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Wednesday, July 29 • 4:00pm - 4:30pm
Distributed Memory Parallel Multigrid Solver for Growth and Self-Assembly of Crystalline Nanostructures

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Reproducing synthesizing and assembling arrays of nanostructures with controlled morphologies and compositions is very important in the study of nanostructured materials, which are basis of many breakthrough technologies. PFC-based models, which allow larger domains to be simulated comparing with the traditional approach, are widely used in this field. However, complicated systems involving gradient, nonlinearity and convolution presented in the governing equation pose the challenge to current state-of-the-art numerical and computational methods. Unconditional stable numerical algorithms and a highly efficient Fortran solver has been developed to address this problem. The solver is a combination of full approximation scheme (FAS) geometric multigrid solver and discrete Fourier transform (DFT) module using FFTW. The former is used to handle the nonlinear problem, and the later is used to calculate the convolution. In two-dimensional simulation, this solver is proved to be very successful. In the extension to three dimensional simulation, however, the scale for the degree of freedom we are interested in reaches trillion and higher. Thus high performance technique needs to be employed to accelerate the current solver. We employ the distributed memory parallelization on both modules through message passing interface (MPI). The multigrid module is paralleled by domain decomposition in all three dimensions (cube) with halo region. The DFT module take the advantage of the MPI interface of FFTW library, which also use the domain decomposition, but only for one dimension (slab). The new solver is installed on STAMPEDE and tested extensively. We studied the strong and weak scalability for both multigrid and FFTW modules, and the strong and weak scalability for the full solver. To our best knowledge, this is the first result in such field. Our results indicates that scalabilities for both multigrid and FFTW modules are both linear, indicating the strong potential for the solver. On the other hand, due to the difference between the domain decomposition dimensions, the scalability of the full solver is slightly less than optimal. Furthermore, this difference introduced an uneven memory distribution between worker processors, which needs to be treated properly.


Wednesday July 29, 2015 4:00pm - 4:30pm
Majestic C

Attendees (4)