CN104573376A - Method of calculating far extrapolation of transient field of electromagnetic scattering through finite difference time domain - Google Patents

Abstract

A method of calculating far extrapolation of a transient field of electromagnetic scattering through finite difference time domain includes the steps of 1 dividing an area to be calculated into a main field area and a scattering field area according to the connecting boundary; 2 setting an extrapolation boundary in the scattering field area, and extrapolating electric fields and magnetic fields on the extrapolation boundary to obtain a far field; 3 setting transient incident waves, and sequentially updating the electric fields and the magnetic fields at each time step until the electromagnetic field distribution becomes steady; 4 writing the far field into a product of frequency factors and integral factors, and performing inverse Fourier transform on the integral factors to obtain a time domain expression; 5 setting an integral factor far field time domain response array; 6 performing Fourier transform on integral factor far field time domain response to obtain integral factor far field frequency domain response; 7 using far field and incident wave frequency domain response to obtain RCS (Radar Cross Section) changes with frequency. The method of calculating far extrapolation of the transient field of electromagnetic scattering through finite difference time domain writes the far field into the form of the product of the frequency factors and the integral factors due to the fact that the forms of frequency-time transform and time-frequency transform of the integral factors are simple, thereby simplifying the calculation and improving the efficiency.

Description

A kind of Finite-Difference Time-Domain Method calculates the transient field far field Extrapolation method of electromagnetic scattering

One, technical field

The invention provides the transient field far field Extrapolation method that a kind of Finite-Difference Time-Domain Method calculates electromagnetic scattering, it is specifically related to Finite-Difference Time-Domain Method (finite-difference time-domain, FDTD) Electromagnetic Simulation method, belongs to electromagnetic-field simulation technical field.

Two, background technology

Finite-Difference Time-Domain Method and FDTD are a kind of important method of Electromagnetic Simulation, have widespread use at electromagnetic arts.The ultimate principle of the method is that maxwell equation group is separated into difference scheme, utilizes the interleaved character of YeeShi grid on room and time, realizes alternately upgrading of Electric and magnetic fields, solves to obtain electromagnetic field and distribute with room and time.When calculating Electromagnetic Scattering of Target with FDTD, first zoning is divided into total place and scattering place, incident electromagnetic wave is added by fillet, according to equivalence principle, the electromagnetic field of scattering place is extrapolated to far field, the RCS (radar crosssection, RCS) of target can be tried to achieve.

If the incident field of humorous form when choosing, when magnetic distribution is tending towards stable state, the amplitude and phase information that draw magnetic distribution can be solved, but the solution of a frequency can only be drawn in this way, the advantage of FDTD method time-domain calculation can not be played completely.For obtaining the frequency domain response of Electromagnetic Scattering of Target, often adopting transient field as incident field, solving and obtain far field transient response, then can frequency domain response be obtained by Fourier transform.The extrapolation of far field, classic method Three dimensional transient field needs the Difference Calculation of carrying out far field time domain response, calculates comparatively complicated.The extrapolation of far field, two-dimensional transient field also needs the frequency domain far zone field expression formula contrasting two and three dimensions, premised on Three dimensional transient field method, derive result.

Far field is expressed as the product of frequency factor and integrating factor by the transient field Extrapolation method that the present invention proposes, only integrating factor is converted, frequency factor remains unchanged, avoid Difference Calculation, simplify the conversion of time domain to frequency domain, two dimension and three-dimensional Extrapolation method are united, two-dimensional transient pushes away outside the venue not to be needed premised on the extrapolating results of Three dimensional transient field yet simultaneously yet.When frequency factor does not participate in frequently and time-frequency conversion, and integrating factor carries out far field extrapolation and obtains time domain response, obtains far field frequency domain response, then is multiplied with frequency factor, finally obtain RCS in each frequency further across Fourier transform.

