A Scalable Domain Decomposition Method for Ultra-Parallel Arterial Flow Simulations †

Ultra-parallel flow simulations on hundreds of thousands of processors re- quire new multi-level domain decomposition methods. Here we present such a new two-level method that has features both of discontinuous and continuous Galerkin formulations. Specifically, at the coarse level the domain is subdivided into several big patches and within each patch a spectral element discretization (fine level) is em- ployed. New interface conditions for the Navier-Stokes equations are developed to connect the patches, relaxing the C 0 continuity and minimizing data transfer at the patch interface. We perform several 3D flow simulations of a benchmark problem and of arterial flows to evaluate the performance of the new method and investigate its accuracy.

[1]  Michael E. Papka,et al.  Simulating and visualizing the human arterial system on the TeraGrid , 2006, Future Gener. Comput. Syst..

[2]  Thomas J. R. Hughes,et al.  A multiscale discontinuous Galerkin method with the computational structure of a continuous Galerkin method , 2006 .

[3]  I. Bica,et al.  Iterative substructuring algorithms for the p-version finite element method for elliptic problems , 1997 .

[4]  Mengping Zhang,et al.  AN ANALYSIS OF THREE DIFFERENT FORMULATIONS OF THE DISCONTINUOUS GALERKIN METHOD FOR DIFFUSION EQUATIONS , 2003 .

[5]  Suchuan Dong,et al.  Dual-level parallelism for high-order CFD methods , 2004, Parallel Comput..

[6]  Robert Michael Kirby,et al.  Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems , 2005, J. Sci. Comput..

[7]  Bernardo Cockburn.  Discontinuous Galerkin methods , 2003 .

[8]  G. Karniadakis,et al.  Spectral/hp Element Methods for CFD , 1999 .

[9]  Spencer J. Sherwin,et al.  Parallel performance of the coarse space linear vertex solver and low energy basis preconditioner for spectral/hp elements , 2009, Parallel Comput..

[10]  Martin J. Gander,et al.  A new cement to glue nonconforming grids with Robin interface conditions: the finite element case. Domain decomposition methods in science and engineering , 2005 .

[11]  S. Orszag,et al.  High-order splitting methods for the incompressible Navier-Stokes equations , 1991 .

[12]  M. A. Casarin,et al.  Low-energy basis preconditioning for elliptic substructured solvers based on unstructured spectral/ hp element discretization , 2001 .

[13]  George Em Karniadakis,et al.  Nεκταr code: Dynamic simulations without remeshing , 1999 .