51,139 research outputs found

    PoisFFT - A Free Parallel Fast Poisson Solver

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    A fast Poisson solver software package PoisFFT is presented. It is available as a free software licensed under the GNU GPL license version 3. The package uses the fast Fourier transform to directly solve the Poisson equation on a uniform orthogonal grid. It can solve the pseudo-spectral approximation and the second order finite difference approximation of the continuous solution. The paper reviews the mathematical methods for the fast Poisson solver and discusses the software implementation and parallelization. The use of PoisFFT in an incompressible flow solver is also demonstrated

    A Massive Data Parallel Computational Framework for Petascale/Exascale Hybrid Computer Systems

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    Heterogeneous systems are becoming more common on High Performance Computing (HPC) systems. Even using tools like CUDA and OpenCL it is a non-trivial task to obtain optimal performance on the GPU. Approaches to simplifying this task include Merge (a library based framework for heterogeneous multi-core systems), Zippy (a framework for parallel execution of codes on multiple GPUs), BSGP (a new programming language for general purpose computation on the GPU) and CUDA-lite (an enhancement to CUDA that transforms code based on annotations). In addition, efforts are underway to improve compiler tools for automatic parallelization and optimization of affine loop nests for GPUs and for automatic translation of OpenMP parallelized codes to CUDA. In this paper we present an alternative approach: a new computational framework for the development of massively data parallel scientific codes applications suitable for use on such petascale/exascale hybrid systems built upon the highly scalable Cactus framework. As the first non-trivial demonstration of its usefulness, we successfully developed a new 3D CFD code that achieves improved performance.Comment: Parallel Computing 2011 (ParCo2011), 30 August -- 2 September 2011, Ghent, Belgiu

    Solving the Klein-Gordon equation using Fourier spectral methods: A benchmark test for computer performance

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    The cubic Klein-Gordon equation is a simple but non-trivial partial differential equation whose numerical solution has the main building blocks required for the solution of many other partial differential equations. In this study, the library 2DECOMP&FFT is used in a Fourier spectral scheme to solve the Klein-Gordon equation and strong scaling of the code is examined on thirteen different machines for a problem size of 512^3. The results are useful in assessing likely performance of other parallel fast Fourier transform based programs for solving partial differential equations. The problem is chosen to be large enough to solve on a workstation, yet also of interest to solve quickly on a supercomputer, in particular for parametric studies. Unlike other high performance computing benchmarks, for this problem size, the time to solution will not be improved by simply building a bigger supercomputer.Comment: 10 page

    Construction and Application of an AMR Algorithm for Distributed Memory Computers

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    While the parallelization of blockstructured adaptive mesh refinement techniques is relatively straight-forward on shared memory architectures, appropriate distribution strategies for the emerging generation of distributed memory machines are a topic of on-going research. In this paper, a locality-preserving domain decomposition is proposed that partitions the entire AMR hierarchy from the base level on. It is shown that the approach reduces the communication costs and simplifies the implementation. Emphasis is put on the effective parallelization of the flux correction procedure at coarse-fine boundaries, which is indispensable for conservative finite volume schemes. An easily reproducible standard benchmark and a highly resolved parallel AMR simulation of a diffracting hydrogen-oxygen detonation demonstrate the proposed strategy in practice

    A Fast Parallel Poisson Solver on Irregular Domains Applied to Beam Dynamic Simulations

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    We discuss the scalable parallel solution of the Poisson equation within a Particle-In-Cell (PIC) code for the simulation of electron beams in particle accelerators of irregular shape. The problem is discretized by Finite Differences. Depending on the treatment of the Dirichlet boundary the resulting system of equations is symmetric or `mildly' nonsymmetric positive definite. In all cases, the system is solved by the preconditioned conjugate gradient algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG) preconditioning. We investigate variants of the implementation of SA-AMG that lead to considerable improvements in the execution times. We demonstrate good scalability of the solver on distributed memory parallel processor with up to 2048 processors. We also compare our SAAMG-PCG solver with an FFT-based solver that is more commonly used for applications in beam dynamics
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