High order expanding domain methods for the solution of Poisson's equation in infinite domains

Anderson, Christopher R.

doi:10.1016/j.jcp.2016.02.074

Cited by 7 publications

(6 citation statements)

References 11 publications

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“…t/T = 1.9 t/T = 1.3 t/T = 1.1 t/T = 0.8 t/T = 0.6 t/T = 0.0 Figure 3: Isocontours of the vorticity magnitude from blue to red |ωb 2 1 /Γ 0 | = [1,4,8,12,16,20,24,28,32] at various times.…”

Section: Resultsmentioning

confidence: 99%

“…For a single free-space and one or more periodic boundary conditions, we note that solving the Poisson equation essentially reduces to solving a one-dimensional modified Helmholtz equation with free-space boundary conditions for each wave number set (when having Fourier transformed the problem in the period directions). A spectrally accurate procedure for doing this has been outlined in [23,24]. This procedure is not applicable when the system has more than one free-space condition.…”

Section: Introductionmentioning

confidence: 99%

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A regularization method for solving the Poisson equation for mixed unbounded-periodic domains

Spietz

Hejlesen

Walther

2018

Journal of Computational Physics

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A regularization method for solving the Poisson equation for mixed unbounded-periodic domains

Spietz

Hejlesen

Walther

2018

Journal of Computational Physics

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“…DDM: Applies the domain decomposition method described in section 2 to solve the Poisson equation with free boundary conditions. MOI: Calculates the electrostatic potential by means of the method of images, using (16).…”

Section: Sample Implementationmentioning

confidence: 99%

“…A different family of methods uses the convolution with Green's function subject to free boundary conditions. They manage the singular behaviour of Green's function by either regularizing it [15], or by replacing the singular component to the integrand of the convolution by an analytical contribution [16]. These methods have achieved an order of convergence greater than two.…”

Section: Introductionmentioning

confidence: 99%

A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges

Malagón-Romero¹,

Luque²

2018

Computer Physics Communications

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At high pressure electric discharges typically grow as thin, elongated filaments. In a numerical simulation this large aspect ratio should ideally translate into a narrow, cylindrical computational domain that envelops the discharge as closely as possible. However, the development of the discharge is driven by electrostatic interactions and, if the computational domain is not wide enough, the boundary conditions imposed to the electrostatic potential on the external boundary have a strong effect on the discharge. Most numerical codes circumvent this problem by either using a wide computational domain or by calculating the boundary conditions by integrating the Green's function of an infinite domain. Here we describe an accurate and efficient method to impose free boundary conditions in the radial direction for an elongated electric discharge. To facilitate the use of our method we provide a sample implementation. Finally, we apply the method to solve Poisson's equation in cylindrical coordinates with free boundary conditions in both radial and longitudinal directions. This case is of particular interest for the initial stages of discharges in long gaps or natural discharges in the atmosphere, where it is not practical to extend the simulation volume to be bounded by two electrodes.

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“…In previous studies, a number of efficient Poisson solvers have been developed in the community [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Those solvers will not handle transverse elliptical conducting pipe and longitudinally open or periodic boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Fast 3D Poisson solvers in elliptical conducting pipe for space-charge simulation

Qiang

2019

Phys. Rev. Accel. Beams

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Space-charge effects play an important role in high intensity accelerators. These effects can be studied self-consistently by solving the Poisson equation with the dynamically evolved charge density distribution subject to appropriate boundary conditions. In this paper, two computationally efficient methods are proposed to solve the Poisson equation inside an elliptical perfectly conducting pipe. One method uses a spectral method and the other uses a spectral finite difference method. The former method has a high accuracy and the latter one has a computational complexity of OðN logðNÞÞ, where N is the total number of unknowns. These methods implemented in a beam dynamics tracking code enable the fast simulation of space-charge effects in an accelerator with an elliptical conducting pipe.

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High order expanding domain methods for the solution of Poisson's equation in infinite domains

Cited by 7 publications

References 11 publications

A regularization method for solving the Poisson equation for mixed unbounded-periodic domains

A regularization method for solving the Poisson equation for mixed unbounded-periodic domains

A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges

Fast 3D Poisson solvers in elliptical conducting pipe for space-charge simulation

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