My research focuses on developing fast integral equation methods for elliptic BVP with variable coefficients.
is a state-of-the-art library for computing particle and volume potentials. For volume potentials, we use high order piecewise polynomial discretization on adaptive octrees and precomputed operators for computing near-interactions. Far-field interactions are computed using the KIFMM. It includes several new performance optimizations, support for GPU accelerators and distributed memory parallelism. It is one of the fastest libraries for computing solutions of elliptic PDEs on the unit cube with free-space and periodic boundary conditions.
We use the PVFMM library along with iterative linear solvers to solve volume integral equation (VIE) formulations of variable coefficient elliptic PDEs.
Implemented algorithms for near-singular integration, collision handling and adaptive time-stepping to allow accurate, long time-scale simulations of concentrated vesicle suspensions in periodic flows.