CN104573376B - A kind of Finite-Difference Time-Domain Method calculates the transient field far field Extrapolation method of electromagnetic scattering - Google Patents
A kind of Finite-Difference Time-Domain Method calculates the transient field far field Extrapolation method of electromagnetic scattering Download PDFInfo
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Abstract
A kind of Finite-Difference Time-Domain Method calculates the transient field far field Extrapolation method of electromagnetic scattering, and step has：1st, zoning is divided into by total place and scattering place Liang Ge regions by fillet；2nd, extrapolated boundary is set in scattering place, the electric field and magnetic field extrapolation on extrapolated boundary is obtained into far zone field；The 3rd, transient state incidence wave is set, electric field and magnetic field are updated successively in each time step, until magnetic distribution tends to stable state；The 4th, far field is write as to the product of frequency factor and integrating factor, inverse Fourier transform is carried out to integrating factor, time-domain expression is obtained；The 5th, integrating factor far field time domain response array is set；6th, the time domain response of integrating factor far field, which is fourier transformed, obtains its frequency domain response；7th, using far field and the frequency domain response of incidence wave, changes of the RCS with frequency is obtained.This method is write as far field the form of the product of frequency factor and integrating factor, and the frequency-time domain transformation and time-frequency conversion form of integrating factor are relatively simple, simplify calculating, improve efficiency.
Description
First, technical field
The present invention provides the transient field far field Extrapolation method that a kind of Finite-Difference Time-Domain Method calculates electromagnetic scattering, and it is specifically related to
And the Electromagnetic Simulation method of Finite-Difference Time-Domain Method (finite-difference time-domain, FDTD), belong to electromagnetic field
Simulation technical field.
2nd, background technology
Finite-Difference Time-Domain Method be FDTD be Electromagnetic Simulation a kind of important method, there is extensive use in electromagnetic arts.
The general principle of this method is that maxwell equation group is separated into difference scheme, using YeeShi grids on room and time
Interleaved character, realize that the alternating in electric field and magnetic field updates, solution obtains electromagnetic field and is distributed with room and time.Counted with FDTD
When calculating Electromagnetic Scattering of Target, zoning is divided into total place and scattering place first, added by fillet into radio
Magnetic wave, is extrapolated to far field by the electromagnetic field for scattering place according to the principle of equal effects, can try to achieve the RCS (radar of target
Cross section, RCS).
If the in-field of humorous form when choosing, it can solve when magnetic distribution tends to stable state and draw electromagnetic field point
The amplitude and phase information of cloth, but the solution of a frequency can only be drawn in this way, it is impossible to FDTD method time domains are played completely
The advantage of calculating.To obtain the frequency domain response of Electromagnetic Scattering of Target, often using transient field as in-field, solution obtains far field
Transient response, then frequency domain response can be obtained by Fourier transformation.The far field extrapolation of conventional method Three dimensional transient needs to carry out
The Difference Calculation of far field time domain response, is calculated complex.The extrapolation of two-dimensional transient far field also needs to contrast two and three dimensions
Frequency domain far zone field expression formula, result is exported premised on Three dimensional transient field method.
Far field is expressed as the product of frequency factor and integrating factor by transient field Extrapolation method proposed by the present invention, only to product
Molecular group enters line translation, frequency factor keeps constant, it is to avoid Difference Calculation, simplifies time domain to the conversion of frequency domain, while
Two dimension is united with three-dimensional Extrapolation method, two-dimensional transient push away outside the venue also without using Three dimensional transient field extrapolating results before
Carry.When frequency factor is not involved in frequency and time-frequency conversion, and integrating factor carries out far field extrapolation and obtains time domain response, further across
Fourier transformation obtains far field frequency domain response, then is multiplied with frequency factor, finally gives RCS in each frequency.
