Practical Guide to Boundary Element Methods with the Software Library BEMLIB

Abstract

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Wetting and Contact Lines of Micrometer-Sized Ellipsoids

“…We derive the distortion field and the shape of the contact line from solution of the Laplace equation of capillarity for the interface height, h x; y 0 [7][8][9]. The latter was solved numerically using a boundary element method [17]. Basically, this method yields the deformation field around a given contact line, L. In our application, we start with an initial line, L 1 , along which we compute the distribution of contact angles, denoted as c L 1 .…”

Optimization of segmented linear Paul traps and transport of stored particles

“…An adequate choice of a numerical solving method is the Boundary Element Method (BEM) [52,53]. BEM is a fast and more accurate method compared to the Finite Element Method (FEM) or Finite Difference Method (FDM).…”

Emergence of flagellar beating from the collective behavior of individual ATP-powered dyneins

“…The velocity and force fields are related by a Green's function that has a singularity proportional to 1/r in three dimensions and ln(r) in two dimensions [69]. The expression of Green's function (G) for the Stokeslets relates the velocity at location r,u, to the forces at location r′, f , throughu = Gf and G ij = 1 4πµ…”

“…A-10 is used to evaluate the velocity in all nodes of the flagellum, we obtain a system of equationsU = G f t that relates the traction t exerted by the flagellum on the fluid to it's velocityU . The integration procedure is adopted from the literature [69]. Once the velocity of the solid surface is known, this relation can be inverted to obtain the nodal tractions: t = G −1 fU .…”