Method for applying standards in electromagnetic field edge element method

Abstract

The invention discloses a method for applying standards in an electromagnetic field edge element method. The method includes the steps that a three-dimensional model of an object to be analyzed is established, and the three-dimensional model is subjected to mesh generation; element matrixes corresponding to a magnetic vector potential double-rotation item,a coulomb standard item and an electric current density item of edge elements obtained through mesh generation are calculated, and integration is performed so that an overall finite element equation can be formed; corresponding boundary conditions are applied to the overall finite element equation; the overall finite element equation to which the corresponding boundary conditions are applied is solved, a unique magnetic vector potential basic solution is obtained, post-processing is performed on the obtained magnetic vector potential basic solution, and a corresponding electromagnetic field quantity solution is obtained. According to the method, on the premise that accuracy is guaranteed, the magnetic vector potential uniqueness problem in the edge element method is effectively solved; the establishment problem of a complex generating tree in a traditional method is avoided; meanwhile, the efficiency of the method is higher than that of a coulomb standard applying method adopted in the edge elements through a Lagrange multiplier method.

Description

technical field [0001] The invention relates to a method for imposing norms in the electromagnetic field edge element method, which belongs to the new numerical method category in computer-aided engineering (CAE) software, specifically relates to the core method for solving the electromagnetic field edge element method, and can be widely used in the electrical industry , such as electromagnetic field analysis of motors, solenoid valves, etc. Background technique [0002] The finite element method of electromagnetic field is a numerical method widely used in the numerical solution of electromagnetic field. However, it has always been a difficult point to solve the uniqueness of the magnetic vector potential under the condition of ensuring the accuracy. Through the detailed inquiry of the existing literature and technical data, four kinds of technical means commonly used in the electromagnetic field finite element are summarized: 1. The edge element method combined with the tr...

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Problems solved by technology

[0003] The first method is the edge element method combined with the tree-cotree method. This method is to establish a Spanning Tree in the grid space to be analyzed, such as figure 1 As shown (the thick solid line is the generated tree), the degree of freedom of the magnetic vector potential on the corresponding edge of the Spanning Tree is constrained to ensure the uniqueness of the solution; the edge element method is used combined with the tree-cotree method, although it avoids the accuracy problem of using the node-element method, but using the tree-co-tree method, it faces the problem that the method of spanning tree is not unique, and unreasonable spanning tree will lead to unreasonable solutions. In addition, the most complex problem There are difficulties in the construction of optimal spanning trees

[0004] The second method is to use the edge element method combined with the CG method (or pretreatment CG method). This method is to use the CG method (or pretreatment CG method) to perform Solve and obtain a reasonable solution in a non-unique solution space; however, using the edge element method combined with the CG method (or pre-processing CG method) needs to re-solve the current density field, which increases the amount of calculation and reduces the calculation accuracy , and the CG iterative method often has convergence problems

The Lagrange multiplier method is used to introduce the Coulomb gauge condition to ensure the uniqueness of the solution, but due to the addition of the Lagrange multiplier degrees of freedom, the equation includes the coupling matrix of the Lagrange multiplier and the magnetic vector potential, so that The size of the matrix becomes larger and the solution efficiency decreases

[0006] The fourth method is the node element method combined with the penalty function method to impose the Coulomb gauge. This method uses the node element method to discretize the electromagnetic field equation. In order to ensure the uniqueness of the magnetic vector potential, the Coulomb gauge condition is used as a penalty Introduce the electromagnetic field functional to obtain the only electromagnetic field solution. There is no extra degree of freedom in the equation, and the constraint on the magnetic vector potential is achieved only through the matrix corresponding to the penalty item; the method of imposing Coulomb gauge by using the node element method combined with the penalty function method Although the uniqueness of the magnetic vector potential is effectively guaranteed, when the node element method is used, the accuracy of the solution on the interface of the material with a large change in magnetic permeability is poor

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