3rd, the content of the invention
The purpose of the present invention is form complexity, the amount of calculation of traditional transient field far field Extrapolation method in being calculated for FDTD
Greatly, the characteristics of two-dimentional Extrapolation method of three peacekeepings has association, proposes a kind of new transient field far field Extrapolation method, i.e., a kind of time domain
Finite difference calculus calculates the transient field far field Extrapolation method of electromagnetic scattering, and this method is specifically comprised the steps of：
Step 1：Zoning is divided into by total place and scattering place Liang Ge regions, the electricity of total place by fillet
Magnetic field contains in-field and scattered field, and scatters place and only include scattered field；
Step 2：Extrapolated boundary is set in scattering place, the electric field and magnetic field extrapolation on extrapolated boundary are obtained into far zone field；
Step 3：Transient state incidence wave is set, electric field and magnetic field are updated successively in each time step, until magnetic distribution becomes
In stable state；
Step 4：Far field is write as to the product of frequency factor and integrating factor, inverse Fourier transform is carried out to integrating factor,
Obtain time-domain expression；
Step 5：Integrating factor far field time domain response array is set, by each time step extrapolated boundary electromagnetic field to far field
Response is added in integrating factor far field time domain response array；
Step 6：The time domain response of integrating factor far field, which is fourier transformed, obtains its frequency domain response；
Step 7：Using far field and the frequency domain response of incidence wave, changes of the RCS with frequency is obtained.
Wherein, described " zoning " in step 1, refers to a cuboid (three-dimensional case) or rectangle (two-dimentional feelings
Shape) region, the sampling of electromagnetic field, iteration are just carried out in this region.Affiliated " is divided into total place and scattering place Liang Ge areas
Domain ", refers to as shown in Fig. 2 with a cuboid (three-dimensional case) or the fillet of rectangle (two-dimensional case), by zoning
It is divided into two, it is scattering place beyond total place, fillet to be within fillet, and scattering object is located at total place.
Wherein, described " extrapolated boundary " in step 2, refers to a cuboid (three-dimensional case) for being located at scattering place
Or rectangle (two-dimensional case) border, total place is included, because extrapolated boundary is located on scattering place, therefore extrapolated boundary
Electromagnetic field there was only scattered field, not comprising in-field, the far field obtained by its extrapolation just only has the contribution of scattered field, can directly count
It is RCS to calculate RCS.
Wherein, described " magnetic distribution tends to stable state " in step 3, refers to the electromagnetic field of total place and scattering place
Do not change substantially.
Wherein, in " product that far field is write as to frequency factor and integrating factor " described in step 4, its three-dimensional case refers to
Following expression：
WhereinIt is radar wave receiving polarization direction, jke-jkr/ (4 π r) is frequency factor, and I is integrating factor, EiIt is
Incident field intensity, integrating factor I expression formula is
WhereinIt is far field reception antenna magnetic field polarised direction, r is distance of the source point to site, and S is extrapolated boundary
Face,It is vacuum wave impedance；
Exemplified by its two-dimensional case is with horizontal magnetic (Transverse Magnetic, TM) ripple, expression formula is as follows：
WhereinIt is the coordinate vector in z directions,It is frequency factor, I ' is integrating factor, and expression formula is
Wherein l is extrapolated boundary, and extrapolated boundary is a rectangle under two-dimensional case, therefore the form with line integral.
Wherein, it is described in steps of 5 " each time step extrapolated boundary electromagnetic field to be added to integration to the response in far field
In factor far field time domain response array ", refer to far field contributor of the diverse location to integrating factor on each time step extrapolated boundary
At the time of being embodied in different, it is therefore desirable to the integrating factor far field time domain response array for being prepared in advance to be filled, when each
Corresponding far field contributor is added in integrating factor far field time domain response array by spacer step.
It is wherein, described " using far field and the frequency domain response of incidence wave, obtaining changes of the RCS with frequency " in step 7,
Refer to the definition according to RCS, RCS is written as form：
(three-dimensional case) (5)
(two-dimensional case) (6)
Wherein f is frequency, and I and I ' are the integrating factor far field frequency domain responses of three peacekeeping two-dimensional cases, and c is the light velocity, EiIt is
Incidence wave.
