CAM colloquium - Friday, January 25, 2008
3:30 p.m.
655 Rhodes Hall
Speaker: George Biros, University of Pennsylvania
Title: Fast algorithms for Stokesian particulate flows
Abstract: The Stokes equations model the motion
of a viscous incompressible fluid that has negligible inertia. Particulate
flow models regard the interaction of a fluid with rigid or deformable
particles. Stokesian particulate flow models are used extensively
in many applications in science, engineering, and medicine. Examples
include modeling of dynamics of bubbles and droplets, blood flow,
particle deposition in the lungs, and the dynamics of intra-cellular
and extra-cellular vesicles. We are interested in developing fast
algorithms for such problems.
In the first part of my talk, I will describe a fast solver for
Stokes fluids interacting with rigid particles. The basic goal in
designing a numerical method is the ability to guarantee certain accuracy
levels in reasonable time. The main difficulties are related to robust
mesh generation for three dimensional complex geometries and to the
efficient solution of the associated linear systems. I present a method
that is based on a classical Fredholm integral equation formulation.
The main components of the new method are a kernel-independent fast
summation method, a manifold surface representation, and a superalgebraically
accurate quadrature method.
In the second part of my talk, I will discuss an extension of these
methods to the time evolution of fluid membranes immersed in a Stokesian
fluid. Fluid membranes are area-preserving interfaces that resist
in bending. They are common in biophysics as they model cell membranes,
vesicles, and viral particles. I will discuss time-stepping and stability
restrictions, and present numerical results that demonstrate the effectiveness
of the overall algorithm.
This is join work with Shravan K. Veerapaneni (University of Pennsylvania),
Denis Zorin (New York University), and Lexing Ying (University of
Texas at Austin)
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Short Bio
George Biros is an assistant professor in Mechanical Engineering and
Applied Mechanics, and Computer and Information Science at the University
of Pennsylvania. He received his BS in Mechanical Engineering from
Aristotle University Greece (1995), his MS in Biomedical Engineering
from Carnegie Mellon (1996), and his PhD in Computational Science
and Engineering also from Carnegie Mellon (2000). He joined Penn in
2003 after serving as a postdoctoral associate at the Courant Institute
of Mathematical Sciences at New York University. He is affiliated
with the Computer Science Research Institute (CSRI) at Sandia National
Laboratories.
Refreshments at 4:30 in 657 Rhodes Hall.