Three, summary of the invention

The object of the invention is the feature that complex forms, calculated amount are large, three peacekeeping two dimension Extrapolation method exist association of traditional transient field far field Extrapolation method in calculating for FDTD, a kind of new transient field far field Extrapolation method is proposed, namely Finite-Difference Time-Domain Method calculates a transient field far field Extrapolation method for electromagnetic scattering, and the method specifically comprises following steps:

Step 1: by fillet, zoning is divided into total place and Liang Ge region, scattering place, the electromagnetic field of total place contains incident field and scattered field, and scattering place only comprises scattered field;

Step 2: arrange extrapolated boundary in scattering place, obtains far zone field by the Electric and magnetic fields extrapolation on extrapolated boundary;

Step 3: arrange transient state incident wave, upgrades Electric and magnetic fields successively at each time step, until magnetic distribution is tending towards stable state;

Step 4: product far field being write as frequency factor and integrating factor, carries out inverse Fourier transform to integrating factor, obtains time-domain expression;

Step 5: arrange integrating factor far field time domain response array, is added in integrating factor far field time domain response array by the response of each time step extrapolated boundary electromagnetic field to far field;

Step 6: the time domain response of integrating factor far field obtains its frequency domain response through Fourier transform;

Step 7: the frequency domain response utilizing far field and incident wave, obtains the change of RCS with frequency.

Wherein, described in step 1 " zoning ", refer to a rectangular parallelepiped (three-dimensional case) or rectangle (two-dimensional case) region, sampling, the iteration of electromagnetic field are just carried out in this region.Affiliated " being divided into total place and Liang Ge region, scattering place ", refer to as shown in Figure 2, with the fillet of a rectangular parallelepiped (three-dimensional case) or rectangle (two-dimensional case), zoning is divided into two, it is total place within fillet, be scattering place beyond fillet, scatterer is positioned at total place.

Wherein, described in step 2 " extrapolated boundary ", refer to the rectangular parallelepiped (three-dimensional case) or rectangle (two-dimensional case) border that are positioned at scattering place, total place is included, because extrapolated boundary is positioned at scattering place, the electromagnetic field therefore on extrapolated boundary only has scattered field, does not comprise incident field, the far field obtained by its extrapolation just only has the contribution of scattered field, can directly calculate RCS and RCS.

Wherein, described in step 3 " magnetic distribution is tending towards stable state ", refer to that the electromagnetic field of total place and scattering place does not change substantially.

Wherein, " far field being write as the product of frequency factor and integrating factor " described in step 4, its three-dimensional case refers to following expression:

${\hat{e}}_s\·E_s=\mathrm{jk}{e}^{\mathrm{jkr}}/\left(4\mathrm{\πr}\right)I---\left(1\right)$

Wherein radar wave receiving polarization direction, jke ^-jkr/ (4 π r) is frequency factor, and I is integrating factor, E _ibe incident field intensity, the expression formula of integrating factor I is

$I={\∫}_S(-\mathrm{\η}{\hat{e}}_s\·\hat{n}\×H+{\hat{h}}_s\·\hat{n}\×E)e^{\mathrm{jk}\hat{s}\·r^{\′}}\mathrm{dS}---\left(2\right)$

Wherein be receiving antenna magnetic field, far field polarised direction, r is the distance that source point is shown up a little, and S is face, extrapolated boundary, it is vacuum wave impedance;

Its two-dimensional case is for horizontal magnetic (Transverse Magnetic, TM) ripple, and expression formula is as follows:

$\hat{z}\·E_z=e^{-\mathrm{jkr}}\sqrt{\frac{\mathrm{jk}}{8\mathrm{\πr}}}{I}^{\′}---\left(3\right)$

Wherein the coordinate vector in z direction, be frequency factor, I ' is integrating factor, and expression formula is

$I^{\′}={\∫}_l(-\mathrm{\η}{\hat{e}}_s\·\hat{n}\×H+{\hat{h}}_s\·\hat{n}\×E)e^{\mathrm{jk}\hat{s}\·r^{\′}}\mathrm{dl}---\left(4\right)$

Wherein l is extrapolated boundary, and under two-dimensional case, extrapolated boundary is a rectangle, therefore has the form of line integral.

