CN105303022B - The Gaussian beam method of quick obtaining electromagnetic characteristic of scattering - Google Patents

The Gaussian beam method of quick obtaining electromagnetic characteristic of scattering Download PDF

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CN105303022B
CN105303022B CN201410364662.7A CN201410364662A CN105303022B CN 105303022 B CN105303022 B CN 105303022B CN 201410364662 A CN201410364662 A CN 201410364662A CN 105303022 B CN105303022 B CN 105303022B
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msub
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transfer factor
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戴成功
丁大志
陈如山
樊振宏
陶孝锋
纪健超
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NANJING HUIHONG ELECTRONIC INFORMATION Co Ltd
Nanjing University of Science and Technology
Xian Institute of Space Radio Technology
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NANJING HUIHONG ELECTRONIC INFORMATION Co Ltd
Nanjing University of Science and Technology
Xian Institute of Space Radio Technology
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Abstract

The invention discloses a kind of Gaussian beam method of quick obtaining electromagnetic characteristic of scattering.Imaginary part displacement is added by the location variable in Fast multipole transfer factor, so that transfer factor has the characteristic of Gaussian beam, that is transfer factor has a larger component on the group group center line connecting direction of far field, and with transfer factor component direction and group center line connecting direction angle increase and rapid decay；Window function is added in transfer factor again, further enhances the directionality of transfer factor.Then cast out less transfer factor component, retain larger component.Compared with calculating transfer factor in traditional Fast multipole, the method in the present invention only needs to calculate the transfer factor component in the range of certain angle, effectively reduces the memory requirements calculated during transfer factor.