The advantage of the method for the invention is：This method is write as far field the form of the product of frequency factor and integrating factor,
Frequency factor is not involved in conversion, and the frequency-time domain transformation of integrating factor and time-frequency conversion form are relatively simple, therefore simplifies meter
Calculate, improve efficiency.
4th, illustrate
Fig. 1 is the method for the invention flow chart；
Fig. 2 is the division schematic diagram of zoning of the present invention.
5th, embodiment
Below in conjunction with drawings and examples, the present invention is described in further detail.
As shown in figure 1, a kind of Finite-Difference Time-Domain Method of the invention calculates the transient field far field Extrapolation method of electromagnetic scattering, it
Comprise the following steps：
Step 1：Zoning is divided into by total place and scattering place by fillet, the electromagnetic field of total place is contained
In-field and scattered field, and the electromagnetic field for scattering place only includes scattered field；
Step 2：The extrapolated boundary of closing is set in scattering place, for far field extrapolation；
Step 3：Transient state incidence wave is set, electric field and magnetic field are updated successively in each time step, until magnetic distribution becomes
In stable state；
Step 4：Far field is write as to the product of frequency factor and integrating factor, integrating factor is subjected to inverse Fourier transform,
Obtain time-domain expression；
Step 5：Far field integrating factor time domain response array is set, by each time step extrapolated boundary electromagnetic field to far field
Response is added in the integrating factor time domain response array of far field；
Step 6：Far field integrating factor time domain response, which is fourier transformed, obtains far field integrating factor frequency domain response；
Step 7：By frequency factor and far field integrating factor frequency domain response product, in conjunction with the frequency domain response of in-field, obtain
To changes of the RCS with frequency.
For being further described below for above-mentioned steps：
Step 1：Calculate dividing field zones
As shown in Fig. 2 zoning has been divided into total place and scattering place by fillet.The electromagnetic field bag of total place
In-field and scattered field are contained, and have scattered place and only include scattered field.Total place is discontinuous in fillet with scattering place
, it is necessary to during time-domain difference consider in-field influence.And the inside of the inside and scattering place in total place, all respectively
From meeting maxwell equation group, it is not necessary to which difference scheme is modified.Border in zoning, by absorbing boundary plus
To block, to simulate infinite space.
Step 2：Extrapolated boundary is set
As shown in Fig. 2 extrapolated boundary is set in scattering place, for far field extrapolation.Extrapolated boundary is located at scattering place, leads to
Cross the field that the principle of equal effects can be on extrapolated boundary and obtain electric field E outside field outside extrapolated boundary, such as extrapolated boundarysExpression-form
For
WhereinIt is empty unit, the π f of ω=2 are angular frequencies, and ε is dielectric constant, and A is electric vector potential function, and F is magnetic
Vector bit function,It is electric scalar bit function, three bit function expression formulas are respectively
Wherein μ is magnetic conductivity,It is normal direction outside extrapolated boundary, E and H are electric field and magnetic field on extrapolated boundary, G=respectively
e-jk|r-r′|/ (4 π | r-r ' |) it is Green's function, r is site position vector, and r ' is the position vector on extrapolated boundary,SIt is extrapolation
Border.If r=| r |, there are r ＞ ＞ 1 for far field,The far field Green's function form in direction isEnter
One step passes through corresponding relationFar field electric field can be written as form：
Section 2 in integration only has the component along scattering direction, without cross stream component, and only considers in RCS calculating process
Cross stream component, therefore Section 2 can not consider in follow-up calculate.