Wherein, described in steps of 5 " response of each time step extrapolated boundary electromagnetic field to far field is added in integrating factor far field time domain response array ", refer to that on each time step extrapolated boundary, the far field contributor of diverse location to integrating factor is embodied in the different moment, therefore need the integrating factor far field time domain response array being prepared in advance to be filled, at each time step, the far field contributor of correspondence is added in integrating factor far field time domain response array.

Wherein, described in step 7 " utilize the frequency domain response of far field and incident wave, obtain the change of RCS with frequency ", refers to the definition according to RCS, is write RCS as following form:

$\mathrm{\σ}\left(f\right)=\frac{{\mathrm{\πf}}^2}{c^2}\frac{I^2\left(f\right)}{{\left|E_i\left(f\right)\right|}^2}$ (three-dimensional case) (5)

$\mathrm{\σ}\left(f\right)=\frac{\mathrm{\πf}}{2c}\frac{I^{\′2}\left(f\right)}{{\left|E_i\left(f\right)\right|}^2}$ (two-dimensional case) (6)

Wherein f is frequency, I and I ' is the integrating factor far field frequency domain response of three peacekeeping two-dimensional case, and c is the light velocity, E _iit is incident wave.

The advantage of the method for the invention is: the long-pending form of frequency factor and integrating factor is write as in far field by the method, frequency factor does not participate in conversion, and the frequency-time domain transformation of integrating factor and time-frequency conversion form are comparatively simple, because this simplify calculating, improve efficiency.

Four, accompanying drawing explanation

Fig. 1 is the method for the invention process flow diagram;

Fig. 2 is the division schematic diagram of zoning of the present invention.

Five, 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 present invention calculates the transient field far field Extrapolation method of electromagnetic scattering, and it comprises the following steps:

Step 1: zoning is divided into total place and scattering place by fillet, the electromagnetic field of total place contains incident field and scattered field, and the electromagnetic field of scattering place only comprises scattered field;

Step 2: arrange closed extrapolated boundary in scattering place, extrapolates for far field;

Step 3: arrange transient state incident wave, upgrades Electric and magnetic fields successively at each time step, until magnetic distribution is tending towards stable state;

Step 4: product far field being write as frequency factor and integrating factor, carries out inverse Fourier transform by integrating factor, obtains time-domain expression;

Step 5: arrange far field integrating factor time domain response array, is added to the response of each time step extrapolated boundary electromagnetic field to far field in far field integrating factor time domain response array;

Step 6: far field integrating factor time domain response obtains far field integrating factor frequency domain response through Fourier transform;

Step 7: by frequency factor and far field integrating factor frequency domain response product, then in conjunction with the frequency domain response of incident field, obtain the change of RCS with frequency.

As follows for further illustrating of above-mentioned steps:

Step 1: calculated field Division

As shown in Figure 2, zoning has been divided into total place and scattering place by fillet.The electromagnetic field of total place contains incident field and scattered field, and scattering place only comprises scattered field.Total place and scattering place are discontinuous at fillet, need the impact considering incident field in time-domain difference process.And in the inside of total place and the inside of scattering place, meet maxwell equation group all separately, do not need to change difference scheme.On the border of zoning, blocked by absorbing boundary, to simulate infinite space.

Step 2: extrapolated boundary is set

As shown in Figure 2, extrapolated boundary is set in scattering place, extrapolates for far field.Extrapolated boundary is positioned at scattering place, can be obtained the field outside extrapolated boundary, as the electric field E outside extrapolated boundary by equivalence principle by the field on extrapolated boundary _sexpression-form is

Wherein shi Xu unit, ω=2 π f is angular frequency, and ε is specific inductive capacity, and A is electric vector potential function, and F is magnetic vector potential function, be electric scalar potential function, three bit function expression formulas are respectively

