CN104915324A - Mixed analysis method for electromagnetic scattering of cavity containing medium target - Google Patents

Abstract

The invention discloses a mixed analysis method for electromagnetic scattering of a cavity containing a medium target. The method comprises the following steps that a cavity body part containing the cavity target is filled to be solid metal, a target discrete model after filling is conducted is established, and a matrix equation is constructed; recursive solving is conducted on node electric field values on tangent planes in sequence; correction is conducted on the electric field values on the last tangent plane, electric field values near discrete nodes are obtained, and phase correction is conducted on the electric field values; solving is conducted on the cavity body part in the target independently by using a body area integral equation, metal surfaces and dielectric bodies in the cavity body are dispersed to obtain sub scatterer grouping, induced currents on the metal surface and polarization currents in inner bodies of the medium are solved by using a fast multilevel method, the electric field values of the discrete points needed by a parabolic equation on an opening surface of the cavity body are solved, and switch solving of a radar discrete section area is conducted on near-field electric field values. The body area integral equation is combined with a meshless parabolic equation, and the defect that cavity body scattering cannot be calculated by the parabolic equation is avoided.

Description

Cavity is containing dielectric object electromagnetic scattering hybrid analysis

Technical field

The invention belongs to electromagnetic characteristic of scattering numerical computation technology field, particularly a kind of cavity containing dielectric object electromagnetic scattering hybrid analysis.

Background technology

In recent ten years, the Electromagnetic Scattering of electrically large sizes complicated cavity causes people and studies interest widely.Parabolic equation method has very large advantage at the complicated metal target of process TV university.The parabolic equation method initial stage is mainly used to process the problem of the aspects such as the propagation problem of sound wave of more complicated and optics.First the method is proposed in nineteen forty-six by Lenontovich.Subsequently, PE method and geometrical optics approach combine by Malyuzhiners, propose a kind of theory about barrier diffraction; Hardin proposes division step fourier method, with the propagation problem solving underwater sound wave; Claerbout introduces finite difference, and PE method is applied to geophysics, it to the calculating of the propagation of long distance sound wave in ocean and seismic wave propagation and research provide one effectively, method accurately.In recent years, Chinese scholars starts parabolic equation method to be applied to process electromagnetic scattering problems. and this algorithm is reduced to parabolic equation wave equation, Scattering Targets is equivalent to a series of bin or line element, then parabolic equation is solved by the Spatial Recursive mode of the boundary condition on scatterer and field, three-dimensional problem is converted into a series of two-dimensional problems to calculate, be converted to far field scattered field by near-field/far-field, and then calculate the dual station RCS of target.

But, parabolic equation has self defect, and the method is for when calculating the scattering of electric small-size target, and the error of calculation is larger, be not suitable for the scattering calculating cavity or concaver, mainly because have large change in the propagation direction at these target surface scattered fields simultaneously.Honorable integral equation based on method of moment is a kind of integration class numerical value emulation method, and it is the exact solution of wave equation, can analyze the electromagnetic scattering of cavity accurately, but when it calculates TV university dielectric object electromagnetic scattering, the internal memory of consumption is very large.

Summary of the invention

The object of the present invention is to provide a kind of efficient, reliable cavity based on honorable anomalous integral mesh free parabolic equation containing dielectric object electromagnetic scattering hybrid analysis, the method cavity portion uses honorable integral Equation Methods, and solve in conjunction with quick multistage son, the Electromagnetic Scattering Characteristics parameter containing cavity configuration target can be obtained fast.

