Local and Parallel Mixed‐Precision Finite Element Methods for the Time‐Dependent Incompressible Flows

ABSTRACT In this article, a local and parallel mixed‐precision finite element method is applied for solving the time‐dependent incompressible flows. We decompose the solution into the large eddy components and small eddy components based on two‐grid method. The analysis shows that the small eddy components carry little part of the total energy compared with the large eddy components. In view of this character, we first obtain the large eddy components by solving the standard nonlinear equation using the high‐precision solvers globally in the coarse mesh space, then get the small eddy components by solving a series of local linearized residual equation using the low‐precision solvers locally and parallel based on the partition of unity. The performance advantages of the mixed‐precision methods are tested with respect to speedups over a high‐precision implementation in time and less storage requirements in space.