Wherein μ is magnetic permeability, be normal direction outside extrapolated boundary, E and H is the Electric and magnetic fields on extrapolated boundary respectively, G=e ^{-jk|r-r ' |}/ (4 π | r-r ' |) be Green function, r is field point position vector, and r ' is the position vector on extrapolated boundary, _sit is extrapolated boundary.If r=|r|, there is r > > 1 for far field, the far field Green function form in direction is further by corresponding relation can far field electric field be write as following form:

$E_s=\frac{e^{-\mathrm{jkr}}}{4\mathrm{\πr}}{\∫}_S(-\mathrm{j\ω\μ}(\hat{n}\×H)+\mathrm{jk}\hat{s}(\hat{n}\·E)-\mathrm{jk}\hat{s}\×(\hat{n}\×E))e^{\mathrm{jk}\hat{s}\·r^{\′}}\mathrm{dS}---\left(9\right)$

Section 2 in integration only has the component along scattering direction, does not have cross stream component, and only considers cross stream component in RCS computation process, and therefore Section 2 will not be able to be considered in subsequent calculations.

Step 3: arrange transient state incident field, carries out Difference Calculation

Transient state incident wave has certain bandwidth, can draw frequency domain response through once emulating.The present invention adopts differential Gauss pulse as transient state incident wave, and expression-form is shown below:

$f\left(t\right)=(t-t_0)e^{-4\mathrm{\π}{\left(\frac{t-t_0}{\mathrm{\τ}}\right)}^2}---\left(10\right)$

Wherein τ is pulse width, t ₀it is time offset.In concrete simulation process, parameter is set to t ₀=0.8 τ, τ=60 Δ t, wherein Δ t is time step.The frequency domain response of this transient state incident wave is

$f\left(\mathrm{\ω}\right)=-\mathrm{j\ω}\frac{{\mathrm{\τ}}^3}{16\mathrm{\π}}{e}^{-\frac{{\mathrm{\τ}}^2{\mathrm{\ω}}^2}{16{\mathrm{\π}}^2}}---\left(11\right)$

Above formula is write as the expression formula of frequency f, as follows:

$f\left(\mathrm{\ω}\right)=-\frac{{\mathrm{\τ}}^{3}f}{8}{e}^{-\frac{{\left(\mathrm{\τf}\right)}^2}{4}}---\left(12\right)$

The space distribution of Electric and magnetic fields is upgraded successively, until magnetic distribution is tending towards stable state at each time step.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 Explicit Form, as follows:

$\begin{array}{c}{H}^{n+1/2}=\frac{2\mathrm{\μ}-{\mathrm{\σ}}_m\mathrm{\Δt}}{2\mathrm{\μ}-{\mathrm{\σ}}_m\mathrm{\Δt}}{H}^{n-1/2}-\frac{2\mathrm{\Δt}}{2\mathrm{\μ}-{\mathrm{\σ}}_m\mathrm{\Δt}}\▿\×E^n\\ E^{n+1}=\frac{2\mathrm{\ϵ}-\mathrm{\σ\Δt}}{2\mathrm{\ϵ}-\mathrm{\σ\Δt}}{E}^n+\frac{2\mathrm{\Δt}}{2\mathrm{\ϵ}-\mathrm{\σ\Δt}}\▿\×H^{n+1/2}\end{array}---\left(13\right)$

In formula, H ^n-1/2and H ^n+1/2the magnetic field intensity of moment (n-1/2) Δ t and (n+1/2) Δ t, E ⁿand E ⁿ⁺¹be the electric field intensity of moment n Δ t and (n+1) Δ t, σ is conductivity, σ _mit is magnetoconductivity.The difference equation of through type (13), can obtain the distribution situation of Electric and magnetic fields in zoning.