The technical solution realizing the object of the invention is: a kind of cavity is containing dielectric object electromagnetic scattering hybrid analysis, and step is as follows:

Step 1, the cavity portion of target with open cavity is filled to solid metal, set up the discrete model of target after filling, determine that the axial direction of parabolic equation is as x-axis, the relation between adjacent two tangent planes of CN difference scheme acquisition is used in x-axis direction, RPIM is all adopted to construct shape function and space derivative in y-axis, z-axis direction, and introduce scatterer boundary condition, construct matrix equation;

Step 2, successively Recursive Solution is carried out to the node electric field value on each tangent plane, solved the electric field value of various discrete Nodes on next tangent plane by the right vector of the information and equation of constantly updating frontier point;

Step 3, the electric field value of last tangent plane to be revised, solve the matrix equation of last tangent plane, obtain the electric field value at discrete nodes place, and this electric field value is carried out the correction of phase place;

Step 4, cavity portion in target to be solved with honorable integral equation separately, by metal covering in cavity and the discrete sub-scatterer grouping obtained of dielectric, adopt diverse ways computing impedance matrix element according to the position relationship of any two sub-scatterer place groups, adopt quick multistage submethod to solve induction current and the medium endosome polarization current of metal surface in cavity;

Step 5, obtained the electric field value of various discrete point needed for parabolic equation on cavity hatch face by the induction current of metal surface in target with open cavity cavity and medium endosome polarization current;

Step 6, aftertreatment is carried out to the electric field on last tangent plane, electric field on the cavity hatch face of step 5 gained is replaced the electric field of the former target cavity opening part of step 3 gained, far to field transformation is carried out to the near field electric field value of gained and solves Radar Cross Section.

Compared with prior art, its remarkable advantage is in the present invention: (1) Modling model is simple, and the object module that mesh free parabolic equation and honorable integral equation are analyzed is separate, simple and clear; (2), when analyzing the electromagnetic scattering problems of target with open cavity of electrically large sizes, consume internal memory than traditional honorable integral equation few, computing velocity is fast; (3) mesh free parabolic equation method formation matrix equation condition is better: because the node field value of various discrete is only relevant with the node field value in its supporting domain, so the matrix formed is a sparse matrix, memory consumption is less, and matrix condition is better easy to solve.

Below in conjunction with accompanying drawing, the present invention is described in further detail.

Accompanying drawing explanation

Fig. 1 is that energy of the present invention is along para-curve Propagation schematic diagram.

Fig. 2 is Scattering Targets schematic diagram of the present invention.

Fig. 3 is the Scattering Targets schematic diagram that mesh free parabolic equation of the present invention solves.

Fig. 4 is the Scattering Targets schematic diagram of the present invention's dignity solution of integral equation.

Fig. 5 is the node schematic diagram of required opening surface place, the chamber electric field separated of Green function.

Fig. 6 is the two-dimensional section figure of target scattering body in the invention process 1.

Fig. 7 is metal target with open cavity given viewpoint RCS curve map at different frequencies in the embodiment of the present invention 1.

Fig. 8 is metal target with open cavity back scattering curve map under 320MHz in the embodiment of the present invention 1.

Embodiment

Below in conjunction with drawings and the specific embodiments, the present invention is described in further detail.

By reference to the accompanying drawings 1 ~ 5, cavity of the present invention is containing dielectric object electromagnetic scattering hybrid analysis, and step is as follows:

Step 1, the cavity portion of target with open cavity is filled to solid metal, set up the discrete model of target after filling, if the axial direction of Fig. 1 determination parabolic equation is as x-axis, the relation between adjacent two tangent planes of CN difference scheme acquisition is used in x-axis direction, RPIM is all adopted to construct shape function and space derivative in y-axis, z-axis direction, and introduce scatterer boundary condition, construct matrix equation, concrete steps are as follows:

Step 1.1, the cavity portion of target with open cavity is filled to solid metal, it is discrete the metal Scattering Targets obtained to be carried out square grid, forms several tangent planes perpendicular to x-axis direction, and finds out the frontier point of solid metal Scattering Targets on each tangent plane; Such as shown in Figure 2 containing the metal cuboid groove of medium, be filled to metal cuboid as shown in Figure 3;

Step 1.2, discrete after zoning be respectively PML layer, free space, the border of Scattering Targets and the inside of Scattering Targets from outside to inside, according to the geometric relationship of target, determine to fill the discrete nodes of rear Scattering Targets inside, borderline discrete nodes, the discrete nodes of air layer and the discrete nodes of PML layer correspondence;

Step 1.3, determine that the axial direction of parabolic equation is as x-axis, under three-dimensional situation, normal vector parabolic equation is expressed as:

