A particle-in-Fourier method with semi-discrete energy conservation for non-periodic boundary conditions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909317631836160 |
|---|---|
| author | Shen, Changxiao Nigel Cerfon, Antoine Muralikrishnan, Sriramkrishnan |
| author_facet | Shen, Changxiao Nigel Cerfon, Antoine Muralikrishnan, Sriramkrishnan |
| contents | We introduce a novel particle-in-Fourier (PIF) scheme that extends its applicability to non-periodic boundary conditions. Our method handles free space boundary conditions by replacing the Fourier Laplacian operator in PIF with a mollified Green's function as first introduced by Vico-Greengard-Ferrando. This modification yields highly accurate free space solutions to the Vlasov-Poisson system, while still maintaining energy conservation up to an error bounded by the time step size. We also explain how to extend our scheme to arbitrary Dirichlet boundary conditions via standard potential theory, which we illustrate in detail for Dirichlet boundary conditions on a circular boundary. We support our approach with proof-of-concept numerical results from two-dimensional plasma test cases to demonstrate the accuracy, efficiency, and conservation properties of the scheme. By avoiding grid heating and finite grid instability we are able to show an order of magnitude speedup compared to the standard PIC scheme for a long time integration cyclotron simulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13911 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A particle-in-Fourier method with semi-discrete energy conservation for non-periodic boundary conditions Shen, Changxiao Nigel Cerfon, Antoine Muralikrishnan, Sriramkrishnan Numerical Analysis Mathematical Physics We introduce a novel particle-in-Fourier (PIF) scheme that extends its applicability to non-periodic boundary conditions. Our method handles free space boundary conditions by replacing the Fourier Laplacian operator in PIF with a mollified Green's function as first introduced by Vico-Greengard-Ferrando. This modification yields highly accurate free space solutions to the Vlasov-Poisson system, while still maintaining energy conservation up to an error bounded by the time step size. We also explain how to extend our scheme to arbitrary Dirichlet boundary conditions via standard potential theory, which we illustrate in detail for Dirichlet boundary conditions on a circular boundary. We support our approach with proof-of-concept numerical results from two-dimensional plasma test cases to demonstrate the accuracy, efficiency, and conservation properties of the scheme. By avoiding grid heating and finite grid instability we are able to show an order of magnitude speedup compared to the standard PIC scheme for a long time integration cyclotron simulation. |
| title | A particle-in-Fourier method with semi-discrete energy conservation for non-periodic boundary conditions |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2403.13911 |