TY - JOUR

T1 - A Parallel Algorithm for a Semi-Implicit Particle-In-Cell Method with Energy and Charge Conservation

AU - Berendeev, E. A.

AU - Timofeev, I. V.

N1 - This work was supported by the Russian Science Foundation (project no. 21-72-10071).

PY - 2024/12

Y1 - 2024/12

N2 - The article is devoted to the construction of a parallel algorithm for calculating plasma dynamics by a particle-in-cell method using a semi-implicit scheme that conserves energy and charge. This is a two-stage predictor–corrector scheme. At the prediction stage a semi-implicit Lapenta-type method is used in which an energy-conserving linear current does not satisfy the local Gauss law. At the correction stage the currents, electromagnetic fields, and particle velocities are corrected so that difference laws of energy and charge conservation are satisfied exactly. This approach turns out to be efficient in modeling of multi-scale phenomena with a sufficiently large time step. However, the method is computer time-consuming, since it requires not only solving two systems of linear equations per step, but also reconstructing the entire matrix of the system. The authors have developed a matrix-operator software implementation algorithm for this scheme, which allows efficient paralleling of the calculations and using the various available libraries for work with matrices and solvers for systems of linear equations. To construct the matrix, a row-by-row storage algorithm is used with search for the elements via a hash table, which reduces the memory capacity required, the number of thread synchronizations, and can significantly speed up the calculations. This algorithm has been successfully applied in a computer code, Beren3D.

AB - The article is devoted to the construction of a parallel algorithm for calculating plasma dynamics by a particle-in-cell method using a semi-implicit scheme that conserves energy and charge. This is a two-stage predictor–corrector scheme. At the prediction stage a semi-implicit Lapenta-type method is used in which an energy-conserving linear current does not satisfy the local Gauss law. At the correction stage the currents, electromagnetic fields, and particle velocities are corrected so that difference laws of energy and charge conservation are satisfied exactly. This approach turns out to be efficient in modeling of multi-scale phenomena with a sufficiently large time step. However, the method is computer time-consuming, since it requires not only solving two systems of linear equations per step, but also reconstructing the entire matrix of the system. The authors have developed a matrix-operator software implementation algorithm for this scheme, which allows efficient paralleling of the calculations and using the various available libraries for work with matrices and solvers for systems of linear equations. To construct the matrix, a row-by-row storage algorithm is used with search for the elements via a hash table, which reduces the memory capacity required, the number of thread synchronizations, and can significantly speed up the calculations. This algorithm has been successfully applied in a computer code, Beren3D.

KW - high-performance computing

KW - parallel algorithm

KW - particle-in-cell method

KW - solving systems of linear algebraic equations

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85211332173&origin=inward&txGid=b667febd41025b0c62ffa6f4ad2dc00e

UR - https://www.mendeley.com/catalogue/0f00ec74-96a8-35cb-98ac-ee6a69829463/

U2 - 10.1134/S1995423924040013

DO - 10.1134/S1995423924040013

M3 - Article

VL - 17

SP - 301

EP - 312

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 4

ER -