$\left\{\begin{array}{c}\frac{{\∂}^2{u}_x^s}{{\∂y}^2}(x,y,z)+\frac{{\∂}^2{u}_x^s}{{\∂z}^2}(x,y,z)+2\mathrm{ik}\frac{{\∂u}_x^s}{\∂x}(x,y,z)=0\\ \frac{{\∂}^2{u}_y^s}{{\∂y}^2}(x,y,z)+\frac{{\∂}^2{u}_y^s}{{\∂z}^2}(x,y,z)+2\mathrm{ik}\frac{{\∂u}_y^s}{\∂x}(x,y,z)=0\\ \frac{{\∂}^2{u}_z^s}{{\∂y}^2}(x,y,z)+\frac{{\∂}^2{u}_z^s}{{\∂z}^2}(x,y,z)+2\mathrm{ik}\frac{{\∂u}_z^s}{\∂x}(x,y,z)=0\end{array}\right.---\left(1\right)$

Wherein, be respectively the component of wave function in x-axis, y-axis, z-axis direction, be respectively the component of electric field in x-axis, y-axis, z-axis direction, k is wave number, and i is imaginary number;

In PML medium, vector parabolic equation is expressed as:

$\left\{\begin{array}{c}{\left(\frac{1}{1-\mathrm{i\σ}\left(y\right)}\right)}^2\frac{{\∂}^2{u}_x^s(x,y,z)}{{\∂y}^2}+\frac{{2\mathrm{i\σ}}_{0}y}{{(1-\mathrm{i\σ}\left(y\right))}^3{\mathrm{\δ}}^2}\frac{{\∂u}_x^s(x,y,z)}{\∂y}+{\left(\frac{1}{1-\mathrm{i\σ}\left(z\right)}\right)}^2\frac{{\∂}^2{u}_x^s(x,y,z)}{{\∂z}^2}\\ +\frac{{2\mathrm{i\σ}}_{0}z}{{(1-\mathrm{i\σ}\left(z\right))}^3{\mathrm{\δ}}^2}\frac{{\∂u}_x^s(x,y,z)}{\∂z}+2\mathrm{ik}\frac{{\∂u}_x^s(x,y,z)}{\∂x}=0\\ \left(\frac{1}{1-\mathrm{i\σ}\left(y\right)}\right)2^{}\frac{{\∂}^2{u}_y^s(x,y,z)}{{\∂y}^2}+\frac{{2\mathrm{i\σ}}_{0}y}{{(1-\mathrm{i\σ}\left(y\right))}^3{\mathrm{\δ}}^2}\frac{{\∂u}_y^s(x,y,z)}{\∂y}+{\left(\frac{1}{1-\mathrm{i\σ}\left(z\right)}\right)}^2\frac{{\∂}^2{u}_y^s(x,y,z)}{{\∂z}^2}\\ +\frac{{2\mathrm{i\σ}}_{0}z}{{(1-\mathrm{i\σ}\left(z\right))}^3{\mathrm{\δ}}^2}\frac{{\∂u}_y^s(x,y,z)}{\∂z}+2\mathrm{ik}\frac{{\∂u}_y^s(x,y,z)}{\∂x}=0\\ \left(\frac{1}{1-\mathrm{i\σ}\left(y\right)}\right)2^{}\frac{{\∂}^2{u}_z^s(x,y,z)}{{\∂y}^2}+\frac{{2\mathrm{i\σ}}_{0}y}{{(1-\mathrm{i\σ}\left(y\right))}^3{\mathrm{\δ}}^2}\frac{{\∂u}_z^s(x,y,z)}{\∂y}+{\left(\frac{1}{1-\mathrm{i\σ}\left(z\right)}\right)}^2\frac{{\∂}^2{u}_z^s(x,y,z)}{{\∂z}^2}\\ +\frac{{2\mathrm{i\σ}}_{0}z}{{(1-\mathrm{i\σ}\left(z\right))}^3{\mathrm{\δ}}^2}\frac{{\∂u}_z^s(x,y,z)}{\∂z}+2\mathrm{ik}\frac{{\∂u}_z^s(x,y,z)}{\∂x}=0\end{array}\right.---\left(2\right)$

