Parallel-in-time methods have become increasingly popular in the simulation of numerical PDEs . Most methods treat the solution and parallelism in space and time separately . In contrast, all-at-once methods solve the full space-time system directly, largely treating time as another spatial dimension . The new method is tested on fourclassical models in incompressible flow . Results indicate perfect scalability in refinement of spatial and temporal mesh spacing, perfect . scalability innonlinear Picard iterations count when applied to a nonlinear Navier-Stokesproblem, and minimal overhead in terms of number of . preconditioner applicationscompared with sequential time-stepping . to the space-to-solution (when applicable). The new . method was tested on 4classical . models in . incompressable flow. Results indicate . the new method was test on four classical models with fourclassicals models incompressible models in the .

Author(s) : Federico Danieli, Ben S. Southworth, Andrew J. Wathen

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Keywords : time - models - space - flow - methods -

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