Dong-Yeop Na , Fernando L. Teixeira , Yuri A. Omelchenko
{"title":"An unstructured body-of-revolution electromagnetic particle-in-cell algorithm with radial perfectly matched layers and dual polarizations","authors":"Dong-Yeop Na , Fernando L. Teixeira , Yuri A. Omelchenko","doi":"10.1016/j.cpc.2024.109247","DOIUrl":null,"url":null,"abstract":"<div><p>A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code, utilizes a set of field scalings and a coordinate mapping, reducing the Maxwell field problem in a cylindrical system to a Cartesian finite element Maxwell solver in the meridian plane. The latter obviates the cylindrical coordinate singularity in the symmetry axis. The choice of an unstructured finite element discretization enhances the geometrical flexibility of the BORPIC++ solver compared to the more traditional finite difference solvers. Symmetries in Maxwell's equations are explored to decompose the problem into two dual polarization states with isomorphic representations that enable code reuse. The particle-in-cell scatter and gather steps preserve charge-conservation at the discrete level. Our previous algorithm (BORPIC+) discretized the <strong>E</strong> and <strong>B</strong> field components of TE<sup><em>ϕ</em></sup> and TM<sup><em>ϕ</em></sup> polarizations on the finite element (primal) mesh <span>[1]</span>, <span>[2]</span>. Here, we employ a new field-update scheme. Using the same finite element (primal) mesh, this scheme advances two sets of field components independently: (1) <strong>E</strong> and <strong>B</strong> of TE<sup><em>ϕ</em></sup> polarized fields, (<span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>,</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math></span>) and (2) <strong>D</strong> and <strong>H</strong> of TM<sup><em>ϕ</em></sup> polarized fields, (<span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><mo>,</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>,</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>ρ</mi></mrow></msub></math></span>). Since these field updates are not explicitly coupled, the new field solver obviates the coordinate singularity, which otherwise arises at the cylindrical symmetric axis, <span><math><mi>ρ</mi><mo>=</mo><mn>0</mn></math></span> when defining the discrete Hodge matrices (generalized finite element mass matrices). A cylindrical perfectly matched layer is implemented as a boundary condition in the radial direction to simulate open space problems, with periodic boundary conditions in the axial direction. We investigate effects of charged particles moving next to the cylindrical perfectly matched layer. We model azimuthal currents arising from rotational motion of charged rings, which produce TM<sup><em>ϕ</em></sup> polarized fields. Several numerical examples are provided to illustrate the first application of the algorithm.</p></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":null,"pages":null},"PeriodicalIF":7.2000,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Physics Communications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S001046552400170X","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code, utilizes a set of field scalings and a coordinate mapping, reducing the Maxwell field problem in a cylindrical system to a Cartesian finite element Maxwell solver in the meridian plane. The latter obviates the cylindrical coordinate singularity in the symmetry axis. The choice of an unstructured finite element discretization enhances the geometrical flexibility of the BORPIC++ solver compared to the more traditional finite difference solvers. Symmetries in Maxwell's equations are explored to decompose the problem into two dual polarization states with isomorphic representations that enable code reuse. The particle-in-cell scatter and gather steps preserve charge-conservation at the discrete level. Our previous algorithm (BORPIC+) discretized the E and B field components of TEϕ and TMϕ polarizations on the finite element (primal) mesh [1], [2]. Here, we employ a new field-update scheme. Using the same finite element (primal) mesh, this scheme advances two sets of field components independently: (1) E and B of TEϕ polarized fields, () and (2) D and H of TMϕ polarized fields, (). Since these field updates are not explicitly coupled, the new field solver obviates the coordinate singularity, which otherwise arises at the cylindrical symmetric axis, when defining the discrete Hodge matrices (generalized finite element mass matrices). A cylindrical perfectly matched layer is implemented as a boundary condition in the radial direction to simulate open space problems, with periodic boundary conditions in the axial direction. We investigate effects of charged particles moving next to the cylindrical perfectly matched layer. We model azimuthal currents arising from rotational motion of charged rings, which produce TMϕ polarized fields. Several numerical examples are provided to illustrate the first application of the algorithm.
期刊介绍:
The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper.
Computer Programs in Physics (CPiP)
These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged.
Computational Physics Papers (CP)
These are research papers in, but are not limited to, the following themes across computational physics and related disciplines.
mathematical and numerical methods and algorithms;
computational models including those associated with the design, control and analysis of experiments; and
algebraic computation.
Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.