% Title: A Fast Convergent Boundary Integral Framework for Slender Bodies

The dynamics of active and passive filaments in viscous fluids is frequently
used as a model for many complex fluids in biological systems such as:
microtubules which are involved in intracellular transport and cell division;
flagella and cilia which aid in locomotion. The numerical simulation of such
systems is generally based on slender-body theory which give asymptotic
approximations of the solution. However, these methods are low-order and cannot
enforce no-slip boundary conditions to high-accuracy, uniformly over the
boundary. Boundary-integral equation methods which completely resolve the fiber
surface have so far been impractical due to the prohibitive cost of current
layer-potential quadratures for such high aspect-ratio geometries. In this talk,
we will present new quadrature schemes which make such computations possible and
new integral equation formulations which lead to well-conditioned linear systems
upon discretization. WE will present numerical results to show the efficiency of
our methods.





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