In formula, σ () represents the function of electrical loss, σ ₀represent the coefficient of electrical loss, δ represents the coefficient of skin depth;

Use the relation between adjacent two tangent planes of CN difference scheme acquisition in x-axis direction, all adopt RPIM to construct shape function and space derivative in y-axis, z-axis direction, electric field u (x, y, z) is launched by shape function, is shown below:

u(x,y,z)＝Φ(x,y,z)U _S(x,y,z) (3)

U in formula _s(x, y, z) is electric field coefficient to be asked, Φ (x, y, z)=[Φ ₁(x, y, z), Φ ₂(x, y, z) ..., Φ _n(x, y, z)] be shape function, N is the number of discrete nodes in supporting domain, passes through to realize Φ (x, y, z) differentiate to the differentiate of u (x, y, z);

Step 1.4, introducing scatterer boundary condition, construct matrix equation: for object boundary point, suppose that P is the point on scatterer surface, n=(n _x, n _y, n _z) be the normal orientation of P point, n × E=0 on the surface of pure conductor, that is:

n(P)×E ^s(P)=-n(P)×E ⁱ(P) (4)

In formula, E ⁱrepresent incident electric fields, E ^srepresent scattered field; Three corresponding equations are obtained by formula (4):

$\left\{\begin{array}{c}{n}_x{E}_y\left(P\right)-n_y{E}_x\left(P\right)=0\\ n_x{E}_z\left(P\right)-n_z{E}_x\left(P\right)=0\\ n_y{E}_z\left(P\right)-n_z{E}_y\left(P\right)=0\end{array}\right.---\left(5\right)$

Formula (5) is transformed to:

$\left\{\begin{array}{c}{n}_x{u}_y^s\left(P\right)-n_y{u}_x^s\left(P\right)=-e^{-\mathrm{ikx}}(n_x{E}_y^i\left(P\right)-n_y{E}_x^i\left(P\right))\\ n_x{u}_z^s\left(P\right)-n_z{u}_x^s\left(P\right)=-e^{-\mathrm{ikx}}(n_x{E}_z^i\left(P\right)-n_z{E}_x^i\left(P\right))\\ n_y{u}_z^s\left(P\right)-n_z{u}_y^s\left(P\right)=-e^{-\mathrm{ikx}}(n_y{E}_z^i\left(P\right)-n_z{E}_y^i\left(P\right))\end{array}\right.---\left(6\right)$

In formula, represent the component of incident electric fields on x-axis, y-axis, z-axis direction respectively, represent the component of wave function on x-axis, y-axis, z-axis direction respectively;

By electric field u (x, y, z) by shape function u (x, y, z)=Φ (x, y, z) U _s(x, y, z) launches, U _s(x, y, z) is electric field coefficient to be asked, Φ (x, y, z)=[Φ ₁(x, y, z), Φ ₂(x, y, z) ..., Φ _n(x, y, z)] be shape function, N is the number of discrete nodes in supporting domain, and above formula can be expressed as following form:

$\left\{\begin{array}{c}{n}_s\mathrm{\Φ}\left(P\right)U_{S,y}\left(P\right)-n_y\mathrm{\Φ}\left(p\right)U_{S,x}\left(P\right)=-e^{-\mathrm{ikx}}(n_x{E}_y^i\left(P\right)-n_y{E}_x^i\left(P\right))\\ n_s\mathrm{\Φ}\left(P\right)U_{S,z}\left(P\right)-n_z\mathrm{\Φ}\left(p\right)U_{S,x}\left(P\right)=-e^{-\mathrm{ikx}}(n_x{E}_z^i\left(P\right)-n_z{E}_x^i\left(P\right))\\ n_y\mathrm{\Φ}\left(P\right)U_{S,z}\left(P\right)-n_z\mathrm{\Φ}\left(p\right)U_{S,y}\left(P\right)=-e^{-\mathrm{ikx}}(n_y{E}_z^i\left(P\right)-n_z{E}_y^i\left(P\right))\end{array}\right.---\left(7\right)$

