An approach to numerically solving the Poisson equation

We introduce an approach for numerically solving the Poisson equation by using a physical model, which is a way to solve a partial differential equation without the finite difference method. This method is especially useful for obtaining the solutions in very many free-charge neutral systems with op...

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Bibliographic Details
Published in:Physica scripta 2015-06, Vol.90 (6), p.65603-8
Main Authors: Feng, Zhichen, Sheng, Zheng-Mao
Format: Article
Language:English
Subjects:
Boundary conditions
electrostatic potential
Exact solutions
Finite difference method
Mathematical analysis
Mathematical models
Multigrid methods
Partial differential equations
plasma simulation
Poisson equation
toroidal geometry
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Summary:We introduce an approach for numerically solving the Poisson equation by using a physical model, which is a way to solve a partial differential equation without the finite difference method. This method is especially useful for obtaining the solutions in very many free-charge neutral systems with open boundary conditions. It can be used for arbitrary geometry and mesh style and is more efficient comparing with the widely-used iterative algorithm with multigrid methods. It is especially suitable for parallel computing. This method can also be applied to numerically solving other partial differential equations whose Green functions exist in analytic expression.
ISSN:0031-8949
1402-4896
DOI:10.1088/0031-8949/90/6/065603