CN105205299B - The quick Dimension Reduction Analysis method of TV university electromagnetic characteristic of scattering - Google Patents
The quick Dimension Reduction Analysis method of TV university electromagnetic characteristic of scattering Download PDFInfo
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Abstract
The invention discloses a kind of quick Dimension Reduction Analysis methods of TV university electromagnetic characteristic of scattering.Object carries out to surface grids are discrete and volume mesh is discrete, and scattering direction to be asked is parabolical axial direction first；Constructing several sections along parabolical axial direction, each section is carried out discrete with Rectangular grid, and different boundary conditions is added to different mesh points physically；The relationship between two neighboring section is obtained using ADI difference scheme on each face, the equation and parabolic equation for being finally 0 according to tangential electric field component on scatterer surface, simultaneous construct matrix equation；The node electric field value on each section carries out Recursive Solution successively, and the electric field value on next section at various discrete node is solved by constantly updating the information of boundary point and the right vector of equation.The present invention can save in the Electromagnetic Scattering of TV university metal target calculates time and memory, and is conducive to Parallel implementation, has very strong practical engineering application value.
Description
Technical field
The invention belongs to electromagnetic characteristic of scattering numerical computation technology field, especially a kind of TV university Electromagnetic Scattering of Target
The quick Dimension Reduction Analysis method of characteristic.
Background technology
The numerical method such as moment method (MOM) that electromagnetism calculates, FInite Element (FEM), time-domain finite difference (FDTD)
The scattering of electric small-size object can be well solved, but when calculating the scattering of electrically large object, to the configuration requirement of computer
It is excessively high.The scattering of the electrically large object of regular shape can only be solved if the approximation method such as high-frequency methods such as ray trace, physical optics.
Iteration propulsion method is a kind of relatively new type method for solving target scattering problem, and many countries are mainly in sky in the world
The iteration recursion of bay, the iteration recursion of electric current and the iteration recursion etc. of time domain field have been done a large amount of research and have been obtained certain
Achievement in research.Parabolic equation method belongs to iteration propulsion method, it is a kind of approximate form of wave equation, it is assumed that electromagnetism
Wave energy is propagated in the conical region along parabola axial direction.Parabolic equation method provides one kind to solve electromagnetic scattering
Accurately and efficiently computational methods, but its existing major defect is can only to be dissipated to the electromagnetism in the near axis area of parabola direction
Capable calculating is injected, parabolical axial direction is limited by incident field direction, and three-dimensional problem is only reduced to two dimension by the prior art
Problem is solved, big, slow-footed disadvantage that there are operands.
Invention content
The purpose of the present invention is to provide a kind of fast and accurately quick Dimension Reduction Analysis sides of TV university electromagnetic characteristic of scattering
Method, this method solve independently of each other the ranks of field value, are solved by accelerating parallel, can quickly obtain Electromagnetic Scattering Characteristics
Parameter.
Realize that the technical solution of the object of the invention is：A kind of quick Dimension Reduction Analysis side of TV university electromagnetic characteristic of scattering
Method, steps are as follows：
Step 1, the discrete model for establishing object determine parabolical axial direction as x-axis, using grid to object edge
Parabolical axial direction carries out discrete processes, is formed perpendicular to several sections of x-axis, by the network of triangle for solving subdivision
Lattice determine the boundary point of the cut object in each section with section intersection point, then the position of all nodes is judged by tetrahedral grid
It sets；
Step 2, structural matrix equation, in x-axis, y-axis, z-axis direction use CN difference schemes, and are write as alternating direction implicit
Difference scheme obtains the relationship between two neighboring section, finally scatterer surface according to tangential electric field component be 0 equation with
And parabolic equation, simultaneous construct matrix equation；
Step 3 enables the scattering direction that x-axis direction is to be asked, successively to the node electric field on each section along the x-axis direction
Value carries out Recursive Solution, each on next section to solve by the information of continuous renewal boundary point and the right vector of equation
Electric field value at a discrete nodes；
Step 4 carries out recursion to the node electric field value on each section, solves the node electric field on the last one section
Value is converted according to far and near field and solves target scattering body dual station RCS.
