CN103186689B - Electromagnetic-field simulation analytical approach - Google Patents

Abstract

The invention discloses a kind of electromagnetic-field simulation analytical approach, comprising: step 1: set up object three-dimensional model to be analyzed, and adopt seamed edge unit to carry out mesh generation to three-dimensional model; Step 2: adopt method of Lagrange multipliers to impose restriction condition to three-dimensional model; Step 3: calculate subdivision the trailing edge unit cell matrix and bright day multiplier constraint matrix carry out integrated to cell matrix; Step 4: to the integrated rear whole matrix equation solution adding Prescribed Properties, obtain analytical result of electromagnetic and shown by display.The electromagnetic-field simulation analytical approach that the present invention proposes introduces new equation of constraint at analysis field, and introduces the scalar multiplication subspace meeting inf-sub condition, adopts method of Lagrange multipliers to realize constraint, ensure that uniqueness of solution.The precision of the system adaptive of the method, reliability, solution can ensure simultaneously.Be applicable to knot vector gesture unit and seamed edge vector potential unit, and be applicable to multi-field face transboundary coupled problem.

Description

Electromagnetic-field simulation analytical approach

Technical field

The invention belongs to computer-aided engineering (CAE) field, is a kind of effective electromagnetic-field simulation analytical approach.

Background technology

Current electromagnetic-field simulation analytic system is application node vector potential method, or the method realization of seamed edge unit and TreeGauge combination.

Knot vector gesture method is using the vector potential of finite element grid node as system degree of freedom, for guaranteeing that uniqueness of solution adopts the method for Coulomb Gauge.The method is widely used in electromagnetic field analysis field, ensure that vector potential is at x in unit interface, y, when but the continuity limitation in z tri-directions is for analyzed area characteristic heterogeneity material, that physically only requires along interface tangential direction is continuous, the accuracy that the continuous Planar Mechanisms impact in three directions is understood, therefore the method is not suitable for analysis field and there is the material parameters such as magnetic permeability problem pockety, but such problem ubiquity in a practical situation.

And in the method combined at another kind of seamed edge unit and Tree Gauge, degree of freedom is the direction along seamed edge, namely ensures the continuity of the tangential direction vector potential at interface, which solves the Planar Mechanisms problem of knot vector gesture method.But it is uniqueness of solution problems that seamed edge unit compares distinct issues, namely there is the rational constraint of null solution space requirement introducing to ensure uniqueness of solution in global matrix equation.

For solving seamed edge unit uniqueness of solution problem, prior art proposes two kinds of methods: one adopts for current density to coordinate field simultaneously for equation system employing CG iterative device, the method can obtain rational electromagnetism potential field in not unique solution space, but there are two more serious problems: 1) need again to solve current density field, increase calculated amount and reduce computational accuracy simultaneously.2) CG alternative manner also exists convergence problem, and particularly for multi-field problem or when adopting the concurrent technique of Segmentation method to adopt, need to adopt interface coupling or Lagrange multiplier space, at this moment convergence problem becomes more outstanding.Another kind method is the method adopting Spanning Tree Gauge, namely set up Spanning Tree at mesh space to be analyzed, as shown in Figure 1, the node electromagnetic potential degree of freedom be positioned on Spanning Tree is retrained thus guarantees uniqueness of solution, the major defect of the existence of the method is: 1) structure of SpanningTree is not unique, although irrational Tree can ensure uniqueness of solution but can affect the precision of electromagnetic potential, difficulty is built with for challenge optimal T ree; 2) for the process of multi-field coupled problem as motor rotation-sliding interface, the technological difficulties across the structure of the reasonable Tree of coupled interface never solve.

Summary of the invention

The present invention is directed to the problems referred to above that prior art exists, propose an electromagnetic-field simulation analytical approach.The technological means that the present invention adopts is as follows:

A kind of electromagnetic-field simulation analytical approach, is characterized in that comprising:

Step 1: set up object three-dimensional model to be analyzed, and adopt seamed edge unit to carry out mesh generation to three-dimensional model;

Step 2: adopt method of Lagrange multipliers to impose restriction condition to three-dimensional model;

Step 3: calculate subdivision the trailing edge unit cell matrix and bright day multiplier constraint matrix carry out integrated to cell matrix;

Step 4: to the integrated rear whole matrix equation solution adding Prescribed Properties, obtain analytical result of electromagnetic and shown by display.

The electromagnetic-field simulation analytical approach that the present invention proposes introduces new equation of constraint at analysis field, and introduces the scalar multiplication subspace meeting inf-sub condition, adopts method of Lagrange multipliers to realize constraint, ensure that uniqueness of solution.The precision of the system adaptive of the method, reliability, solution can ensure simultaneously.Be applicable to knot vector gesture unit and seamed edge vector potential unit, and be applicable to multi-field face transboundary coupled problem (interface coupling comprising interface degree of freedom direct-coupling and realized by method of Lagrange multipliers).