Step 4: product far field being write as frequency factor and integrating factor, and integrating factor is carried out inverse Fourier transform obtain forms of time and space

If be radar wave receiving polarization direction, then consider formula (9), the party's far field electric field upwards can be expressed as

${\hat{e}}_s\·E_s=\mathrm{jk}{e}^{\mathrm{jkr}}/\left(4\mathrm{\πr}\right)I---\left(14\right)$

Wherein jke ^-jkr/ (4 π r) is frequency factor, and I is integrating factor, E _ibe incident field intensity, the expression formula of integrating factor I is

$I={\∫}_S(-\mathrm{\η}{\hat{e}}_s\·\hat{n}\×H+{\hat{h}}_s\·\hat{n}\×E)e^{\mathrm{jk}\hat{s}\·r^{\′}}\mathrm{dS}---\left(15\right)$

Wherein be receiving antenna magnetic field, far field polarised direction, r is the distance that source point is shown up a little, and S is face, extrapolated boundary, it is vacuum wave impedance.According to k=ω/c, wherein c is the light velocity, and integrating factor I can be written as:

$I\left(\mathrm{\ω}\right)={\∫}_S(-\mathrm{\η}{\hat{e}}_s\·\hat{n}\×H+{\hat{h}}_s\·\hat{n}\×E)e^{\mathrm{j\ω}\frac{\hat{s}\·r^{\′}}{c}}\mathrm{dS}---\left(16\right)$

Above formula is carried out inverse Fourier transform, write as contributed by magnetic field and electric field two parts and form:

I(t)＝I _H(t)+I _E(t) (17)

Wherein I _ht () represents the far zone field caused by tangential magnetic field, I _et () represents the far zone field caused by tangential electric field, expression formula is.

$I_H\left(t\right)={\∫}_S-\mathrm{\η}{\hat{e}}_s\·\hat{n}\×H(t+\frac{\hat{s}\·r^{\′}}{c})\mathrm{dS}---\left(18\right)$

$I_E\left(t\right)={\∫}_S{\hat{h}}_s\·\hat{n}\×E(t+\frac{\hat{s}\·r^{\′}}{c})\mathrm{dS}---\left(19\right)$

There is similar form in the far field of two-dimensional case, and for horizontal magnetic (Transverse Magnetic, TM) ripple, expression formula is as follows:

$\hat{z}\·E_z=e^{-\mathrm{jkr}}\sqrt{\frac{\mathrm{jk}}{8\mathrm{\πr}}}{I}^{\′}---\left(20\right)$

Wherein the coordinate vector in z direction, be frequency factor, I ' is the integrating factor under two-dimensional case, and expression formula is

$I^{\′}={\∫}_l(-\mathrm{\η}{\hat{e}}_s\·\hat{n}\×H+{\hat{h}}_s\·\hat{n}\×E)e^{\mathrm{jk}\hat{s}\·r^{\′}}\mathrm{dl}---\left(21\right)$

Wherein l is extrapolated boundary.Under two-dimensional case, extrapolated boundary is a rectangle, therefore has the form of line integral.

Step 5: the far field time domain response of calculated product molecular group

Time domain response array in integrating factor far field is set, the response of each time step extrapolated boundary electromagnetic field to far field is added in integrating factor far field time domain response array.

By I _h(t) and I _et the expression formula (18) of () and (19) can be found out, because r ' is on the face, extrapolated boundary of integration, the integrating factor expression formula obtaining t needs first to try to achieve magnetic field H and the value of electric field E within a period of time, and general FDTD computation process only retains the value of current time step, use constant.The method that the present invention adopts is the far-field response array first arranging integrating factor, the contribution of each grid to far field on each time step extrapolated boundary is added in far-field response array, so just do not need to preserve the value of Electric and magnetic fields within a period of time, greatly reduce memory cost.By the integration discretize of formula (18), as follows:

$I_H\left(t\right)=\underset{m}{\mathrm{\Σ}}{I}_{\mathrm{Hm}}\left(t\right)---\left(22\right)$

Wherein I _hmt () is expressed as the contribution of each grid on face, extrapolated boundary, it is expressed as the value of grid midpoint and the product of grid area, as follows:

