IPAC2015 - List of Authors (Liu, H.)

Paper	Title	Page
MOPWA003	Optimal Generalized Finite Difference Solution to the Particle-in-Cell Problem	77
	X. Wang, X. Jiao, H. Liu, V. Samulyak, K. Yu SBU, Stony Brook, USA V. Samulyak BNL, Upton, Long Island, New York, USA
	The particle-in-cell (PIC) method is widely used in applications, such as in electromagnetics, but the accuracy of its solutions degrades when the particle distribution is highly non-uniform. In our work, we propose an adaptive PIC method with optimal point distribution and a generalized finite difference (GFD) scheme. Our method replaces the Cartesian grid in the classical PIC with adaptive computational nodes or particles, to which the charges from the sample particles are assigned by a weighted least-square approximations. The partial differential equation is then discretized using a GFD method and solved with fast linear solvers. The density of computational particles is chosen adaptively, so that the error from GFD and that from Monte Carlo integration are balanced and the total error is approximately minimized. We also present the verification results using electrostatic problems and comparison of accuracy and solution time of our method with the classical PIC.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2015-MOPWA003
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Paper

Title

Page

Optimal Generalized Finite Difference Solution to the Particle-in-Cell Problem

77

X. Wang, X. Jiao, H. Liu, V. Samulyak, K. Yu
SBU, Stony Brook, USA
V. Samulyak
BNL, Upton, Long Island, New York, USA

The particle-in-cell (PIC) method is widely used in applications, such as in electromagnetics, but the accuracy of its solutions degrades when the particle distribution is highly non-uniform. In our work, we propose an adaptive PIC method with optimal point distribution and a generalized finite difference (GFD) scheme. Our method replaces the Cartesian grid in the classical PIC with adaptive computational nodes or particles, to which the charges from the sample particles are assigned by a weighted least-square approximations. The partial differential equation is then discretized using a GFD method and solved with fast linear solvers. The density of computational particles is chosen adaptively, so that the error from GFD and that from Monte Carlo integration are balanced and the total error is approximately minimized. We also present the verification results using electrostatic problems and comparison of accuracy and solution time of our method with the classical PIC.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2015-MOPWA003

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)