Compared with prior art, the present invention its remarkable advantage is：(1) equation is formed simply：One three-dimensional problem is converted
It is solved for a series of two-dimensional problems, matrix forms fast and simple；(2) the field value ranks in each face calculate independent mutually,
It can be by improving computational efficiency parallel；(3) solution matrix is triple diagonal matrix, can be solved by chasing method, and calculating speed is improved.
Present invention is further described in detail below in conjunction with the accompanying drawings.
Description of the drawings
Fig. 1 is energy of the present invention along parabola Propagation schematic diagram.
Fig. 2 is the schematic diagram of unknown quantity distribution on a certain section of the present invention.
Fig. 3 is incident field direction of the invention and vector parabola axial direction schematic diagram.
Fig. 4 is scatterer dual station RCS curve graphs in the embodiment of the present invention.
Specific implementation mode
Below in conjunction with the accompanying drawings and specific embodiment present invention is further described in detail.
In conjunction with attached drawing 1~4, the quick Dimension Reduction Analysis method of TV university electromagnetic characteristic of scattering of the present invention, this method is based on handing over
For the implicit parabolic equation in direction, it is as follows：
Step 1, the discrete model for establishing object determine parabolical axial direction as x-axis, as shown in Figure 1, using net
Lattice carry out discrete processes to object along parabolical axial direction, are formed perpendicular to several sections of x-axis, by solving subdivision
Triangular mesh and section intersection point determine the boundary point of the cut object in each section, then judge to own by tetrahedral grid
The position of node, i.e., by all nodes and tetrahedral geometrical relationship decision node be the internal point of scatterer, external point or
Person's boundary point, it is specific as follows：
The face subdivision that Triangular object model is carried out to object, determines the equation of each section of axis direction, obtains the one of body surface
A little discrete nodal informations.It is parabola axial direction perpendicular to x-axis, forms many sections, these sections is intersected with triangle, are led to
The geological information for crossing node solves intersection point with section, then will with the intersection point apart from nearest standard mesh point labeled as scattering
Body current section boundary point and find out the normal direction.Tetrahedral body subdivision is carried out to scatterer simultaneously, to each section
On point carry out cycle criterion, by judge certain point whether inside tetrahedron come distinguish the point be in scatterer inside or
Outside scatterer, think that the point is the internal point of scatterer if the point is in tetrahedral inside, otherwise it is assumed that at the point
It is marked in air layer, and to these points.The boundary point and internal point of scatterer are quickly found by Octree, and can be passed through
The parallel quickening of non-empty array is found；Think that the point with a certain distance from air cartridge boundary is the point in PML layers.
The node that object boundary on each section can be obtained by above method, in conjunction with the ginseng outside scatterer on each face
Examination point constitutes unknown quantity total on a section, and the unknown quantity of each section is respectively by intrinsic outside scatterer on each face
Discrete reference point be added to obtain with boundary point.The distribution schematic diagram of unknown quantity is as shown in Fig. 2, according to each point on some section
Geometry site and coordinate relationship determine where position an attribute, specifically judge that standard is：For strictly all rules
Mesh point, apart from section, the label of a wavelength is to mark the standard mesh point of immediate body surface up and down
For boundary point, remaining is still internal point interior of articles, and the label outside object is.
The modeling of target can be completed above, lay a good foundation for following matrix construction and solution.
Step 2, structural matrix equation, in x-axis, y-axis, z-axis direction use CN difference schemes, and are write as alternating direction implicit
Difference scheme obtains the relationship between two neighboring section, finally scatterer surface according to tangential electric field component be 0 equation with
And parabolic equation, simultaneous construct matrix equation, are as follows：
(2.1) first, we provide low-angle parabolic equation：
K is wave number in formula (9), and i is imaginary number；(9) formula is write as CN difference forms, in xmAnd xm+1Between introduce midpointUtilize the differential form of centered difference：
Wherein xm、xm+1Respectively m-th point of x-axis direction and the m+1 point, ξmFor xm、xm+1Intermediate point, Δ x be xm、
xm+1The distance between, u (xm,yi,zj), u (xm+1,yi,zj) it is respectively on m-th of face and the m+1 face at the i-th row jth row
Wave function.