Description

The Gaussian beam method of quick obtaining electromagnetic characteristic of scattering
Technical field
The invention belongs to the quick computing technique of electromagnetic characteristic of scattering, particularly a kind of Fast Multiple Method that improves calculates The numerical method of efficiency.
Background technology
The radar return characteristic of target has having very important significance in military affairs, proposes a kind of accurate and effective electromagnetism point Analysis model seems particularly important.A kind of effective method for solving the radar return of target is to establish integration side in target surface Journey, it is converted into solving equations.Fast multipole is a kind of efficient numerical side for analyzing Electromagnetic Scattering of Target problem Method (J.Song, C.C.Lu, and W.C.Chew, " Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,”IEEE Trans.Antennas Propag., vol.45, no.10, pp.1488-1493,1997.), the general principle of this method is the addition using Green's function Theorem is deployed, and the effect between far field is converted into polymerizing factor, transfer factor and the form for configuring fac-tor, to reach The purpose for accelerating matrix vector to multiply.
But when analyzing TV university or super Electrically large size object, it is huge that quick multistage son still suffers from computing resource consumption The problem of big.Because in fast multipole techniques, the transferance between group and group is defined in unit Ewald spheres On, and need substantial amounts of sampling to calculate (R.L.Wagner and W.C.Chew, " A ray- in the sphere upper integral propagation fast multipole algorithm,”Microwave Opt.Tech.Lett.,vol.7,no.10, pp.435–438,1994).Therefore, even if efficient interpolation and extrapolation technique can be used.The calculating of transfer process is also very Consumption calculations resource, actually when the distance between two groups are farther apart, it is not necessary that all turns between calculating group Move factor component.
The content of the invention
It is an object of the invention to provide a kind of Gaussian beam method of quick obtaining electromagnetic characteristic of scattering.
The technical scheme for realizing the object of the invention is：A kind of Gaussian beam side of quick obtaining electromagnetic characteristic of scattering Method, step are as follows：
1st step, working frequency f is set, establishes the geometrical model of target, and mesh generation is carried out to model；
2nd step, improved Electric Field Integral Equation is established according to boundary condition in target surface, square is obtained using the golden method of testing of gal the Liao Dynasty Battle array equation group；
3rd step, the Green's function in free space is deployed using addition theorem；
4th step, the locus for the source point being unfolded in Green's function is added into imaginary part displacement, obtained with Gaussian beam The transfer factor of form；
5th step, window function is added in the transfer factor with Gauss velocity of wave form；
6th step, retain angular spectrum component big in transfer factor, cast out small angular spectrum component.
7th step, using alternative manner solution matrix equation group, induced-current expansion coefficient is obtained, and calculate radar scattering Section RCS.
The present invention compared with prior art, its remarkable advantage：(1) transfer factor simple structure.The construction of transfer factor The transfer factor location variable for needing only to deploy Green's function in item in journey adds imaginary part displacement.(2) construction transfer because Sub- high directivity.The transfer factor of construction has the attenuation characteristic of Gaussian beam, and high directivity, the introducing of window function can be further Strengthen the directionality of transfer factor.
Brief description of the drawings
Fig. 1 is target triangular mesh subdivision schematic diagram of the present invention.
Fig. 2 is RWG basic functions schematic diagram of the present invention.
Fig. 3 is the interphase interaction schematic diagram of far field group of the present invention.
Fig. 4 is the disconnected schematic diagram of transfer factor of the present invention.
Fig. 5 is F15 model aircrafts schematic diagram of the present invention.
Fig. 6 is F15 model aircrafts Bistatic RCS result of calculation of the present invention.
Embodiment
In the scheme that the present invention uses, imaginary part position is added by the location variable in Fast multipole transfer factor Move so that transfer factor has the characteristic of Gaussian beam, i.e. transfer factor has larger on the group group center line connecting direction of far field Component, and with transfer factor component direction with group center line connecting direction angle increase and rapid decay；Again in transfer factor It is upper to add window function, further enhance the directionality of transfer factor.Then cast out less transfer factor component, retain larger Component.
