implement stabilized direction-splitting solvers that mixed time marching schemes with residual minimization method.

We analyze the concurrency of the designed algorithms by using trace theory, Petri nets, and graph grammar models.

We combine Isogometric Analysis with the reziduum minimization method (iGRM method) and Alternating-Directions Solver to create efficient and stable simulations of time-dependent problems.

We also work on incorporating data assimilation methods like e.g. supermodeling which couples several instances of simulators for more realistic simulations.

We design, analyze and apply different memetic strategies for solving irremediably ill-conditioned inverse parametric problems.

We focus on several challenging applications including tumor progression/regression after medical treatment simulations, atmospheric phenomena simulations including pollution propagations, environmental aspect of the oil-gas exploration process, material science simulations, and propagation of electromagnetic waves.

Our scientific interests include:

applying fast direct solvers (in particular the Alternating Direction Solver) to simulations of non-stationary processes using Isogeometric Analysis (IgA)

combining IgA with stabilization methods based on residuum minimization (main idea of DPG) to facilitate stable simulations using higher-order basis functions

developing time stepping schemes compatible with fast direct solvers

Application and analysis of memetic strategies in solving irremediably ill-conditioned inverse parametric problems.

population-based, stochastic algorithms for solving continuous global optimization problems,

algorithms of solving ill-conditioned inverse parametric problems for PDEs coupled with the hp-FEM adaptive strategies for solving direct problems,

computing multi-agent systems.