Second order local derviation is written as form：
(10) formula substitution (9) formula is then had：
In formulaBe distributed on respectively m-th of face the i-th row continuous three points (i, j-1), (i,
J), the field value of (i, j+1),Be distributed on respectively m-th of face jth row continuous three points (i-1,
J), the field value of (i, j), (i+1, j),Continuous three of the i-th row are respectively distributed on the faces m+1
The field value of point (i, j-1), (i, j), (i, j+1),The company of jth row is respectively distributed on the faces m+1
The field value of continuous three points (i-1, j), (i, j), (i+1, j), Δ x, Δ y, Δ z are respectively standard grid in x, y, z axis direction
The length of point, k is wave number, and i is imaginary number.
Formula (11) abbreviation is：
Wherein
Define operator：δzui,j=ui,j+1+ui,j-1-2ui,j, δyui,j=ui-1,j+ui+1,j-2ui,j
Then (12) formula can turn to：
Wherein
(13) formula both sides are carried out at the same time transformation：
Introduce middle entryThen formula (14) is decomposed into two steps：
By operator δzui,j=ui,j+1+ui,j-1-2ui,j, δyui,j=ui-1,j+ui+1,j-2ui,j(15) are substituted into obtain based on friendship
It is expressed as the implicit parabolic equation in direction：
It is apparent to find out the unknown-value on median surface by row by previous face by formula (16), formula (17) can be by median surface
On value find out value on next face by row.In formulaJth row is respectively distributed on median surface
Continuous three points (i-1, j), (i, j), (i+1, j) field value,Divide respectively on median surface
Cloth is in continuous three points (i, j-1) of the i-th row, the field value of (i, j), (i, j+1).
Vector parabolic equation is made of the scalar parabolic equation on three directions of x, y, z axis：
(2.2) according to derivation above as, (18) formula can be write to the Alternating Direction Implicit Scheme in three directions of x, y, z,
In PML mediums, it is expressed as based on alternating direction implicit parabolic equation：
In formula, σ () represents the function of electrical loss, σ0Represent the coefficient of electrical loss, δ represent the factor sigma (y) of skin depth=
σ0(y/δ)2, σ (z)=σ0(z/δ)2,η=120 π, R0=10-3；
(2.3) addition of metal boundary condition and Recursive Solution, are as follows：
For object boundary point, it is assumed that P is the point on scatterer surface, n=(nx,ny,nz) be P points normal orientation,
The tangential electric field in metal surface is zero, byElectric field is indicated with each component：
In formula, Ex(P)、Ey(P)、Ez(P) be respectively P point electric fields x-axis, y-axis, z-axis direction component；
It is that x-axis direction propagates wave function to define field amount：
In formula,Scattering electric field value is represented,Scattered field value after representation transformation；
Such as down conversion is then carried out, corresponding three equations are obtained by formula (21), (22)：
Wherein under spherical coordinate system, in-field is：
E in formulaiFor incident electric fields, vee (1), vee (2), vee (3) are respectively the incidence wave side in x-axis, y-axis, z-axis
To,Respectively wave function x-axis, y-axis, z-axis direction component,Respectively indicate scattering electric field x-axis, y-axis, z-axis direction component,It indicates respectively incident
Electric field x-axis, y-axis, z-axis direction component.Since the rank of matrix that formula (23) is constituted is 2, boundary condition cannot be uniquely determined, draw
Enter parabolic equation and may make up the matrix that order is 3, simultaneous constructs matrix equation, and equation group is made to have unique solution.
In order to improve solving speed, matrix is write as triple diagonal matrix, some approximations have been introduced in BORDER PROCESSING.By formula
(23) it is divided into 7 kinds of situations：
1. not the case where normal vector for three directions of x, y, z is not 0,
It will in first formulaIt is approximately previous faceIt will in second formulaIt is approximately previous faceAt this time
Simultaneous be the directions x parabolic equation.
