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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]

We present a framework using the Quantized Tensor Train ( qtt ) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the qtt decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage costs of the inversion scheme are extremely modest O ( log ⁡ N ) and once the inverse is computed, it can be applied in O ( N log ⁡ N ) . We analyze the qtt ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as fmm and hss . We prove that the qtt ranks are bounded for translation-invariant systems and argue that this behavior extends to non-translation invariant volume and boundary integrals. For volume integrals, the qtt decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers. We present results demonstrating the remarkable performance of the qtt -based solver when applied to both translation and non-translation invariant volume integrals in 3d . For boundary integral equations, we demonstrate that using a qtt decomposition to construct preconditioners for a Krylov subspace method leads to an efficient and robust solver with a small memory footprint. We test the qtt preconditioners in the iterative solution of an exterior elliptic boundary value problem (Laplace) formulated as a boundary integral equation in complex, multiply connected geometries. [ABSTRACT FROM AUTHOR]

• Collision resolution by convex quadratic programming. • Scalable and efficient parallel algorithm and implementation. • Accurate second-kind boundary integral formulation. We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle collisions. This algorithm extends the well-known complementarity method for non-smooth multi-body dynamics to resolve collisions in dense rigid body suspensions. This approach formulates the collision resolution problem as a linear complementarity problem with geometric 'non-overlapping' constraints imposed at each time-step. It is then reformulated as a constrained quadratic programming problem and the Barzilai-Borwein projected gradient descent method is applied for its solution. This framework is designed to be applicable for any convex particle shape, e.g., spheres and spherocylinders, and applicable to any Stokes mobility solver, including the Rotne-Prager-Yamakawa approximation, Stokesian Dynamics, and PDE solvers (e.g., boundary integral and immersed boundary methods). In particular, this method imposes Newton's Third Law and records the entire contact network. Further, we describe a fast, parallel, and spectrally-accurate boundary integral method tailored for spherical particles, capable of resolving lubrication effects. We show weak and strong parallel scalings up to 8 × 10 4 particles with approximately 4 × 10 7 degrees of freedom on 1792 cores. We demonstrate the versatility of this framework with several examples, including sedimentation of particle clusters, and active matter systems composed of ensembles of particles driven to rotate. [ABSTRACT FROM AUTHOR]