Coupling method for processing moving boundary problems in electromagnetic field based on edge element method

Abstract

The invention discloses a coupling method for processing moving boundary problems in an electromagnetic field based on an edge element method. The method includes: establishing a three-dimensional model, generating meshes of a moving region and a stationary region of the model, and forming a slip plane at a boundary of the two regions; establishing a basic equation for solving the electromagnetic field, adopting a Lagrangian multiplier method to apply standard conditions, calculating an edge element matrix of each region and integrating the edge element matrixes; when the meshes in the moving region move along the slip plane, adopting the Lagrangian multiplier method to couple degree of freedom of magnetic vector potential on the slip plane, generating a Lagrangian multiplier constraint matrix, and integrating the constraint matrix; on the slip plane, standardizing an introduced Lagrangian scalar multiplier, and coupling by adopting an MPC (multi-point constraint) method; applying boundary conditions to a finite element population equation obtained through the above steps and solving to obtain an electromagnetic field analysis result of a to-be-analyzed object. A finite element matrix obtained by the method is good in behavior, and computed results are accurate and reliable.

Description

technical field [0001] The present invention relates to the technical field of electromagnetic field simulation, in particular to a coupling method for dealing with the moving boundary problem in the electromagnetic field based on the edge element method, which can be used to solve the moving boundary problem of the electromagnetic field in electrical equipment, such as dealing with the rotor rotation problem in the motor , to deal with the coupling between the external rotating magnetic field and the magnetic field in the chamber in IC (integrated circuit) equipment, and to deal with the relative motion between the moving iron and the valve body in the dynamic process of the solenoid valve. Background technique [0002] The edge element method is a numerical method widely used in the numerical solution of the electromagnetic field. It has always been a difficult problem to use the edge element method to deal with the moving boundary in the electromagnetic field. Through the...

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Problems solved by technology

[0006] MPC method based on Ladder grid: Since the degree of freedom of the magnetic vector potential on the slip surface is directional (tangential along the edge), in order to ensure that the MPC method can effectively constrain it, it is necessary to use Ladder elements on the slip surface ; During the motion process, when the nodes on the slip surface no longer maintain a one-to-one correspondence, the MPC method can directly couple the degrees of freedom of the Ladder grid nodes, thereby ensuring the continuity of the degrees of freedom on the slip surface; but based on The MPC method of the Ladder grid has restrictions on the grid of the slip surface, and can only deal with the trapezoidal grid, so it is difficult to apply to complex models;

[0007] Lagrangian multiplier method based on CG method (or preprocessing CG method): This method establishes the constraints of magnetic vector potential and Lagrange vector multiplier by introducing Lagrange vector multiplier on the slip surface Matrix, so as to ensure the continuity of the degree of freedom of the magnetic vector potential on the slip surface; because the generated overall matrix has ill-conditioned characteristics, it is also necessary to use the CG method (or pre-processing CG method) to iteratively solve the equations to solve the equations in a non-unique solution A reasonable solution can be obtained in the space; based on the Lagrange multiplier method of the CG method (or pre-processing CG method), when the CG method (or pre-processing CG method) is used to solve the equation system, the convergence of the solution is often not obtained. Guaranteed, resulting in a failure to solve

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