Accelerated Boundary Element Method for 3D Simulations of Bubble Cluster Dynamics in an Acoustic Field

In this study, we develop a numerical approach based on the fast multipole method (FMM) to accelerate the iterative solution of the boundary element method (BEM) for bubble dynamics in the presence of an acoustic field. The FMM for 3D Laplace equation is accelerated by applying heterogeneous hardware, including multi-core CPUs and graphics processors. Problems of mesh stabilization are resolved by using a shape filter based on the spherical harmonic expansions of the bubble surface. We discuss the accuracy and performance of the algorithm. We demonstrate that the approach enables the simulation of the dynamics of regular monodisperse bubble clusters with thousands of bubbles and millions of boundary elements on modern personal workstations. The algorithm is scalable and can be extended to larger systems.