A scalable O(N) computational framework for spheres in Stokes and Laplace fields

The balance of flexibility, accuracy, and efficiency is one long-standing topic in the design and implementation of computational tool. Based on recent advances in Boundary Integral Equation (BIE) theories, we developed a software framework which fits modern computers and inherits the flexibility of BIE. Further, this framework is spectrally accurate because spherical harmonics are used and special formulas are derived for close pairs. Due to such accuracy, lubrication effects can be directly resolved. This framework is also coupled to a new collision resolving algorithm formulated as a solution to a linear complementarity problem, to guarantee the stability of time stepping at large timestep sizes. We demonstrate the capability of this framework in sedimentation and other problems.