# A fast parallel 3D Poisson solver with longitudinal periodic and transverse open boundary conditions for space-charge simulations

## Abstract

A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. Here, we present a fast efficient method to solve the Poisson equation using a spectral finite-difference method. This method uses a computational domain that contains the charged particle beam only and has a computational complexity of $$O(N_u (logN_{mode}))$$, where $$N_u$$ is the total number of unknowns and $$N_{mode}$$ is the maximum number of longitudinal or azimuthal modes. This saves both the computational time and the memory usage of using an artificial boundary condition in a large extended computational domain. The new 3D Poisson solver is parallelized using a message passing interface (MPI) on multi-processor computers and shows a reasonable parallel performance up to hundreds of processor cores.

- Authors:

- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1571086

- Alternate Identifier(s):
- OSTI ID: 1550326

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Computer Physics Communications

- Additional Journal Information:
- Journal Volume: 219; Journal Issue: C; Journal ID: ISSN 0010-4655

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Poisson solver; spectral finite-difference method; periodic and open boundary conditions

### Citation Formats

```
Qiang, Ji. A fast parallel 3D Poisson solver with longitudinal periodic and transverse open boundary conditions for space-charge simulations. United States: N. p., 2017.
Web. doi:10.1016/j.cpc.2017.06.002.
```

```
Qiang, Ji. A fast parallel 3D Poisson solver with longitudinal periodic and transverse open boundary conditions for space-charge simulations. United States. doi:10.1016/j.cpc.2017.06.002.
```

```
Qiang, Ji. Tue .
"A fast parallel 3D Poisson solver with longitudinal periodic and transverse open boundary conditions for space-charge simulations". United States. doi:10.1016/j.cpc.2017.06.002. https://www.osti.gov/servlets/purl/1571086.
```

```
@article{osti_1571086,
```

title = {A fast parallel 3D Poisson solver with longitudinal periodic and transverse open boundary conditions for space-charge simulations},

author = {Qiang, Ji},

abstractNote = {A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. Here, we present a fast efficient method to solve the Poisson equation using a spectral finite-difference method. This method uses a computational domain that contains the charged particle beam only and has a computational complexity of $O(N_u (logN_{mode}))$, where $N_u$ is the total number of unknowns and $N_{mode}$ is the maximum number of longitudinal or azimuthal modes. This saves both the computational time and the memory usage of using an artificial boundary condition in a large extended computational domain. The new 3D Poisson solver is parallelized using a message passing interface (MPI) on multi-processor computers and shows a reasonable parallel performance up to hundreds of processor cores.},

doi = {10.1016/j.cpc.2017.06.002},

journal = {Computer Physics Communications},

number = C,

volume = 219,

place = {United States},

year = {2017},

month = {6}

}