  We propose a novel integral model describing the motion of curved slender
fibers in viscous flow, and develop a numerical method for simulating dynamics
of rigid fibers. The model is derived from nonlocal slender body theory (SBT),
which approximates flow near the fiber using singular solutions of the Stokes
equations integrated along the fiber centerline. In contrast to other models
based on (singular) SBT, our model yields a smooth integral kernel which
incorporates the (possibly varying) fiber radius naturally. The integral
operator is provably negative definite in a non-physical idealized geometry, as
expected from PDE theory. This is numerically verified in physically relevant
geometries. We propose a convergent numerical method for solving the integral
equation and discuss its convergence and stability. The accuracy of the model
and method is verified against known models for ellipsoids. Finally, a fast
algorithm for computing dynamics of rigid fibers with complex geometries is
developed.