The case where 2. normal vector for the directions x is 0, and the normal vector in the direction y, z is not 0,
It will in second formulaIt is approximately previous faceAt this time simultaneous be the directions y parabolic equation.
The case where 3. normal vector for the directions y is 0, and the normal vector in the direction x, z is not 0,
It will in first formulaIt is approximately previous faceAt this time simultaneous be the directions x parabolic equation.
The case where 4. normal vector for the directions z is 0, and the normal vector in the direction x, y is not 0,
It will in above formulaIt is approximately previous faceAt this time simultaneous be the directions x parabolic equation.
5. not the case where normal vector that the normal vector for the direction x, y is the directions 0, z is not 0,
The parabolic equation in the directions simultaneous z.
6. not the case where normal vector that the normal vector for the direction x, z is the directions 0, y is not 0,
The parabolic equation in the directions simultaneous y.
7. not the case where normal vector that the normal vector for the direction y, z is the directions 0, x is not 0,
The parabolic equation in the directions simultaneous x.
Thus the matrix that order is 3 can be constituted in the hope of boundary field value.
Step 3 enables the scattering direction that x-axis direction is to be asked, successively to the node electric field on each section along the x-axis direction
Value carries out Recursive Solution, each on next section to solve by the information of continuous renewal boundary point and the right vector of equation
Electric field value at a discrete nodes, detailed process are as follows：
(3.1) the right vector when solving the electric field value of the node of previous section various discrete as current section；
(3.2) at the boundary point determined by current section, boundary condition and parabolic that tangential electric field component is 0 is added
Line equation, the node electric field value in interior of articles are assigned a value of 0, form the updated matrix equation in current section；
(3.3) updated matrix equation in (3.2) is solved, non trivial solution is the node of current section various discrete
Electric field value.
The number of the unknown quantity of each section is that the number of reference point adds the number of this section boundary point, according in not
Same position, brings different discrete equations into, the electric field value in next face is acquired by the electric field value in previous face, continuous recursion obtains
To the electric field value of a last section；Under three-dimensional system of coordinate, the dual station RCS in the direction (θ, φ) is：
Wherein, EsIndicate the electric field component of scattered field, EiIndicate the electric field component of in-field,π is
Pi.
Vector parabolic line method has fully considered polarized influence, will be converted into the solution of wave equation to parabola side
The solution of journey, in conjunction with boundary condition appropriate, using the parabolical form of low-angle vector, each vector parabolic equation calculates
Go out the scattered field within the scope of the taper along parabola axial direction size no more than 15 °.As shown in figure 3, passing through rotary parabolic line
Axial direction calculate the scattered field of all directions, the scattered field for obtaining far field is then far pushed away by near field, to calculating
To the dual station RCS of target.
Embodiment 1
The present embodiment has carried out the exemplary simulation of electromagnetic scattering, emulates the personal computer in dominant frequency 2.5GHz, memory 4GB
Upper realization, with a height of 1.1m, width 3.3m, for the aircraft of a length of 4.8m, incident wave frequency rate is 5GHz, the direction θ of incidence wave
=0 °,In order to verify the correctness of the method for the present invention, using business software FEKO simulation results as reference.Fig. 4 is two
The RCS curve graphs of kind Electromagnetic Scattering Characteristics emulation can be seen that context of methods from the curve in figure and be kissed with correct numerical result
It closes, and there is apparent advantage above the time, the method calculating time only needs 173s, and FEKO calculates time needs one
Hour or so, illustrate that context of methods is capable of the Electromagnetic Scattering Characteristics of high-speed simulation analysis target object.
In conclusion the problem that complicated three-dimensional problem is decomposed into many two dimensions by the present invention solves, by simultaneously
Row improves computational efficiency, and chasing method solution triple diagonal matrix more accelerates calculating speed, realizes that process flexible is free, has very strong
Practical engineering application value.
