Regularized Stokeslet segments

We present a variation of the method of regularized Stokeslet (MRS) specialized for the case of forces and torques distributed over filaments in three dimensions. The new formulation is based on the exact solution of Stokes equation generated by a linear continuous distribution of regularized forces along a line segment. Therefore, a straight filament with linearly varying forces does not require discretization. A general filament is approximated by a piecewise linear curve in three dimensions where the length of each line segment is chosen only based on the variation of the force field and the desired accuracy of its piecewise linear approximation. The most significant advantage of this formulation is that the values of the regularization parameter ϵ and the length of the segments h are decoupled as long as ϵ