Step 3：Transient state in-field is set, Difference Calculation is carried out
Transient state incidence wave has certain bandwidth, can draw frequency domain response through once emulating.The present invention uses differential Gauss
Pulse is shown below as transient state incidence wave, expression-form：
Wherein τ is pulse width, t0It is time offset.In specific simulation process, parameter is set to t0The Δ of=0.8 τ, τ=60
T, wherein Δ t are time steps.The frequency domain response of the transient state incidence wave is
Above formula is write as to frequency f expression formula, it is as follows：
The spatial distribution in electric field and magnetic field is updated successively in each time step, until magnetic distribution tends to stable state.Update
Method is that the differential form of maxwell equation group is separated into difference form, then electric field and magnetic field are expressed as into Explicit Form,
It is as follows：
In formula, Hn-1/2And Hn+1/2It is moment (n-1/2) Δ t and (n+1/2) Δ t magnetic field intensity, EnAnd En+1It is moment n
Δ t and (n+1) Δ t electric-field intensity, σ is electrical conductivity, σmIt is permeability.Pass through the difference equation of formula (13), you can obtain electricity
Field and distribution situation of the magnetic field in zoning.
Step 4：Far field is write as to the product of frequency factor and integrating factor, and integrating factor is subjected to inverse Fourier transform
Obtain forms of time and space
IfIt is radar wave receiving polarization direction, then in view of formula (9), far field electric field in this direction is represented by
Wherein jke-jkr/ (4 π r) is frequency factor, and I is integrating factor, EiIt is incident field intensity, integrating factor I table
It is up to formula
WhereinIt is far field reception antenna magnetic field polarised direction, r is distance of the source point to site, and S is extrapolated boundary
Face,It is vacuum wave impedance.According to k=ω/c, wherein c is the light velocity, and integrating factor I can be written as：
Above formula is subjected to inverse Fourier transform, is write as the form of the sum by magnetic field and the contribution of electric field two parts：
I (t)=IH(t)+IE(t) (17)
Wherein IH(t) far zone field as caused by tangential magnetic field, I are representedE(t) far zone field, table as caused by tangential electric field are represented
It is up to formula.
There is similar form in the far field of two-dimensional case, by taking horizontal magnetic (Transverse Magnetic, TM) ripple as an example, expression
Formula is as follows：
WhereinIt is the coordinate vector in z directions,Frequency factor, I ' be integration under two-dimensional case because
Son, expression formula is
Wherein l is extrapolated boundary.Extrapolated boundary is a rectangle under two-dimensional case, therefore the form with line integral.
Step 5：Calculate the far field time domain response of integrating factor
Integrating factor far field time domain response array is set, each time step extrapolated boundary electromagnetic field is folded to the response in far field
It is added in integrating factor far field time domain response array.
By IHAnd I (t)E(t) expression formula (18) and (19) are as can be seen that because r ' is on the extrapolated boundary face of integration,
Obtaining the integrating factor expression formula of t needs to try to achieve the value of magnetic field H and electric field E within a period of time first, and general
FDTD calculating process only retains the value of current time step, uses constant.The method that the present invention is used is to set integration first
The far-field response array of the factor, contribution of each grid to far field on each time step extrapolated boundary is added to far-field response number
In group, so there is no need to preserve the value of electric field and magnetic field within a period of time, memory cost is greatly reduced.By formula (18)
Discretization is integrated, it is as follows：
Wherein IHm(t) be expressed as the contribution of each grid on the face of extrapolated boundary, by it be expressed as the value of grid midpoint with
The product of grid area, it is as follows：
Wherein m represents grid sequence number on extrapolated boundary,Represent m-th of grid midpoint
The magnetic field intensity at moment, δ is size of mesh opening, then δ2It is grid area.Formula (23) can also be written as form：
The magnetic field that above formula can be walked by current time obtains not far field contributor in the same time.By space, time discretization, following institute
Show：
Wherein s=c Δs t/ δ are time factor, nx,ny,nzIt is r 'mIn x, y, the coordinate in z directions to the grid number of origin, n
It is emulation current time step number.Electric field is sampled in n time steps in the present invention, and magnetic field is sampled in n+1/2 time steps, therefore formula (25)
Contain n+1/2 in expression formula.With the discrete grid block sequence number in FDTD, time step expression (25), obtain
