Electric potential finite element solution algorithm applied to PIC electrostatic model

A finite element and potential technology, applied in the field of potential finite element solution algorithms, can solve problems such as poor boundary matching and low solution accuracy, and achieve the effects of optimizing spatial grids and time steps, high calculation accuracy, and simple calculation.

Active Publication Date: 2018-07-13
UNIV OF ELECTRONICS SCI & TECH OF CHINA
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Problems solved by technology

[0021] In view of the above-mentioned problems and deficiencies, in order to solve the problems of low boundary matching and low solution accuracy in the potential solution of the FD and IFE methods, the present invention provides a potential finite element (FEM) solution applied to the PIC electrostatic model method

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  • Electric potential finite element solution algorithm applied to PIC electrostatic model
  • Electric potential finite element solution algorithm applied to PIC electrostatic model
  • Electric potential finite element solution algorithm applied to PIC electrostatic model

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Embodiment Construction

[0056] The present invention will be described in further detail below through the embodiments and the accompanying drawings.

[0057] Taking the ion thruster seven-hole double-grid ion optical system as an example, the schematic diagram is as follows image 3 shown. Adopt algorithm among the present invention to carry out the specific implementation steps of PIC electrostatic simulation to this example as follows:

[0058] Step 1. Potential solution: adopt FEM algorithm based on unstructured grid.

[0059] Solve the Possion equation for the potential to satisfy:

[0060]

[0061] In the formula, ρ is the charge density, ε 0 is the vacuum dielectric constant.

[0062] Transformed into an equivalent variational problem as:

[0063]

[0064] Since the Possion equation is being solved, α x = 1, α y = 1, α z = 1, β = 0, Then you can get:

[0065]

[0066] Then the three-dimensional calculation area volume V is discretized into M tetrahedrons, and the grid divis...

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Abstract

The invention belongs to the field of numerical simulation of particle-in-cell (PIC) and particularly relates to an electric potential finite element solution algorithm applied to a PIC electrostaticmodel. According to the algorithm, a complete unstructured grid is used and can better fit the shape of a model boundary, and accordingly an electric potential solution of the PIC electrostatic modelunder the complex boundary condition has higher calculation precision and solution speed; an FEM electric potential solution method which is used for solving non-particle-source problems such as passive electromagnetic field distribution, thermal analysis and mechanical analysis is combined with a typical PIC method, the good characteristics of simple and quick calculation of the typical PIC method are kept, and meanwhile the higher finite element calculation precision is obtained by using an FEM; since the FEM can be well matched with the complex boundary, an uneven grid can also be used according to the simulation demand, and the FEM is not limited by a numerical stability condition, under the condition that the calculation precision is guaranteed, the spatial grid and the time step canbe optimized, and accordingly the simulation efficiency is greatly improved.

Description

technical field [0001] The invention belongs to the field of numerical simulation of particle-in-cell (abbreviated as PIC), and specifically relates to a potential finite element solution algorithm applied to a PIC electrostatic model. Background technique [0002] The PIC method is a numerical simulation method widely used in the physical problems of the interaction between charged particles and electromagnetic fields. It obtains the macroscopic characteristics and laws of motion by tracking the motion of a large number of charged particles in external and self-consistent electromagnetic fields and statistically averaging them. After decades of development, the PIC simulation method has become a powerful numerical method to study the physical problems of the interaction between charged particles and electromagnetic fields, and is widely used in many fields involved in the interaction of charged particles and electromagnetic fields, such as magnetic confinement fusion plasma ...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/50
CPCG06F30/23
Inventor 黄桃金晓林杨中海李斌
Owner UNIV OF ELECTRONICS SCI & TECH OF CHINA
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