$I_{\mathrm{Hm}}\left(t\right)=-\mathrm{\η}{\hat{e}}_s\·{\hat{n}}_m\×H_m(t+\frac{\hat{s}\·r_m^{\′}}{c}){\mathrm{\δ}}^2---\left(23\right)$

Wherein m represents grid sequence number on extrapolated boundary, represent m grid midpoint the magnetic field intensity in moment, δ is size of mesh opening, then δ ²it is grid area.Formula (23) can also be write as following form:

$I_{\mathrm{Hm}}(t-\frac{\hat{s}\·r_m^{\′}}{c})=-\mathrm{\η}{\hat{e}}_s\·{\hat{n}}_m\×H_m\left(t\right){\mathrm{\δ}}^2---\left(24\right)$

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, as follows:

$I_{\mathrm{Hm}}((n+\frac{1}{2})\mathrm{\Δt}-\frac{\hat{s}\·(n_x\hat{x}+n_y\hat{y}+n_z\hat{z})\mathrm{\δ}}{c})=-{\hat{e}}_s\·{\hat{n}}_m\×H_m\left((n+\frac{1}{2})\mathrm{\Δt}\right)---\left(25\right)$

Wherein s=c Δ t/ δ is time factor, n _x, n _y, n _zr ' _mcoordinate in x, y, z direction is to the grid number of initial point, and n is emulation current time step number.In the present invention, electric field is in the sampling of n time step, and n+1/2, in the sampling of n+1/2 time step, is therefore contained in formula (25) expression formula in magnetic field.With the discrete grid block sequence number in FDTD, time step expression (25), obtain

$I_{\mathrm{Hm}}(n+n_{\mathrm{Hf}})=-\mathrm{\η}{\hat{e}}_s\·{\hat{n}}_m\×H_m(n+\frac{1}{2})---\left(26\right)$

Wherein n _hf=1/2-(s _xn _x+ s _yn _y+ s _zn _z)/ _s.Formula (26) means gives n+n by the magnetic field tangential component of n+1/2 time step _hfthe far field integrating factor of time step, but in program implement far field integrating factor only in integer time step value, and n+n _hfin general not integer.The method that the present invention adopts the integrating factor in this moment is distributed to by a certain percentage two adjacent integers, and the integer more closed on is shared larger than proportion.If [n _hf] be n _hfintegral part, { n _hfn _hffraction part, then can by I _hmaccording to 1-{n _hfand { n _hfproportional distribution to n+ [n _hf] and n+ [n _hf] the far field integrating factor of+1 time step.Consider that the subscript of array all gets positive integer value, therefore add fully large time step side-play amount n _τ, meeting array index is positive requirement, obtains:

$I_{\mathrm{Hm}}(n+[n_{\mathrm{Hf}}]+n_{\mathrm{\τ}})=-\mathrm{\η}{\hat{e}}_s\·{\hat{n}}_m\×H_m(n+\frac{1}{2})(1-\{n_{\mathrm{Hf}}\left\}\right)---\left(27\right)$

$I_{\mathrm{Hm}}(n+[n_{\mathrm{Hf}}]+n_{\mathrm{\τ}}+1)=-\mathrm{\η}{\hat{e}}_s\·{\hat{n}}_m\×H_m(n+\frac{1}{2})\left\{n_{\mathrm{Hf}}\right\}---\left(28\right)$

For the contribution of electric field on extrapolated boundary to far field, need to modify to formula (25), in the formula of both sides, do not occur 1/2, because electric field is in integer time step value.The integrating factor time domain response formula of being tried to achieve far zone field by the tangential electric field of time step n is as follows

$I_{\mathrm{En}}(n+[n_{\mathrm{Ef}}]+n_{\mathrm{\τ}})={\hat{h}}_s\·{\hat{n}}_m\×E_m\left(n\right)(1-\{n_{\mathrm{Ef}}\left\}\right)---\left(29\right)$

$I_{\mathrm{En}}(n+[n_{\mathrm{Ef}}]+1+n_{\mathrm{\τ}})={\hat{h}}_s\·{\hat{n}}_m\×E_m\left(n\right)\left\{n_{\mathrm{Ef}}\right\}---\left(30\right)$

Wherein I _emrepresent that tangential electric field on m grid is to the contribution in far field, n _ef=-(s _xn _x+ s _yn _y+ s _zn _z)/s, [n _ef] represent n _efintegral part, { n _efrepresent n _effraction part.