Wherein nHf=1/2- (sxnx+syny+sznz)/s.Formula (26) means the magnetic field tangential component of n+1/2 time steps
Assign n+nHfThe far field integrating factor of time step, but far field integrating factor only takes in integer time step in program implement
Value, and n+nHfIn general it is not integer.The method that the present invention is used is to distribute the integrating factor at the moment by a certain percentage
It is bigger than proportion shared by the integer more closed on to two adjacent integers.If [nHf] it is nHfInteger part, { nHfIt is nHf's
Fractional part, then can be by IHmAccording to 1- { nHfAnd { nHfPro rate give n+ [nHf] and n+ [nHf]+1 time step far field product
Molecular group.Subscript in view of array all takes positive integer value, therefore along with fully big time step offset nτ, meet array
Under be designated as positive requirement, obtain：
The contribution in far field is occurred without in the formula of both sides, it is necessary to modified to formula (25) for electric field on extrapolated boundary
1/2, because electric field is in integer time step value.The integrating factor time domain for trying to achieve far zone field by time step n tangential electric field is rung
Answer formula as follows
Wherein IEmRepresent contribution of the tangential electric field to far field on m-th of grid, nEf=-(sxnx+syny+sznz)/s,
[nEf] represent nEfInteger part, { nEfRepresent nEfFractional part.
Step 6：Far field integrating factor time domain response Fourier transformation
Far field integrating factor time domain response, which is fourier transformed, obtains far field integrating factor frequency domain response, and transformation for mula is
Due to I (t) the only values on integer time step, therefore integration can be written as
Wherein N is the time step sum in integrating factor far field.Formula (32) is write as to frequency f form, can obtain integration because
Sub- far field frequency domain response, i.e.,
Step 7：Calculate changes of the RCS with frequency
It is required that RCS, in addition it is also necessary to try to achieve the frequency domain response of incidence wave, computational methods are as follows：
M is the step number of emulation, E in formulai(n) it is incident field intensity on n-th of time step.Further according to formula (14), i.e.,
It can obtain changes of the RCS with frequency：
Above formula has used k=2 π f/c, further tries to achieve RCS value
For two-dimensional case, RCS has similar expression formula, is
It should be pointed out that this example only listing property illustrates the application process of the present invention, not for the limitation present invention.It is any ripe
The personnel of such a use technology are known, above-described embodiment can be modified without departing from the spirit and scope of the present invention.Cause
This, the scope of the present invention should be as listed by claims.
Claims (6)
1. a kind of Finite-Difference Time-Domain Method calculates the transient field far field Extrapolation method of electromagnetic scattering, it is characterised in that：This method bag
Containing following steps：
Step 1：Zoning is divided into by total place and scattering place Liang Ge regions, the electromagnetic field of total place by fillet
In-field and scattered field are contained, and scatters place and only includes scattered field；
Step 2：Extrapolated boundary is set in scattering place, the electric field and magnetic field extrapolation on extrapolated boundary are obtained into far zone field；
Step 3：Transient state incidence wave is set, electric field and magnetic field are updated successively in each time step, until magnetic distribution tends to be steady
State；
Step 4：Far field is write as to the product of frequency factor and integrating factor, inverse Fourier transform is carried out to integrating factor, obtained
Time-domain expression；
Step 5：Integrating factor far field time domain response array, the response by each time step extrapolated boundary electromagnetic field to far field are set
It is added in integrating factor far field time domain response array；
Step 6：The time domain response of integrating factor far field, which is fourier transformed, obtains its frequency domain response；
Step 7：Using far field and the frequency domain response of incidence wave, changes of the RCS with frequency is obtained；
Wherein, the product that far field is write as to frequency factor and integrating factor described in step 4, its three-dimensional case expression formula is：
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WhereinIt is far field reception antenna magnetic field polarised direction, r is distance of the source point to site, and S is extrapolated boundary face,It is vacuum wave impedance；R ' is the position vector on extrapolated boundary；
Its two-dimensional case is that transverse magnetic wave is TM ripples, and expression formula is：
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Wherein l is extrapolated boundary, and extrapolated boundary is a rectangle under two-dimensional case, therefore the form with line integral.
