A Fast Poisson Solver Amenable to Parallel Computation

Buzbee, B.L.

doi:10.1109/tc.1973.5009160

Cited by 38 publications

(10 citation statements)

References 4 publications

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“…A parallelization of the solution of the Poisson equation using fast Fourier transforms was proposed in a number of publications [36,37,38]. Recently, an application using such a parallel algorithm for the solver of the GradShafranov equation has been successfully implemented.…”

Section: Unbounded Domainmentioning

confidence: 99%

A data acquisition system for real-time magnetic equilibrium reconstruction on ASDEX Upgrade and its application to NTM stabilization experiments

Giannone

Reich

Maraschek

et al. 2013

Fusion Engineering and Design

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The pre-emptive stabilization of a neoclassical tearing mode, NTM, requires the calculation of the tokamak magnetic equilibrium in real-time. A launcher mirror is positioned to deposit electron cyclotron current drive on the rational surface where the NTM should appear. A real-time Grad-Shafranov solver using constraints from magnetic probe, flux loop and Motional Stark Effect measurements has been developed to locate these rational surfaces and deliver this information to the mirror controller in real-time. A novel algorithm significantly reduces the number of operations required in the first and second step of the solver. Contour integrals are carried out to calculate the q profile as a function of normalized radius and the rational surfaces are found by spline interpolation. A cycle time of 0.6 ms for calculating two tokamak equilibria in parallel using four current basis functions with magnetic constraints only and using six current basis functions with magnetic and MSE constraints has been achieved. Using these tools, pre-emptive stabilization

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Section: Unbounded Domainmentioning

confidence: 99%

A data acquisition system for real-time magnetic equilibrium reconstruction on ASDEX Upgrade and its application to NTM stabilization experiments

Giannone

Reich

Maraschek

et al. 2013

Fusion Engineering and Design

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“…It is written in dimensionless quantities T = 2π k B T E J , τ = (2eI c R n /h)t. Then, at each timestep a linear system has to be solved of size N 2 . This is done using the fast Poisson solver technique which is described in Appendix B [24]. Furthermore, the computation was done on a GPU for which this algorithm is well suited.…”

Section: Methodsmentioning

confidence: 99%

Annealed Low Energy States in Frustrated Large Square Josephson Junction Arrays

et al. 2018

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Numerical simulations were done to find low energy states in frustrated large square Josephson Junction arrays in a perpendicular magnetic field using simulated annealing on the coupled RSJ model. These simulations were made possible by a new algorithm suitable for parallel gpu computing and reduced complexity. Free boundary conditions were used so that values of the frustration factor f that are incommensurate with the array size are permitted. The resulting energy as a function of f is continuous with logarithmic discontinuities in the derivative dE/d f at rational frustration factors f = p/q with small q, substantiating the mathematical proof that this curve is continuous and further showing that the staircase state hypothesis is incorrect. The solution shows qualitative similarities with the lowest energy branch of the Hofstadter butterfly, which is a closely related problem. Furthermore, it is found that at the edge of an array there are either extra vortices or missing vortices depending the frustration factor, and the width of this region is independent of the array size.

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“…Buzbee [21] observed that Fourier analysis, or the matrix decomposition Poisson solver (MD-Poisson solver), is ideally suited for parallel computation. It consists of performing a set of independent sine transforms, and solving a set of independent tridiagonal systems.…”

Section: Mflopsmentioning

confidence: 99%

Parallel Algorithms for Dense Linear Algebra Computations

Gallivan¹,

Plemmons²,

Sameh³

1990

SIAM Rev.

167

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Scientific and engineering research is becoming increasingly dependent upon the development and implementation of efficient parallel algorithms on modern high-performance computers. Numerical linear algebra is an indispensable tool in such research and this paper attempts to collect and describe a selection of some of its more important parallel algorithms. The purpose is to review the current status and to provide an overall perspective of parallel algorithms for solving dense, banded, or block-structured problems arising in the major areas of direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers. A major emphasis is given here to certain computational primitives whose efficient execution on parallel and vector computers is essential in order to obtain high performance algorithms.

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A Fast Poisson Solver Amenable to Parallel Computation

Cited by 38 publications

References 4 publications

A data acquisition system for real-time magnetic equilibrium reconstruction on ASDEX Upgrade and its application to NTM stabilization experiments

A data acquisition system for real-time magnetic equilibrium reconstruction on ASDEX Upgrade and its application to NTM stabilization experiments

Annealed Low Energy States in Frustrated Large Square Josephson Junction Arrays

Parallel Algorithms for Dense Linear Algebra Computations

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