A Method of Imposing Codes in Electromagnetic Field Edge Element Method

Abstract

The invention discloses a method for imposing norms in the electromagnetic field edge element method, comprising: establishing a three-dimensional model of an object to be analyzed, and performing grid division on the three-dimensional model; calculating the magnetic vector of the edge unit after division The element matrix corresponding to the potential double-curl term, the Coulomb gauge term, and the current density term is integrated to form the overall finite element equation; the corresponding boundary conditions are applied to the overall finite element equation; the overall finite element equation with corresponding boundary conditions is applied Solve to obtain the only basic solution of the magnetic vector potential, and post-process the obtained basic solution of the magnetic vector potential to obtain the corresponding solution of the electromagnetic field. On the premise of ensuring accuracy, the present invention effectively solves the uniqueness problem of the magnetic vector potential in the edge element method; avoids the problem of complex spanning tree construction in the traditional method; at the same time, the efficiency is higher than that of the lager adopted in the edge element The method of imposing a Coulomb gauge by the Langerian 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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