A scalable time-parallel spectral Stokes solver for biological flows

Simulation of unsteady creeping flows in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. To reduce the cost and allow for computations at much larger scales, we propose an alternative approach that is formulated based on the unsteady Stokes equation expressed in the time-spectral domain. This advantages of this new formulation is that 1) it resolves time-variation of the solution using a few modes rather than thousands of time steps, thus offering significant saving in cost and time-to-solution, 2) it exhibits a super convergence behavior versus the number of computed modes, and 3) it is embarrassingly parallelizable owing to the independence of the solution modes, thus enabling scalable calculations at a much larger number of processors. The comparison of the proposed technique against a standard stabilized finite element solver is performed using two- and three-dimensional canonical and complex geometries. The results show that the proposed method can produce more accurate results at 1\% to 11\% of the cost of the standard technique for the studied cases.