Accompanying drawing explanation

The Spanning Tree schematic diagram (thick line portion seamed edge) that Fig. 1 sets up for application existing Spanning Tree Gauge method.

Fig. 2 is the process flow diagram of electromagnetic-field simulation analytical approach of the present invention.

Fig. 3 is the schematic diagram of seamed edge unit of the present invention.

Fig. 4 is the rotating cylindrical body physical model schematic diagram that the present invention creates.

Fig. 5 is the rotating cylindrical body mesh generation front elevation that the present invention creates.

Fig. 6 is the rotating cylindrical body mesh generation 3-D view that the present invention creates.

Fig. 7 is with the unreasonable analysis result schematic diagram of the employing Tree Gauge method of magnetic field intensity vector representation.

Fig. 8 is with the reasonable analysis result schematic diagram of the employing of magnetic field intensity vector representation electromagnetic field analysis of the present invention.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.

As shown in Figure 2, electromagnetic-field simulation analytical approach of the present invention comprises the following steps:

Step 1: set up object three-dimensional model to be analyzed, and adopt seamed edge unit to carry out mesh generation to three-dimensional model.

Step 2: adopt method of Lagrange multipliers to impose restriction condition to three-dimensional model, this constraint condition is expressed as:

div(A)＝0 in Ω (1)

Wherein, A is electromagnetic field vector potential, and Ω is nonconducting three dimensions territory.

Step 3: calculate subdivision the trailing edge unit cell matrix and bright day multiplier constraint matrix carry out integrated to cell matrix.This step 3 comprises the following steps again: adopt seamed edge unit for electromagnetic potential, degree of freedom direction is the tangential direction along seamed edge, calculates the shape function of seamed edge cell node, and then obtains the seamed edge unit form function matrix of electromagnetic potential vector; The quasistatic magnetic field equation in non-conductive space and formula (1) is utilized to calculate its weak form equation; Seamed edge unit shape function is substituted into weak form equation discretize is carried out to analytical model, obtain the cell matrix of seamed edge unit; Carry out integrated to the cell matrix of seamed edge unit.

Quasistatic magnetic field equation in non-conductive space is expressed as:

$\▿\×\left[v\right]\▿\×A=J_s\mathrm{in\Ω}---\left(2\right)$

The weak form the Representation Equation utilizing formula (1) and formula (2) to calculate is:

$\left\{\begin{array}{cc}\left(\right[v]\mathrm{curl}A,\mathrm{curl}v)+(\mathrm{grad}p,v)=(J_s,v)& \mathrm{in\Ω}\∀v\∈H_0(\mathrm{curl};\mathrm{\Ω})\\ (A,\mathrm{grad}q)=(0,q)& \mathrm{in\Ω}\∀q\∈H_0^1\left(\mathrm{\Ω}\right)\end{array}\right.---\left(3\right)$

Wherein, [v] is magnetic resistance matrix, i.e. magnetic permeability inverse of a matrix; J _sit is current density vectors source item; P is Lagrange multiplier scalar freedom.

The seamed edge unit shape function of electromagnetic potential is expressed as:

A＝[W][A _e]

Wherein, [W] is form function matrix; [A _e] be electromagnetic potential seamed edge degree of freedom.

The cell matrix of seamed edge unit is expressed as:

$\left[\begin{array}{cc}{K}^{\mathrm{AA}}& G^{\mathrm{AV}}\\ {\left(G^{\mathrm{AV}}\right)}^T& 0\end{array}\right]\left\{\begin{array}{c}{A}_e\\ V_e\end{array}\right\}=\left\{\begin{array}{c}{J}_e^s\\ 0\end{array}\right\}\mathrm{in\Ω}$

Wherein, unit magnetic resistance matrix $\left[K^{\mathrm{AA}}\right]={\∫}_{\mathrm{Ve}}{(\▿\×{\left[W\right]}^T)}^T\left[v\right](\▿\×{\left[W\right]}^T)\mathrm{dV};$ Unit Lagrange multiplier matrix $\left[G^{\mathrm{AV}}\right]={\∫}_{\mathrm{Ve}}\left[W\right](\▿{\left\{N\right\}}^T)\mathrm{dV};$ Cell current density source item vector $\left\{J_e^s\right\}={\∫}_{\mathrm{Ve}}{\left[W\right]}^T\left\{J^S\right\}\mathrm{dV}.$

Step 4: to the integrated rear whole matrix equation solution adding Prescribed Properties, obtain analytical result of electromagnetic and shown by display, the electromagnetic potential vector of this analytical result of electromagnetic comprises (but being not limited to) object to be analyzed, the field strength values obtained by electromagnetism vector calculation and flux density vectors.

For multizone coupled problem, comprise the following steps between step 3 and step 4: set up Lagrange multiplier space at coupled interface, the continuity across zones of different interface electromagnetic potential vector tangential direction is ensured by method of Lagrange multipliers.

