Numerical Analysis Seminar

Date: April 19, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Maciej Paszynski, Department of Computer Science, AGH University, Krakow, Poland

Title: Fast isogeometric finite element method solver for melanoma tumor growth simulations

Abstract: In this talk, we present an application of the fast algorithm for isogeometric L2 projections for simulations of the tumor growth. We introduce first the system of PDEs describing the model of the melanoma growth, including tumor cell density, flux, pressure, extracellular and degraded extracellular matrices. We also introduce a discrete L-systems model of the vasculature, that provides an oxygen source to the system. The system is solved using explicit scheme and fast isogeometric L2 projections, utilizing the alternating directions solver. Every ten-time steps of the simulation, we couple our continuous model with the discrete vasculature model. We also discuss shared-memory based parallelization of the isogeometric L2 projections solver, using the GALOIS framework [1]. We conclude the presentation with the two-dimensional numerical results from [2], and preliminary parallel three-dimensional results. [1] Marcin Los, Maciej Wozniak, Maciej Paszynski, Andrew Lenharth, Muhamm Amber Hassaan, Keshav Pingali, IGA-ADS : Isogeometric Analysis FEM using ADS solver, Computers & Physics Communications (2017) in press.DOI:10.1016/j.cpc.2017.02.023 [2] Marcin Los, Maciej Paszynski, Adrian Klusek, Witold Dzwinel, Application of fast isogeometric L2 projection solver for tumor growth simulations, Computer Methods in Applied Mechanics and Engineering, 316 (2017) 1257-1269