The present invention is described in further detail below in conjunction with the accompanying drawings.
The first step, working frequency f is set, establishes the geometrical model of target, and triangular grids are carried out to target, three The average side length of hexagonal lattice is 0.1 λ, and wherein λ represents incident plane wave wavelength.Fig. 1 show target gridding subdivision schematic diagram.
Second step, improved Electric Field Integral Equation is established according to boundary condition in target surface, obtained using the golden method of testing of gal the Liao Dynasty Matrix division ZI=V.Improved Electric Field Integral Equation is expressed as：
Wherein,For imaginary unit, k is wave number, and η is free space wave impedanceFor target surfacePlace Induced-current,For free spaceWithBetween Green's function.To enter Plane wave electric field is penetrated, ▽ represents gradient operator, and ▽ ' represents divergence operator, |tanExpression takes tangential component.In the every of triangle RWG basic functions are defined on bar side
Wherein, l represents the length of side of triangle, A+And A-Represent two triangle Ts where this side+、T-Area.Respectively from the T corresponding to side+、T-Summit set out toThe vector of point, RWG basic functions schematic diagram such as Fig. 2 institutes Show.
By induced-currentIt is expressed as RWG basic functionsCombination, and using the golden method of testing of gal the Liao Dynasty, obtain matrix Equation group ZI=V, wherein Z are impedance matrix, its matrix element ZmnIt is expressed as：
Wherein m and n represents m and nth bar side numbering, s respectivelymAnd snRepresent respectively m and where nth bar side three It is angular.V is that the right is vectorial, its matrix element VmIt is expressed as：
3rd step, the concrete form deployed using addition theorem to the free space Green's function in Matrix division It is as follows：
Wherein,Represent the group center where source pointTo the group center where siteVector,RepresentList Bit vector,Represent source pointTo the group center at placeVector,Represent to organize center to site where siteArrow Amount, as shown in figure 3, L represents to block a number,Represent l rank Hankel function of the second kind, PlRepresent that the Legendre of l ranks is multinomial Formula,For unit surface integral.
(5) in formulaFor transfer factor, it is expressed as
4th step, the locus for the source point being unfolded in Green's function is added into imaginary part displacement, obtained with high bass wave The transfer factor of beam form, transfer factor are embodied as：
Wherein, Δ represents the size of the imaginary part introduced, transfer factorConcrete form be
5th step, window function is added in the transfer factor with Gauss velocity of wave form, by taking cosine window function as an example, transfer Factor representation is
Wherein, ωlFor cosine window function, concrete form is
6th step, set angle threshold θr, when angular spectrum directionWith a group center position vectorBetween angle be less than θr When, transfer factor corresponding to reservationOtherwise when angular spectrum directionWith a group center position vectorBetween angle More than θrWhen, cast out the transfer factor, obtain Matrix division Z'I=V, as shown in Figure 4.
7th step, using alternative manner solution matrix equation Z'I=V, induced-current expansion coefficient I is obtained, is then calculated The far-field RCS of target, is expressed as：
WhereinRepresent Far-field scattering.
In order to verify the correctness of the inventive method and validity, it shown below is and calculate F15 rebecca scattering sections Example, and result of calculation compares with traditional Fast Multiple Method algorithm, coincide very well.
Fig. 5 is F15 model aircrafts, and three direction sizes are in its space：X × Y × Z=26.306m × 18.423m × 5.851m, incident plane wave are 300MHz, and incidence angle is θ=90 °,Discrete trigonometric figurate number mesh is 188952, using six Layer Fast Multiple Method is calculated.Most sub-layers grouping dimension is 0.2 wavelength, and transfer factor introduces imaginary part displacement in layer 6, Size is 3 wavelength.Threshold θrIt is taken as 30 °.By the RCS values that multilevel fast multipole method and the inventive method calculate as schemed Shown in 6, as can be seen from the figure both results are coincide preferable.Due to the transfer factor component that is calculated needed for this method method more It is few, for this example, save as 1.18MB in the consumption of the inventive method layer 6 transfer factor, and multilevel fast multipole method Layer 6 transfer factor consumption in save as 6.25MB, in the process of the present invention relative to traditional Fast multipole based on Less calculating internal memory is needed when calculating transfer factor.

