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In transient simulations of particulate Stokes flow, to accurately capture the interaction between the constituent particles and the confining wall, the discretization of the wall often needs to be locally refined in the region approached by the particles. Consequently, standard fast direct solvers lose their efficiency since the linear system changes at each time step. This manuscript presents a new computational approach that avoids this issue by pre-constructing a fast direct solver for the wall ahead of time, computing a low-rank factorization to capture the changes due to the refinement, and solving the problem on the refined discretization via a Woodbury formula. Numerical results illustrate the efficiency of the solver in accelerating particulate Stokes simulations. [ABSTRACT FROM AUTHOR]

This article presents a new boundary integral approach for finding optimal shapes of peristaltic pumps that transport a viscous fluid. Formulas for computing the shape derivatives of the standard cost functionals and constraints are derived. They involve evaluating physical variables (traction, pressure, etc.) on the boundary only. By employing these formulas in conjunction with a boundary integral approach for solving forward and adjoint problems, we completely avoid the issue of volume remeshing when updating the pump shape as the optimization proceeds. This leads to significant cost savings and we demonstrate the performance on several numerical examples. [ABSTRACT FROM AUTHOR]

We present a novel computational framework for the simulation of rigid spherical Janus particle suspensions in Stokes flow. For a wide array of Janus particle types, we show long-range interactions may be resolved using fast, spectrally accurate boundary integral methods. We incorporate this to our rigid body Stokes platform, which resolves hydrodynamic interactions and contact. Our approach features the use of spherical harmonic expansions for spectrally accurate integral operator evaluation, complementarity-based collision resolution, and optimal O (n) scaling with the number of particles when accelerated via fast summation techniques. We demonstrate the versatility of our simulation platform through three test cases involving Janus particle systems prominent in applications: amphiphilic, bipolar electric and phoretic particles. For each test case, we formulate Janus particle interactions in boundary integral form and use our framework to demonstrate examples of self-assembly and complex collective behavior characteristic of these systems. [ABSTRACT FROM AUTHOR]