"High-order Fast Integral Equation Methods for PDEs with moving interfaces"

Shravan Veerapaneni
 Ph.D. Candidate
Advisor: Prof. George Biros
Department of Mechanical Engineering and Applied Mechanics
University of Pennsylvania

Abstract
Vesicles are locally-inextensible closed membranes that possess tension and bending energies. Vesicle flows model numerous biophysical phenomena that involve deforming particles interacting with a Stokesian fluid. For instance, they are used to model red blood cell motion and the transport of drug-carrying capsules.  While conventional techniques can be used to simulate isolated vesicles, new approaches are needed for large number of interacting vesicles. Integral equation methods are attractive for these problems as they avoid the need for volume mesh generation and re-meshing. They lead to a system of nonlinear integro-differential equations whose unknowns reside on the fluid-vesicle interfaces. We have developed a novel numerical scheme for such equations. The scheme is high-order accurate and achieves optimal algorithmic complexity.  It incorporates a new time-stepping scheme that allows much larger time-steps than the existing explicit schemes. The associated linear systems are solved in optimal time using spectral preconditioners, FFTs and the fast multipole method. We present numerical results that demonstrate the effectiveness of our scheme.

Thursday, November 29th
337 Towne Bldg.
2:00 PM