Wherein, U _s,x(x, y, z), U _s,y(x, y, z), U _s,z(x, y, z) is electric field coefficient the to be asked component on x-axis, y-axis, z-axis direction; Three equations in formula (7) are not separate, and the order of its matrix of coefficients is 2, does not surely separate, and only adds the divergence equation of Maxwell, and just can form the system of linear equations that rank is 3, solution has uniqueness.Substituted into by the parabolic equation of correspondence, the divergence equation under the three-dimensional coordinate of P point is transformed to:

$\frac{i}{2k}(\frac{{\∂}^2{u}_x^s}{{\∂y}^2}\left(P\right)+\frac{{\∂}^2{u}_x^s}{{\∂z}^2}\left(P\right))+{\mathrm{iku}}_x^s\left(P\right)+\frac{{\∂u}_y^s}{\∂y}\left(P\right)+\frac{{\∂u}_z^s}{\∂z}\left(P\right)=0---\left(8\right)$

To electric field u _x(x, y, z), u _y(x, y, z), u _z(x, y, z) adopts RPIM to construct shape function and space derivative, and pass through to realize shape function Φ (x, y, z) differentiate about the differentiate of y-axis and z-axis to electric field u (x, y, z), formula (8) is discrete is:

$\frac{i}{2k}(\frac{{\∂}^2}{{\∂y}^2}+\frac{{\∂}^2}{{\∂z}^2})\mathrm{\Φ}\left(P\right)U_{S,x}\left(P\right)+\mathrm{ik\Φ}\left(P\right)U_{S,x}\left(P\right)+\frac{\∂\mathrm{\Φ}\left(P\right)}{\∂y}{U}_{S,y}\left(P\right)+\frac{\∂\mathrm{\Φ}\left(P\right)}{\∂z}{U}_{S,z}\left(P\right)=0---\left(9\right)$

Formula (7) and formula (9) simultaneous are constructed the system of linear equations that rank is 3, coupled relation is filled in matrix equation, the interpolation of nonhomogeneous boundary condition can be completed, construct final matrix equation.

Step 2, successively Recursive Solution is carried out to the node electric field value on each tangent plane, solved the electric field value of various discrete Nodes on next tangent plane by the right vector of the information and equation of constantly updating frontier point, specific as follows:

Step 2.1, the right vector when the electric field value of previous tangent plane various discrete node is solved as current tangent plane;

Step 2.2, at the determined frontier point place of current tangent plane, add tangential component be 0 and divergence be the boundary condition of 0, the node electric field value assignment being in interior of articles is 0, formed current tangent plane upgrade after matrix equation;

Matrix equation after step 2.3, solution procedure 2.2 upgrade, obtains the electric field value of the node of current tangent plane various discrete.

The number of the unknown quantity of each tangent plane is the number that the number of substrate discrete point adds this tangent plane frontier point, according to being in different positions, bring different discrete equations into, tried to achieve the electric field value in next face by the electric field value of previous, continuous recursion obtains the electric field value of last tangent plane.

Step 3, revise the electric field value of last tangent plane, solve the matrix equation of last tangent plane, obtain the electric field value at discrete nodes place, and this electric field value is carried out the correction of phase place, concrete steps are as follows:

Because the incident electric fields of parabolic equation method differs a phase place relative to the incident electric fields of honorable integral Equation Methods, so the electric field of the scattered field of finally trying to achieve is also by difference phase place, this phase place is compensated, the electric field that parabolic equation method is determined is multiplied by as the electric field value required for final parabolic equation method, wherein θ is incident wave and x-axis angle, for incident wave and y-axis angle.

Step 4, cavity portion in target to be solved with honorable integral equation separately, by metal covering in cavity and the discrete sub-scatterer grouping obtained of dielectric, diverse ways computing impedance matrix element is adopted according to the position relationship of any two sub-scatterer place groups, quick multistage submethod is adopted to solve induction current and the medium endosome polarization current of metal surface in cavity, composition graphs 4, detailed process is as follows:

Step 4.1, the metallic member surface triangles of cavity is carried out subdivision, obtain the numbering of each triangular element, the coordinate of point, normal vector; Media fraction tetrahedron carries out subdivision, obtains the unit normal vector in each tetrahedral numbering, tessarace coordinate, four faces;

Step 4.2, use honorable integral equation, do the gold test of gal the Liao Dynasty, and accelerate solution procedure by quick multistage sub-technology,

Obtain induction current and the medium endosome polarization current of metal surface in cavity.

