Abstract. Dense particulate flow simulations using integral equation methods demand accurate evaluation of Stokes layer potentials on arbitrarily close interfaces. In this paper, we generalize techniques for close evaluation of Laplace double-layer potentials in J. Helsing and R. Ojala, J. Comput. Phys. 227 (2008) 2899-2921. We create a "globally compensated" trapezoid rule quadrature for the Laplace single-layer potential on the interior and exterior of smooth curves. This exploits a complex representation, a product quadrature (in the style of Kress) for the sawtooth function, careful attention to branch cuts, and second-kind barycentric-type formulae for Cauchy integrals and their derivatives. Upon this we build accurate single-and double-layer Stokes potential evaluators by expressing them in terms of Laplace potentials. We test their convergence for vesicle-vesicle interactions, for an extensive set of Laplace and Stokes problems, and when applying the system matrix in a boundary value problem solver in the exterior of multiple close-to-touching ellipses. We achieve typically 12 digits of accuracy using very small numbers of discretization nodes per curve. We provide documented codes for other researchers to use.

We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex-possibly nonsmooth-geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of evaluating weakly-singular, nearly-singular and hyper-singular integrals to high accuracy. Near-singular integral evaluation, in particular, is done using an extension of the scheme developed in J. Helsing and R. Ojala, J. Comput. Phys. 227 (2008) 2899-2921. The boundary of the given geometry is "panelized" automatically to achieve user-prescribed precision. We show that this adaptive panel refinement procedure works well in practice even in the case of complex geometries with large number of corners. In one example, for instance, a model 2D vascular network with 378 corners required less than 200K discretization points to obtain a 9-digit solution accuracy.

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The electrohydrodynamics of vesicle suspensions is characterized by studying their pairwise interactions in applied DC electric fields in two dimensions. In the dilute limit, the rheology of the suspension is shown to vary nonlinearly with the electric conductivity ratio of the interior and exterior fluids. The prolate-oblate-prolate transition and other transitionary dynamics observed in experiments and previously confirmed via numerical simulations is further investigated here for smaller reduced areas. When two vesicles are initially un-aligned with the external electric field, three different responses are observed when the key parameters are varied: (i) chain formation-they self-assemble to form a chain that is aligned along the field direction, (ii) circulatory motion-they rotate about each other, (iii) oscillatory motion-they form a chain but oscillate about each other.