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- Title: Efficient Convergent Boundary Integral Methods for Slender Bodies
- Abstract: 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, I will present new quadrature schemes
- which make such computations possible and new integral equation formulations
- which lead to well-conditioned linear systems upon discretization. I will
- present numerical results to show the efficiency of our methods.
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