Step 6: far field integrating factor time domain response Fourier transform

Far field integrating factor time domain response obtains far field integrating factor frequency domain response through Fourier transform, and transformation for mula is

$I\left(\mathrm{\ω}\right)={\∫}_{-\∞}^{\∞}I\left(t\right)e^{-\mathrm{j\ωt}}\mathrm{dt}---\left(31\right)$

Due to I (t) only value on integer time step, therefore integration can be written as

$I\left(\mathrm{\ω}\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}I\left(n\right)e^{-\mathrm{j\ωn\Δt}}\mathrm{\Δt}---\left(32\right)$

Wherein N is the time step sum in integrating factor far field.Formula (32) is write as the form of frequency f, integrating factor far field frequency domain response can be obtained, namely

$I\left(f\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}I\left(n\right)e^{-j2\mathrm{\πfn\Δt}}\mathrm{\Δt}---\left(33\right)$

Step 7: calculate the change of RCS with frequency

The RCS required, also need the frequency domain response of trying to achieve incident wave, computing method are as follows:

$E_i\left(f\right)=\underset{n=1}{\overset{M}{\mathrm{\Σ}}}{E}_i\left(n\right)e^{-j2\mathrm{\πfn\Δt}}\mathrm{\Δt}---\left(34\right)$

In formula, M is the step number of emulation, E _in () is the incident field intensity on the n-th time step.Again according to formula (14), the change of RCS with frequency can be obtained:

$\sqrt{\mathrm{\σ}\left(f\right)}=j\sqrt{\mathrm{\π}}\frac{f}{c}\frac{I\left(f\right)}{\left|E_i\left(f\right)\right|}---\left(35\right)$

Above formula has used k=2 π f/c, tries to achieve the value of RCS further

$\mathrm{\σ}\left(f\right)=\frac{{\mathrm{\πf}}^2}{c^2}\frac{I^2\left(f\right)}{{\left|E_i\left(f\right)\right|}^2}---\left(36\right)$

For two-dimensional case, RCS has similar expression formula, for

$\mathrm{\σ}\left(f\right)=\frac{\mathrm{\πf}}{2c}\frac{I^{\′2}\left(f\right)}{{\left|E_i\left(f\right)\right|}^2}---\left(37\right)$

It should be pointed out that this example only listing property application process of the present invention is described, but not for limiting the present invention.Any personnel being familiar with this kind of operation technique, all can without departing from the spirit and scope of the present invention, modify to above-described embodiment.Therefore, the scope of the present invention, should listed by claims.

Claims (7)

1. Finite-Difference Time-Domain Method calculates a transient field far field Extrapolation method for electromagnetic scattering, it is characterized in that: the method includes the steps of:

Step 1: by fillet, zoning is divided into total place and Liang Ge region, scattering place, the electromagnetic field of total place contains incident field and scattered field, and scattering place only comprises scattered field;

Step 2: arrange extrapolated boundary in scattering place, obtains far zone field by the Electric and magnetic fields extrapolation on extrapolated boundary;

Step 3: arrange transient state incident wave, upgrades Electric and magnetic fields successively at each time step, until magnetic distribution is tending towards stable state;

Step 4: product far field being write as frequency factor and integrating factor, carries out inverse Fourier transform to integrating factor, obtains time-domain expression;

Step 5: arrange integrating factor far field time domain response array, is added in integrating factor far field time domain response array by the response of each time step extrapolated boundary electromagnetic field to far field;

Step 6: the time domain response of integrating factor far field obtains its frequency domain response through Fourier transform;

Step 7: the frequency domain response utilizing far field and incident wave, obtains the change of RCS with frequency.

