Annual Report 2008.pdf - SAMSI

9:35 – 10:10 John Strain, University of California, Berkeley
“Elliptic Systems and Moving Interfaces”
10:10 – 10:40 Coffee Break
10:40 – 11:15 Robert Dillion, Washington State University
“An Integrative Model of Internal Axoneme Mechanics and External Fluid
Dynamics in Sperm Motility”
11:15 - 11:50 Guowei He, Iowa State University
“A Hybrid Approach of Large-Eddy Simulation and Immersed Boundary
for Flapping Wings at Moderate Reynolds Numbers”
11:50 - 1:00 Lunch
1:00 – 1:35 David Chopp, Northwestern University
“Modeling and Simulation of Bacterial Biofilms”
1:35 – 2:10 Richard Tsai, University of Texas, Austin
“Redistancing by Flow of Time Dependent Eikonal Equation”
2:10 – 2:45 Alina Chertock, North Carolina State University
“Interface-Tracking Method for Compressible Multifluids”
2:45 – 3:15 Coffee Break
3:15 – 4:00 Discussion Session
4:00 Workshop adjourns
SPEAKER ABSTRACTS
J. Thomas Beale
Duke University
Department of Mathematics
beale@math.duke.edu
“Computing with Singular and Nearly Singular Integrals”
We will describe a simple, direct approach to computing a singular or nearly singular integral,
such as a harmonic function given by a layer potential on a curve in 2D or a surface in 3D. This
approach could be useful for moving interfaces since the representation of the interface requires
less work than elements. The value is found by a standard quadrature, using a regularized form
of the singularity, with correction terms added for the errors due to regularization and
discretization. These corrections are found by local analysis near the singularity. The accurate
evaluation of a layer potential near the curve or surface on which it is defined is not routine,
since the integral is nearly singular. For a surface in 3D, integrals are computed in overlapping