Claims (8)

  1. A kind of 1. Gaussian beam method of quick obtaining electromagnetic characteristic of scattering, it is characterised in that step is as follows：
    1st step, working frequency f is setreq, the geometrical model of target is established, and mesh generation is carried out to model；
    2nd step, improved Electric Field Integral Equation is established according to boundary condition in target surface, matrix side is obtained using the golden method of testing of gal the Liao Dynasty Journey group ZI=V；
    3rd step, the free space Green's function in Matrix division is deployed using addition theorem；
    4th step, the locus for the source point being unfolded in Green's function is added into imaginary part displacement, obtained with Gaussian beam form Transfer factor；
    5th step, window function is added in the transfer factor with Gauss velocity of wave form；
    6th step, retain angular spectrum component big in transfer factor, cast out small angular spectrum component, obtain Matrix division Z'I=V；
    7th step, using alternative manner solution matrix equation group, induced-current expansion coefficient is obtained, and calculate RCS RCS。
  2. 2. the Gaussian beam method of quick obtaining electromagnetic characteristic of scattering according to claim 1, it is characterised in that the 1st Triangular grids are carried out in step to target, the average side length of triangular mesh is 0.1 λ, and wherein λ represents incident plane wave ripple It is long.
  3. 3. the Gaussian beam method of quick obtaining electromagnetic characteristic of scattering according to claim 1, it is characterised in that institute State the 2nd step and improved Electric Field Integral Equation is established according to boundary condition in target surface：
    Wherein,For imaginary unit, k is wave number, and η is free space wave impedanceFor target surfaceThe induced electricity at place Stream,For free spaceWithBetween Green's function；For incident plane wave Electric field,Represent gradient operator,Divergence operator is represented, |tanExpression takes tangential component；Defined in each edge of triangle RWG basic functions
    Wherein, l represents the length of side of triangle, A+And A-Represent two triangle Ts where this side+、T-Area, Point Wei not be from the T corresponding to side+、T-Summit set out toThe vector of point；
    By induced-currentIt is expressed as RWG basic functionsCombination, and using the golden method of testing of gal the Liao Dynasty, obtain Matrix division ZI=V, wherein Z are impedance matrix, and I is unknown current expansion coefficient, and V is the right vector.
  4. 4. the Gaussian beam method of quick obtaining electromagnetic characteristic of scattering according to claim 1, it is characterised in that the 3rd It is as follows to walk the concrete form deployed using addition theorem to the Green's function in free space：
    Wherein,Represent the group center where source pointTo the group center where siteVector,RepresentUnit vector,Represent source pointTo the group center at placeVector,Represent to organize center to site where siteVector, L represent block Item number,Represent l rank Hankel function of the second kind, PlThe Legnedre polynomial of l ranks is represented, For unit surface integral；
    (3) in formulaFor transfer factor, it is expressed as
    <mrow> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mover> <mi>k</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> <msub> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>l</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>L</mi> </munderover> <msup> <mrow> <mo>(</mo> <mo>-</mo> <mi>j</mi> <mo>)</mo> </mrow> <mi>l</mi> </msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>l</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msubsup> <mi>h</mi> <mi>l</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>kr</mi> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>P</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mover> <mi>k</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> <msub> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
  5. 5. the Gaussian beam method of quick obtaining electromagnetic characteristic of scattering according to claim 1, it is characterised in that the 4th It is as follows to walk concrete form：
    Wherein, Δ represents the size of the imaginary part introduced, transfer factorConcrete form be
    <mrow> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mover> <mi>k</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> <msub> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mover> <mi>k</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;CenterDot;</mo> <mi>&amp;Delta;</mi> <msub> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> </mrow> </msup> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>l</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>L</mi> </munderover> <msup> <mrow> <mo>(</mo> <mo>-</mo> <mi>j</mi> <mo>)</mo> </mrow> <mi>l</mi> </msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>l</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msubsup> <mi>h</mi> <mi>l</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>(</mo> <mrow> <msub> <mi>r</mi> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mo>-</mo> <mi>j</mi> <mi>&amp;Delta;</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <msub> <mi>P</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mover> <mi>k</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> <msub> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
  6. 6. the Gaussian beam method of quick obtaining electromagnetic characteristic of scattering according to claim 1, it is characterised in that the 5th Added window function is cosine window function in step, and transfer factor is expressed as
    <mrow> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mover> <mi>k</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> <msub> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mover> <mi>k</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;CenterDot;</mo> <mi>&amp;Delta;</mi> <msub> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> </mrow> </msup> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>l</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>L</mi> </munderover> <msup> <mrow> <mo>(</mo> <mo>-</mo> <mi>j</mi> <mo>)</mo> </mrow> <mi>l</mi> </msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>l</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msubsup> <mi>h</mi> <mi>l</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>(</mo> <mrow> <msub> <mi>r</mi> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mo>-</mo> <mi>j</mi> <mi>&amp;Delta;</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <msub> <mi>P</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mover> <mi>k</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> <msub> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>p</mi> <mi>q</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;omega;</mi> <mi>l</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, ωlFor cosine window function, concrete form is
    <mrow> <msub> <mi>&amp;omega;</mi> <mi>l</mi> </msub> <mo>=</mo> <mo>{</mo> <mrow> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mi>l</mi> <mo>&amp;le;</mo> <mi>L</mi> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mi>l</mi> <mi>L</mi> </mfrac> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>l</mi> <mo>&gt;</mo> <mi>L</mi> <mo>/</mo> <mn>2</mn> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> </mrow> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
  7. 7. the Gaussian beam method of quick obtaining electromagnetic characteristic of scattering according to claim 1, it is characterised in that the 6th In step, set angle threshold θr, when angular spectrum directionWith a group center position vectorBetween angle be less than θrWhen, retain corresponding Transfer factorOtherwise when angular spectrum directionWith a group center position vectorBetween angle be more than θrWhen, cast out The transfer factor.
  8. 8. the Gaussian beam method of quick obtaining electromagnetic characteristic of scattering according to claim 1, it is characterised in that the 7th Step utilizes alternative manner solution matrix equation Z'I=V, obtains induced-current expansion coefficient I, then calculates the far-field RCS of target, It is expressed as：
    <mrow> <mi>R</mi> <mi>C</mi> <mi>S</mi> <mo>=</mo> <munder> <mi>lim</mi> <mrow> <mi>x</mi> <mo>&amp;RightArrow;</mo> <mi>&amp;infin;</mi> </mrow> </munder> <mn>4</mn> <msup> <mi>&amp;pi;r</mi> <mn>2</mn> </msup> <mfrac> <mrow> <mo>|</mo> <msup> <mover> <mi>E</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>s</mi> <mi>c</mi> <mi>a</mi> <mo>)</mo> </mrow> </msup> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <mrow> <mo>|</mo> <msup> <mover> <mi>E</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>i</mi> <mi>n</mi> <mi>c</mi> <mo>)</mo> </mrow> </msup> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    WhereinRepresent Far-field scattering.
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