Professor Maciej Paszynski presents
Fast and Smooth simulations of time-dependent problems
We present fast and smooth simulations of time dependent-problems, in one, two and three dimensions. We discretize the time axis, by introducing several time steps. Theus the time-dependent problem is transformed into a sequence of the stationary problems to be solved at particular time steps.
What makes the simulations smooth is the fact that we use higher order B-splines basis functions for spatial discretization at every time step. We approximate the solution at every time step with a linear combination of tensor product B-spline basis functions that span over the regular computational mesh. What makes the simulations fast, is the fact that we have the so-called alternating directions algorithm which solves these problems in every time step with the highest possible linear computational cost.
Our simulations can be performed on a multi-core laptop, and they will run for around 30 minutes. In our simulations, we can use both so-called explicit and implicit schemes. This means that we can increase the accuracy of a simulation by increasing arbitrarily the number of B-spline basis functions used.
We show how to apply our method for time-dependent simulations of several physical phenomena, including the heat transfer, non-linear flow in heterogeneous media, elastic wave propagation problem, tumor growth simulations, and the simulation of the pollutant from a chimney. We present movies generated from the performed simulations.
Maciej Paszynski is a Full Professor of Computer Science at Department of Computer Science at AGH University, Krakow, Poland. He did his PhD in Mathematics with Applications to Computer Science from Jagiellonian University, Krakow, Poland from 2009 to 2013. He is a former postdoc of Prof. Leszek Demkowicz from the Institute for Computational and Engineering Sciences (ICES), The University of Texas at Austin (UT).
Maciej collaborates with Prof Victor Calo from Curtin University, Prof Leszek from ICES, UT, Prof David Pardo from Basque Center for Applied Mathematics (BCAM), Bilbao, Spain, Prof Keshav Pingali from ICES, UT, Prof Ignacio Muga from The Catholic University of Valparaiso, Chile, Pro. Frederick Valentine from LNCC, Petropolis, Brasil and Prof Rafael Montenegro-Armass from The University of Las Palmas de Gran Canaria.
His research interest includes fast solvers for mesh-based computations. He co-authored over 40 papers in indexed journals and gave over 100 presentations.