Implicit interface boundary integral methods

Series: 
Applied and Computational Mathematics Seminar
Friday, March 13, 2015 - 14:00
1 hour (actually 50 minutes)
Location: 
Skiles 168
,  
University of Texas at Austin
I will present a new approach for computing boundary integrals that are defined on implicit interfaces, without the need of explicit parameterization. A key component of this approach is a volume integral which is identical to the integral over the interface. I will show results applying this approach to simulate interfaces that evolve according to Mullins-Sekerka dynamics used in certain phase transition problems. I will also discuss our latest results in generalization of this approach to summation of unstructured point clouds and regularization of hyper-singular integrals.