An interpolating particle method for the Vlasov–Poisson equation

• Extending the Numerical Flow Iteration to the multi-species Vlasov--Maxwell system through Hamiltonian Splitting

  2026 SSRN Electronic Journal preprint Mathematics Numerical methods for differential equations Open access

  0

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• Quasi-3D Sparse Particle-In-Cell Simulation of a Vlasov-Poisson System

  2026 SSRN Electronic Journal preprint Mathematics Gas Dynamics and Kinetic Theory Open access

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• Convergence Study of Quasi-3D Gauss-Law Particle-in-Cell for Hall Thruster Simulation

  2025 AIAA SciTech Forum conference-paper Engineering Plasma Diagnostics and Applications

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  citations
• On finite-dimensional smoothed-particle Hamiltonian reductions of the Vlasov equation

  2025 Journal of Mathematical Physics article Mathematics Gas Dynamics and Kinetic Theory

  0

  citations
• High fidelity simulations of the multi-species Vlasov equation in the electro-static, collisional-less limit

  2024 Plasma Physics and Controlled Fusion article Physics and Astronomy Magnetic confinement fusion research

  4

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• The Numerical Flow Iteration for the Vlasov–Poisson Equation

  2024 SIAM Journal on Scientific Computing article Mathematics Gas Dynamics and Kinetic Theory

  6

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• On a 1D-electrostatic test problem for the PIC method

  2024 Russian Journal of Numerical Analysis and Mathematical Modelling article Engineering Numerical methods in engineering

  1

  citations
• On errors in the PIC-method when modeling Langmuir oscillations

  2024 Vyčislitelʹnye metody i programmirovanie article Earth and Planetary Sciences Geophysics and Gravity Measurements Open access

  1

  citations
• Introduction to the numerical flow iteration for the Vlasov–Poisson equation

  2023 PAMM article Mathematics Gas Dynamics and Kinetic Theory Open access

  4

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9 results

• Reproducing kernel particle methods

  1995 International Journal for Numerical Methods in Fluids article Engineering Numerical methods in engineering

  2,863

  citations
• Scattered Data Approximation

  2004 Cambridge University Press eBooks book Engineering Numerical methods in engineering Open access

  2,605

  citations
• Meshfree Approximation Methods with Matlab

  2007 Interdisciplinary mathematical sciences book Engineering Numerical methods in engineering

  1,876

  citations
• The Cauchy Problem in Kinetic Theory

  1996 Society for Industrial and Applied Mathematics eBooks book Mathematics Gas Dynamics and Kinetic Theory

  722

  citations
• Collected papers of L. D. Landau

  1966 Nuclear Physics article Arts and Humanities History of Science and Medicine

  613

  citations
• Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data

  1992 Journal of Differential Equations article Mathematics Gas Dynamics and Kinetic Theory Open access

  607

  citations
• Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system

  1991 Inventiones mathematicae article Mathematics Gas Dynamics and Kinetic Theory

  548

  citations
• On Landau damping

  2011 Acta Mathematica article Mathematics Gas Dynamics and Kinetic Theory Open access

  467

  citations
• The formation of vortices from a surface of discontinuity

  1931 Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character article Engineering Fluid Dynamics and Turbulent Flows Open access

  461

  citations
• Conservative Numerical Schemes for the Vlasov Equation

  2001 Journal of Computational Physics article Mathematics Gas Dynamics and Kinetic Theory

  413

  citations
• Solving partial differential equations by collocation using radial basis functions

  1998 Applied Mathematics and Computation article Engineering Numerical methods in engineering

  413

  citations
• Comparison of Eulerian Vlasov solvers

  2002 Computer Physics Communications article Mathematics Gas Dynamics and Kinetic Theory Open access

  292

  citations
• An analysis of particle methods

  2006 Springer eBooks book-chapter Engineering Fluid Dynamics Simulations and Interactions

  266

  citations
• A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov–Poisson equations

  2011 Journal of Computational Physics article Mathematics Gas Dynamics and Kinetic Theory Open access

  194

  citations
• The Particle-In-Cell Method for Hydrodynamic Calculations

  1957 Defense Technical Information Center (DTIC) article Engineering Computational Fluid Dynamics and Aerodynamics

  164

  citations
• On classical solutions in the large in time of two-dimensional Vlasov's equation

  1978 Osaka City University (Osaka City University) article Mathematics Gas Dynamics and Kinetic Theory Open access

  142

  citations
• A Critical Comparison of Eulerian-Grid-Based Vlasov Solvers

  2002 Journal of Computational Physics article Mathematics Gas Dynamics and Kinetic Theory

  141

  citations
• Global existence of a weak solution of vlasov's system of equations

  1975 USSR Computational Mathematics and Mathematical Physics article Mathematics Gas Dynamics and Kinetic Theory

  134

  citations
• Particle Methods for the One-Dimensional Vlasov–Poisson Equations

  1984 SIAM Journal on Numerical Analysis article Mathematics Gas Dynamics and Kinetic Theory

  126

  citations
• Numerical simulation of plasmas with periodic smoothing in phase space

  1972 Journal of Computational Physics article Mathematics Gas Dynamics and Kinetic Theory

  107

  citations