Below to carry out electromagnetic field analysis to rotating cylindrical body, above-mentioned steps is described:

1. first set up the three-dimensional model of analytic target rotary body, adopt D modeling tool to set up the three-dimensional model (as shown in Figure 4) of three dimensional analysis object rotary body.

2. pair three-dimensional model carries out mesh generation, is 10 node, 4 body seamed edge unit as shown in Figure 2, obtains view as shown in Figure 5 and Figure 6 by three-dimensional model subdivision.

3. create physical model, create the physical model of cylinder and the physical model of outer toroid in rotating cylindrical body respectively.

4. compose material property value, reluctivity parameter to interior cylinder and outer toroid.

5. apply edge-restraint condition.Whole model upper bottom surface, all nodes of bottom surface, and the seamed edge electromagnetic potential A degree of freedom of all nodes on the outer ring surface of outer toroid, and Lagrange multiplier p degree of freedom retrains.

6. cylinder and outer toroid coupled interface condition in applying.In selecting, the outer ring surface of cylinder and the inner ring surface of outer toroid are as coupled interface, apply the coupling condition based on method of Lagrange multipliers, need coupling seamed edge electromagnetic potential degree of freedom and Lagrange multiplier spatial degrees of freedom here.

7. calculate seamed edge cell matrix and carry out integrated to seamed edge cell matrix, obtaining whole matrix.

8. the whole matrix pair adding constraint condition solves.

9. show analytical result of electromagnetic.

As seen from Figure 7, the magnetic field intensity adopting existing Tree Gauge method to obtain is unreasonable, finds out that Tree Gauge method often can not get rational result for the multi-field coupled problem of process thus.As seen from Figure 8, the seamed edge unit new Gauge method based on method of Lagrange multipliers that the present invention proposes obtains rational result.

The electromagnetic-field simulation analytical approach that the present invention proposes introduces new equation of constraint at analysis field, and introduces the scalar multiplication subspace meeting inf-sub condition, adopts method of Lagrange multipliers to realize constraint, ensure that uniqueness of solution.The precision of the system adaptive of the method, reliability, solution can ensure simultaneously.Be applicable to knot vector gesture unit and seamed edge vector potential unit, and be applicable to multi-field face transboundary coupled problem (interface coupling comprising interface degree of freedom direct-coupling and realized by method of Lagrange multipliers).

The above; be only the present invention's preferably embodiment; but protection scope of the present invention is not limited thereto; anyly be familiar with those skilled in the art in the technical scope that the present invention discloses; be equal to according to technical scheme of the present invention and inventive concept thereof and replace or change, all should be encompassed within protection scope of the present invention.

Claims (2)

1. an electromagnetic-field simulation analytical approach, is characterized in that comprising:

Step 1: set up object three-dimensional model to be analyzed, and adopt seamed edge unit to carry out mesh generation to three-dimensional model;

Step 2: adopt method of Lagrange multipliers to impose restriction condition to three-dimensional model;

Step 3: calculate subdivision the trailing edge unit cell matrix and bright day multiplier constraint matrix carry out integrated to cell matrix;

Step 4: to the integrated rear whole matrix equation solution adding Prescribed Properties, obtain analytical result of electromagnetic and shown by display;

Described constraint condition is expressed as:

div(A)＝0 inΩ

Wherein, A is electromagnetic field vector potential, and Ω is nonconducting three dimensions territory;

Described step 3 comprises the following steps:

Adopt seamed edge unit for electromagnetic potential, degree of freedom direction is the tangential direction along seamed edge, calculates the shape function of seamed edge cell node, and then obtains the seamed edge unit form function matrix of electromagnetic potential vector;

The quasistatic magnetic field equation in non-conductive space and edge-restraint condition formulae discovery is utilized to obtain its weak form equation;

Seamed edge unit shape function is substituted into weak form equation discretize is carried out to analytical model, obtain the cell matrix of seamed edge unit; Carry out integrated to the cell matrix of seamed edge unit;

Wherein, the quasistatic magnetic field equation in non-conductive space is expressed as:

The weak form the Representation Equation calculated is:

Wherein, [v] is magnetic resistance matrix, i.e. magnetic permeability inverse of a matrix; J _sit is current density vectors source item; P is Lagrange multiplier scalar freedom;

The seamed edge unit shape function of electromagnetic potential is expressed as:

A＝[W][A _e]

Wherein, [W] is form function matrix; [A _e] be electromagnetic potential seamed edge degree of freedom;

The cell matrix of seamed edge unit is expressed as:

Wherein, unit magnetic resistance matrix unit Lagrange multiplier matrix cell current density source item vector

2. method according to claim 1, multizone coupled problem be is characterized in that comprising the following steps between step 3 and step 4: set up Lagrange multiplier space at coupled interface, the continuity across zones of different interface electromagnetic potential vector tangential direction is ensured by method of Lagrange multipliers.