Integrating an N-Body Problem with SDC and PFASST
Vortex methods for the Navier–Stokes equations are based on a Lagrangian particle discretization, which reduces the governing equations to a first-order initial value system of ordinary differential equations for the position and vorticity of N particles. In this paper, the accuracy of solving this system by time-serial spectral deferred corrections (SDC) as well as by the time-parallel Parallel Full Approximation Scheme in Space and Time (PFASST) is investigated. PFASST is based on intertwining SDC iterations with differing resolution in a manner similar to the Parareal algorithm and uses a Full Approximation Scheme (FAS) correction to improve the accuracy of coarser SDC iterations. It is demonstrated that SDC and PFASST can generate highly accurate solutions, and the performance in terms of function evaluations required for a certain accuracy is analyzed and compared to a standard Runge–Kutta method.
KeywordsQuadrature Point Vortex Method Kutta Scheme Parallel Efficiency Quadrature Node
This research is partly funded by the Swiss “High Performance and High Productivity Computing” initiative HP2C; the Director, DOE Office of Science, Office of Advanced Scientific Computing Research, Office of Mathematics, Information, and Computational Sciences, Applied Mathematical Sciences Program, under contract DE-SC0004011; and the ExtreMe Matter Institute (EMMI) in the framework of the German Helmholtz Alliance HA216. Computing resources were provided by Jülich Supercomputing Centre under project JZAM04.
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