Speaker
Svetlana Tlupova, Frarmingdale State University
Abstract
We will give an overview of joint work with J. Thomas Beale on numerical methods for computing the single and double layer integrals on closed surfaces in Stokes flow. The Stokeslet and stresslet kernels are singular when evaluated on the surface and nearly singular when evaluated near the surface, which is the most difficult case to compute accurately. The kernels are regularized, or smoothed out, using a length scale parameter, so that a standard quadrature can be used. Corrections for the smoothing error can be derived analytically using local analysis. As a simpler approach, an extrapolation strategy is to compute the regularized integral for several choices of the smoothing parameter and solve for the extrapolated value of the integral with a higher order of accuracy. For evaluation on the surface, as needed when solving integral equations, special smoothing can be used so that high accuracy is obtained without needing corrections or extrapolation. In recent work, we derive formulas to regularize the integrals with high accuracy both on and off the surface without the need to extrapolate. We also present a method for obtaining values at all grid points from those near the surface in an efficient way based on the technique of A. Mayo.