Claims (3)
1. a kind of quick Dimension Reduction Analysis method of TV university electromagnetic characteristic of scattering, which is characterized in that steps are as follows：
Step 1, the discrete model for establishing object determine parabolical axial direction as x-axis, using grid to object along parabolic
The axial direction of line carries out discrete processes, is formed perpendicular to several sections of x-axis, by solve the triangular mesh of subdivision with
Section intersection point determines the boundary point of the cut object in each section, then the position of all nodes is judged by tetrahedral grid；
Step 2, structural matrix equation, in x-axis, y-axis, z-axis direction use CN difference schemes, and are write as alternating direction implicit difference
Format obtains the relationship between two neighboring section, finally the equation on scatterer surface according to tangential electric field component for 0 and throwing
Object line equation, simultaneous construct matrix equation；
Step 3 enables the scattering direction that x-axis direction is to be asked, successively to the node electric field value on each section along the x-axis direction into
Row Recursive Solution, by constantly update boundary point information and equation the right vector come solve on next section it is each from
Dissipate the electric field value at node；
Step 4 carries out recursion to the node electric field value on each section, solves the node electric field value on the last one section, root
It is converted according to far and near field and solves target scattering body dual station RCS；
Structural matrix equation described in step 2, specifically includes following steps：
(2.1) it under three-dimensional situation, is expressed as based on alternating direction implicit parabolic equation：
In formula,Be distributed on respectively m-th of face continuous three points (i, j-1) of the i-th row, (i, j),
The field value of (i, j+1),Respectively be distributed on median surface jth row continuous three points (i-1,
J), the field value of (i, j), (i+1, j),It is distributed in the continuous of the i-th row on respectively the m+1 face
Three points (i, j-1), (i, j), (i, j+1) field value；ry=2 Δ x/ Δs y2, rz=2 Δ x/ Δs z2, Δ x, Δ y, Δ z difference
For the length of standard mesh point in x, y, z axis direction, k is wave number, and i is imaginary number；
(2.2) it in PML mediums, is expressed as based on alternating direction implicit parabolic equation：
In formula, σ () represents the function of electrical loss, σ0The coefficient of electrical loss is represented, δ represents factor sigma (y)=σ of skin depth0(y/
δ)2, σ (z)=σ0(z/δ)2,η=120 π, R0=10-3；
(2.3) for object boundary point, it is assumed that P is the point on scatterer surface, n=(nx,ny,nz) be P points normal orientation,
In the tangential electric field in metal surfaceIt is zero, byElectric field is indicated with each component：
In formula, Ex(P)、Ey(P)、Ez(P) be respectively P point electric fields x-axis, y-axis, z-axis direction component；
It is that x-axis direction propagates wave function to define field amount：
In formula,Scattering electric field value is represented,Scattered field value after representation transformation；
Such as down conversion is then carried out, corresponding three equations are obtained by formula (5), (6)：
In formula,Respectively wave function x-axis, y-axis, z-axis direction component；Respectively indicate scattering electric field x-axis, y-axis, z-axis direction component,It indicates respectively incident
Electric field x-axis, y-axis, z-axis direction component；
Formula (7) is the equation group that order is 2, and boundary condition cannot be uniquely determined, and introducing parabolic equation makes equation group have uniquely
Solution, simultaneous constructs matrix equation.
2. the quick Dimension Reduction Analysis method of TV university electromagnetic characteristic of scattering according to claim 1, which is characterized in that step
Recursive Solution is carried out to the node electric field value on each section along the x-axis direction successively described in 3, it is specific as follows：
(3.1) the right vector when solving the electric field value of the node of previous section various discrete as current section；
(3.2) at the boundary point determined by current section, boundary condition and the parabola side that tangential electric field component is 0 is added
Journey, the node electric field value in interior of articles are assigned a value of 0, form the updated matrix equation in current section；
(3.3) updated matrix equation in (3.2) is solved, non trivial solution is the electric field of the node of current section various discrete
Value.
3. the quick Dimension Reduction Analysis method of TV university electromagnetic characteristic of scattering according to claim 1, which is characterized in that step
The 4 solution target scattering body dual station RCS, expression formula are：
Under three-dimensional system of coordinate, the dual station RCS in the direction (θ, φ) is：
Wherein, EsIndicate the electric field component of scattered field, EiIndicate the electric field component of in-field,π is circumference
Rate.
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