2. a kind of Finite-Difference Time-Domain Method according to claim 1 calculates the transient field far field Extrapolation method of electromagnetic scattering,
It is characterized in that：In step 1 described " zoning ", the cuboid of a three-dimensional case is referred to, or two-dimensional case
Rectangular area, the sampling of electromagnetic field or iteration are just carried out in this region；Described " is divided into total place and scattering place Liang Ge areas
Domain ", refers to the cuboid with a three-dimensional case, or two-dimensional case rectangle fillet, zoning is divided into two,
It is scattering place beyond total place, fillet to be within fillet, and scattering object is located at total place.
3. a kind of Finite-Difference Time-Domain Method according to claim 1 calculates the transient field far field Extrapolation method of electromagnetic scattering,
It is characterized in that：In step 2 described " extrapolated boundary ", the cuboid for being located at a three-dimensional case of scattering place is referred to,
Or the border of two-dimensional case rectangle, total place is included, because extrapolated boundary is located at scattering place, therefore extrapolated boundary
On electromagnetic field there was only scattered field, not comprising in-field, the far field obtained by its extrapolation just only has the contribution of scattered field, directly meter
It is RCS to calculate RCS.
4. a kind of Finite-Difference Time-Domain Method according to claim 1 calculates the transient field far field Extrapolation method of electromagnetic scattering,
It is characterized in that：In step 3 described " magnetic distribution tends to stable state ", on the electromagnetic field for referring to total place and scattering place
Do not change.
5. a kind of Finite-Difference Time-Domain Method according to claim 1 calculates the transient field far field Extrapolation method of electromagnetic scattering,
It is characterized in that：It is described in steps of 5 " by each time step extrapolated boundary electromagnetic field the response in far field is added to integration because
In sub- far field time domain response array ", refer to far field contributor body of the diverse location to integrating factor on each time step extrapolated boundary
At the time of now different, it is therefore desirable to the integrating factor far field time domain response array for being prepared in advance to be filled, in each time
Corresponding far field contributor is added in integrating factor far field time domain response array by step.
6. a kind of Finite-Difference Time-Domain Method according to claim 1 calculates the transient field far field Extrapolation method of electromagnetic scattering,
It is characterized in that：In step 7 described " using far field and the frequency domain response of incidence wave, obtaining changes of the RCS with frequency ", it is
Refer to the definition according to RCS, RCS is written as form：
Corresponding three-dimensional case：Formula (5)
Corresponding three-dimensional case：Formula (6)
Wherein f is frequency, and I and I ' are the integrating factor far field frequency domain responses of three peacekeeping two-dimensional cases, and c is the light velocity, EiIt is incident
Ripple.
Priority Applications (1)
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| CN105572652B (en) * | 2016-03-18 | 2018-01-05 | 西北工业大学 | It is a kind of to obtain the method with Multiple Scattering target far-field RCS using extrapolation |
| CN106326659B (en) * | 2016-08-26 | 2019-04-26 | 上海无线电设备研究所 | Metal medium composite object electromagnetism Scattering Calculation method based on ray tracing |
| CN106526543B (en) * | 2016-11-09 | 2019-01-25 | 北京环境特性研究所 | A kind of pulse accumulation algorithm for far-field RCS measurement |
| CN107169174B (en) * | 2017-04-24 | 2019-11-05 | 西安电子科技大学 | Umbrella antenna electromechanics Integrated Optimal Design method under optimal focal length |
| CN107203680A (en) * | 2017-06-23 | 2017-09-26 | 欢鼎科技成都有限公司 | A kind of new explicit time iteration Time Domain Electromagnetic computational methods and device |
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