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: described in step 1 " zoning ", refer to the rectangular parallelepiped of a three-dimensional case, also can be the rectangular area of two-dimensional case, sampling, the iteration of electromagnetic field be just carried out in this region; Affiliated " being divided into total place and Liang Ge region, scattering place ", referring to the rectangular parallelepiped by a three-dimensional case, also can be the fillet of two-dimensional case rectangle, zoning is divided into two, be total place within fillet, be scattering place beyond fillet, scatterer is positioned 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: described in step 2 " extrapolated boundary ", refer to the rectangular parallelepiped of the three-dimensional case being positioned at scattering place, also can be the border of two-dimensional case rectangle, total place is included, because extrapolated boundary is positioned at scattering place, therefore the electromagnetic field on extrapolated boundary only has scattered field, do not comprise incident field, the far field obtained by its extrapolation just only has the contribution of scattered field, directly calculates RCS and 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: described in step 3 " magnetic distribution is tending towards stable state ", refer to that the electromagnetic field of total place and scattering place does not change substantially.

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: " far field being write as the product of frequency factor and integrating factor " described in step 4, its three-dimensional case refers to following expression:

${\hat{e}}_s\·E_s={\mathrm{jke}}^{\mathrm{jkr}}/\left(4\mathrm{\πr}\right)I---\left(1\right)$

Wherein radar wave receiving polarization direction, jke ^-jkr/ (4 π r) is frequency factor, and I is integrating factor, E _ibe incident field intensity, the expression formula of integrating factor I is

$I={\∫}_S(-\mathrm{\η}{\hat{e}}_s\·\hat{n}\×H+{\hat{h}}_s\·\hat{n}\×E)e^{\mathrm{jk}\hat{s}\·r^{\′}}\mathrm{dS}---\left(2\right)$

Wherein be receiving antenna magnetic field, far field polarised direction, r is the distance that source point is shown up a little, and S is face, extrapolated boundary, it is vacuum wave impedance;

Its two-dimensional case is for transverse magnetic wave and TM ripple, and expression formula is as follows:

$\hat{z}\·E_z=e^{-\mathrm{jkr}}\sqrt{\frac{\mathrm{jk}}{8\mathrm{\πr}}}{I}^{\′}---\left(3\right)$

Wherein the coordinate vector in z direction, be frequency factor, I ' is integrating factor, and expression formula is

$I^{\′}={\∫}_l(-\mathrm{\η}{\hat{e}}_s\·\hat{n}\×H+{\hat{h}}_s\·\hat{n}\×E)e^{\mathrm{jk}\hat{s}\·r^{\′}}\mathrm{dl}---\left(4\right)$

Wherein l is extrapolated boundary, and under two-dimensional case, extrapolated boundary is a rectangle, therefore has the form of line integral.

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: described in steps of 5 " response of each time step extrapolated boundary electromagnetic field to far field is added in integrating factor far field time domain response array ", refer to that on each time step extrapolated boundary, the far field contributor of diverse location to integrating factor is embodied in the different moment, therefore the integrating factor far field time domain response array being prepared in advance to be filled is needed, at each time step, the far field contributor of correspondence is added in integrating factor far field time domain response array.

7. 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: described in step 7 " utilizing the frequency domain response of far field and incident wave; obtain the change of RCS with frequency ", refer to the definition according to RCS, write RCS as following form:

$\mathrm{\σ}\left(f\right)=\frac{\mathrm{\π}{f}^2}{c^2}\frac{I^2\left(f\right)}{{\left|E_i\left(f\right)\right|}^2}$ (three-dimensional case) (5)

$\mathrm{\σ}\left(f\right)=\frac{\mathrm{\π}f}{2c}\frac{I^{\′2}\left(f\right)}{{\left|E_i\left(f\right)\right|}^2}$ (two-dimensional case) (6)

Wherein f is frequency, I and I ' is the integrating factor far field frequency domain response of three peacekeeping two-dimensional case, and c is the light velocity, E _iit is incident wave.