The essence of our research is the creation and analysis of the algorithms and software systems that can adapt to the problem being solved, and to the computing environment. The main purpose of the adaptation is to stabilize the numerical computations, to minimize the cost of the solution, and to maximize the numerical accuracy.
We aim to integrate knowledge in computer science, computational science, and mathematics. We perform research oriented toward the applications of artificial intelligence (AI) and high-performance computing (HPC) in advanced simulations, advanced simulations of phenomena often governed by Partial Differential Equations (PDEs): linear, non-linear, stationary, and time-dependent (e.g., finite element simulations of stationary problems using AI adaptive algorithms, HPC isogeometric analysis simulations of time-dependent problems, AI applications for stabilized Petrov-Galerkin simulations).
We also work on applications and analysis of such advanced simulation methods, including the development of advanced inversion methods, including
artificial intelligence including soft computing for simulation and inversion of PDEs or and complex systems,
efficient adaptive algorithms for large problems,
ultra-fast solvers for Isogeometric Analysis,
artificial intelligence in Isogeometric Analysis and Petrov-Galerkin methods,
memetic algorithms,
multi-agent systems,
supermodeling techniques,
advanced parallelization techniques,
high-performance computing,
computational and mathematical analysis of advanced simulation methods,
advanced methods applied to inverse problems, and
applications of advanced simulation methods.
Our team was formally created in March 2013, at the request of prof. Robert Schaefer, who led the team until October 2019, when he handed over the management to Prof. Maciej Paszyński.