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In this paper, we present a novel numerical scheme for simulating deformableand extensible capsules suspended in a Stokesian fluid. The main feature of ourscheme is a partition-of-unity (POU) based representation of the surface thatenables asymptotically faster computations compared to spherical-harmonicsbased representations. We use a boundary integral equation formulation torepresent and discretize hydrodynamic interactions. The boundary integrals areweakly singular. We use the quadrature scheme based on the regularized Stokeskernels. We also use partition-of unity based finite differences that arerequired for the computational of interfacial forces. Given an N-point surfacediscretization, our numerical scheme has fourth-order accuracy and O(N)asymptotic complexity, which is an improvement over the O(N^2 log(N))complexity of a spherical harmonics based spectral scheme that usesproduct-rule quadratures. We use GPU acceleration and demonstrate the abilityof our code to simulate the complex shapes with high resolution. We studycapsules that resist shear and tension and their dynamics in shear andPoiseuille flows. We demonstrate the convergence of the scheme and compare withthe state of the art.

Numerical simulation of an extensible capsule using regularized Stokes kernels and overset finite differences