2020/02/22 by Richter, Thomas, Mizerski, Jeremi
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2002.09705
We describe a temporal multiscale approach for the simulation of long-term processes with short-term influences involving partial differential equations. The specific problem under consideration is a growth process in blood vessels. The Candy Wrapper Process describes a restenosis in a vessel that has previously be widened by inserting a stent. The development of a new stenosis takes place on a long time horizon (months) while the acting forces are mainly given by the pulsating blood flow. We describe a coupled pde model and a finite element simulation that is used as basis for our multiscale approach, which is based on averaging the long scale equation and approximating the fast scale impact by localized periodic-in-time problems. Numerical test cases in prototypical 3d configurations demonstrate the power of the approach.