A Scalable Parallel Poisson Solver in Three Dimensions with Infinite-Domain Boundary Conditions

McCorquodale, Peter; Colella, Phillip; Balls, Gregory T.; Baden, Scott B.

doi:10.1109/icppw.2005.17

Cited by 8 publications

(6 citation statements)

References 17 publications

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“…Second, because of the singularity of the Green's functions at r = r , special quadrature schemes must be designed to obtain high accuracy. In the last two decades, numerical schemes have been developed to address both difficulties in an efficient manner, even for cases where the charge distribution ρ is highly inhomogeneous and requires adaptive discretization [9][10][11][12] .…”

Section: Motivationmentioning

confidence: 99%

FFT-based free space Poisson solvers: why Vico-Greengard-Ferrando should replace Hockney-Eastwood

Zou,

Kim,

Cerfon

2021

Preprint

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Section: Motivationmentioning

confidence: 99%

FFT-based free space Poisson solvers: why Vico-Greengard-Ferrando should replace Hockney-Eastwood

Zou,

Kim,

Cerfon

2021

Preprint

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“…To model beam problems, the Poisson equation with infinite domain boundary conditions needs to be solved. We compute the solution using a new version of the James-Lackner method [20] by McCorquodale et al [23,24]. This method solves two Dirichlet boundary problems plus a boundary to boundary convolution.…”

Section: Solving the Poisson Equation With Infinite Domain Boundary C...mentioning

confidence: 99%

An Adaptive, High-Order Phase-Space Remapping for the Two Dimensional Vlasov--Poisson Equations

Wang¹,

Miller²,

Colella³

2012

SIAM J. Sci. Comput.

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The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the distribution function in phase space. To control the numerical error, we introduce an adaptive phase-space remapping which regularizes the particle distribution by periodically reconstructing the distribution function on a hierarchy of phase-space grids with high-order interpolations. The positivity of the distribution function can be preserved by using a local redistribution technique. The method has been successfully applied to a set of classical plasma problems in one dimension. In this paper, we present the algorithm for the two dimensional Vlasov-Poisson equations. An efficient Poisson solver with infinite domain boundary conditions is used. The parallel scalability of the algorithm on massively parallel computers will be discussed.

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“…It uses a new algorithm based on the method of James [5] for solving on infinite domains, combined with a Method of Local Corrections by Balls and Colella [6] for high performance on larger parallel computers. The algorithm and implementation of this solver is described in detail in [7]. The computational cost for this method is dominated by the convolution.…”

Section: Solving Poisson's Equationmentioning

confidence: 99%

Advanced 3D Poisson solvers and particle-in-cell methods for accelerator modeling

Serafini¹,

McCorquodale²,

Colella³

2005

J. Phys.: Conf. Ser.

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We seek to improve on the conventional FFT-based algorithms for solving the Poisson equation with infinite-domain (open) boundary conditions for large problems in accelerator modeling and related areas. In particular, improvements in both accuracy and performance are possible by combining several technologies: the method of local corrections (MLC); the James algorithm; and adaptive mesh refinement (AMR). The MLC enables the parallelization (by domain decomposition) of problems with large domains and many grid points. This improves on the FFT-based Poisson solvers typically used as it doesn't require the all-to-all communication pattern that parallel 3d FFT algorithms require, which tends to be a performance bottleneck on current (and foreseeable) parallel computers. In initial tests, good scalability up to 1000 processors has been demonstrated for our new MLC solver. An essential component of our approach is a new version of the James algorithm for infinite-domain boundary conditions for the case of three dimensions. By using a simplified version of the fast multipole method in the boundary-to-boundary potential calculation, we improve on the performance of the Hockney algorithm typically used by reducing the number of grid points by a factor of 8, and the CPU costs by a factor of 3. This is particularly important for large problems where computer memory limits are a consideration. The MLC allows for the use of adaptive mesh refinement, which reduces the number of grid points and increases the accuracy in the Poisson solution. This improves on the uniform grid methods typically used in PIC codes, particularly in beam problems where the halo is large. Also, the number of particles per cell can be controlled more closely with adaptivity than with a uniform grid. To use AMR with particles is more complicated than using uniform grids. It affects depositing particles on the non-uniform grid, reassigning particles when the adaptive grid changes and maintaining the load balance between processors as grids and particles move. New algorithms and software are being developed to solve these problems efficiently. We are using the Chombo AMR software framework as the basis for this work.

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A Scalable Parallel Poisson Solver in Three Dimensions with Infinite-Domain Boundary Conditions

Cited by 8 publications

References 17 publications

FFT-based free space Poisson solvers: why Vico-Greengard-Ferrando should replace Hockney-Eastwood

FFT-based free space Poisson solvers: why Vico-Greengard-Ferrando should replace Hockney-Eastwood

An Adaptive, High-Order Phase-Space Remapping for the Two Dimensional Vlasov--Poisson Equations

Advanced 3D Poisson solvers and particle-in-cell methods for accelerator modeling

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