Spectral Solvers of Maxwell’s Equations in Particle-in-Cell Codes: Numerical Schemes and Parallel Implementation

To solve Maxwell’s equations, particle-in-cell (PIC) simulation codes typically use the Finite-Difference Time-Domain (FDTD) method, which is subject to numerical dispersion. In contrast, spectral solvers are free of numerical dispersion effects and provide a high-quality solution. This paper discus...

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Veröffentlicht in:Lobachevskii journal of mathematics Jg. 46; H. 1; S. 133 - 142
1. Verfasser: Panova, E.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Moscow Pleiades Publishing 01.01.2025
Springer Nature B.V
Schlagworte:
Algebra
Analysis
Approximation
Computational grids
Electromagnetic fields
Fast Fourier transformations
Finite difference time domain method
Fourier transforms
Geometry
Magnetic fields
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Maxwell's equations
Particle in cell technique
Perfectly matched layers
Probability Theory and Stochastic Processes
Simulation
Solvers
finite-difference solvers
particle-in-cell
perfectly matched layer (PML)
performance
2010 Mathematics Subject Classification: 37M05, 65Y05, 65Z05
spectral solvers
total-field/scattered-field boundary (TFSF)
ISSN:1995-0802, 1818-9962
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Zusammenfassung:To solve Maxwell’s equations, particle-in-cell (PIC) simulation codes typically use the Finite-Difference Time-Domain (FDTD) method, which is subject to numerical dispersion. In contrast, spectral solvers are free of numerical dispersion effects and provide a high-quality solution. This paper discusses some issues encountered when integrating spectral solvers into PIC codes. We describe a technique to implement a Perfectly Matched Layer (PML) in PIC codes with spectral solvers. We also propose a modified total-field/scattered-field (TFSF) method for effectively generating electromagnetic field at the boundary of a computational domain in case of an arbitrary-order field solver. The schemes under consideration have been successfully implemented in the PICADOR code using the OpenMP and MPI technologies. We demonstrate that spectral field solvers allow us to significantly decrease a computational grid resolution and achieve a performance gain, despite the additional overhead of performing Fast Fourier Transform (FFT).
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224608282