Improving the performance of regularized Stokeslet simulations using linearly implicit integrators

Using the test problem of a flexible, undulating filament in a viscous fluid, we explore the computational performance of different time integrators in regularized Stokeslet simulations. While explicit integrators are commonly used, stability considerations require prohibitively small time steps. While fully implicit methods have no such restrictions, these require the solution of nonlinear equations at each time step. To address these difficulties, here we consider both Rosenbrock and Implicit-Explicit (IMEX) methods, which are linearly implicit integrators. Using these methods, we have achieved approximately 50 times speedup in simulation timings compared to explicit methods. We will discuss these successes, as well as challenges and directions of further improvements.