Mathematical Sciences - Harold J. Gay Lecture Series - "Asymptotic coupling of models of different dimensions: MAPDD" by Dr. Grigory Panasenko (Institute Camille Jordan, University of Lyon, France)

Friday, April 06, 2018
4:00 pm to 5:30 pm
Floor/Room #: 
116

Dr. Grigory Panasenko
Institute Camille Jordan,
University of Lyon, France

TITLE:
Asymptotic coupling of models of different dimensions: MAPDD

ABSTRACT: 
The lecture is devoted to the problem of coupling of models of
different dimension. Many real-world problems are related to
solving partial differential equations in domains of complex
geometry, combining multiple thin parts with massive parts:
the set of blood vessels, structures in aircraft and spacecraft,
industrial installations, pipelines with reservoirs. The direct
numerical computations with standard codes are impossible
because such complex geometry needs a very fine mesh “feeling”
all elements of the structure and so the 3D computations need
too much time-memory resources. That is why the dimension
reduction is a very popular trend in reducing computational cost;
however, the completely reduced models lose very important
local information and are not precise. For example, in the blood
circulation modeling one-dimensional models are widely applied
but the description of the clot formation and blood flow near a
stent needs 3D local zoom. How to glue the models of different
dimension? The lecture presents an asymptotic approach to this
problem, based on asymptotic analysis of partial differential
equations in domains containing thin parts and connected sets of
thin cylinders. For example the Navier-Stokes equations are used
in hemodynamic modeling. We present the method of partial
asymptotic decomposition of domains (MAPDD) giving a high
precision coupling of models of different dimension.