Solved with honorable integral equation separately by cavity portion in object, concrete steps are as follows:

Scattered field in cavity on metal and medium can represent by the form of magnetic vector potential and electric scalar potential sum; Following formula (10) represents that the scattered field that dielectric polarization current is corresponding, formula (10) represent the scattered field that the induction current of metal surface is corresponding:

$E_V^{\mathrm{sca}}=-(\mathrm{i\ω}{A}_V\left(\stackrel{\→}{r}\right)+\▿{\mathrm{\Φ}}_V\left(\stackrel{\→}{r}\right))---\left(10\right)$

$E_S^{\mathrm{sca}}=-({\mathrm{i\ωA}}_S\left(r\right)+{\▿\mathrm{\Φ}}_S\left(r\right))---\left(11\right)$

In formula:

$A_V\left(r\right)=\frac{\mathrm{\μ}}{4\mathrm{\π}}\underset{V}{\∫}{J}_V\left(r\right)\mathrm{Gdr},A_S\left(r\right)=\frac{\mathrm{\μ}}{4\mathrm{\π}}\underset{S}{\∫}{J}_S\left(r\right)\mathrm{Gdr}---\left(12\right)$

${\mathrm{\Φ}}_V\left(r\right)=\frac{\mathrm{\μ}}{4\mathrm{\π\ϵ}}\underset{V}{\∫}\mathrm{\ρ}\left(r\right)\mathrm{Gdr},\mathrm{i\ω\ρ}\left(r\right)=-\▿\·J_V\left(r\right)---\left(13\right)$

${\mathrm{\Φ}}_S\left(r\right)=\frac{\mathrm{\μ}}{4\mathrm{\π\ϵ}}\underset{S}{\∫}\mathrm{\ρ}\left(r\right)\mathrm{Gdr},\mathrm{i\ω\ρ}\left(r\right)=-\▿\·J_s\left(r\right)---\left(14\right)$

Wherein, ω is angular frequency, and μ is magnetoconductivity, and ε is specific inductive capacity, and π is circular constant, and ρ (r) is magnetic permeability, for the scattered field in the V of dielectric region, for the scattered field on the S of metal covering region.Vector magnetic potential A in formula _vr () represents the radiation produced by body polarization electric current, A _sr () represents the radiation that the induction current of metal surface produces, electric scalar potential Φ _vr () is that the electric charge two parts produced by volume charge and different media area intersection are contributed, Φ _sr () is the radiation that the induced charge of conductive surface is corresponding, G is the Green function of free space, is specifically expressed as follows: G=exp (-jkR)/R, R=|r-r'|.What subscript V and S represented respectively is media fraction region and metal covering district

Territory.When analyzing metal medium compound target, total scattering field E ^scacan be written as the superposition of above-mentioned (10) and (11) two formulas:

E ^sca＝-(iωA _S(r)+▽Φ _S(r)+iωA _V(r)+▽Φ _V(r)) (15)

Electric field in dielectric and on metal surface meets following equalities respectively:

E=D (r)/ε (r) r (16) on medium

E _tan=0 r is in metal surface (17)

Can be obtained by formula (10) and (11):

$E^{\mathrm{inc}}=\frac{D\left(r\right)}{\mathrm{\ϵ}\left(r\right)}+(\mathrm{i\ω}{A}_S\left(r\right)+\▿{\mathrm{\Φ}}_S\left(r\right)+\mathrm{i\ω}{A}_V\left(r\right)+\▿{\mathrm{\Φ}}_V\left(r\right))---\left(18\right)$

$E_{\tan }^{\mathrm{inc}}={[\mathrm{i\ω}{A}_S\left(r\right)+\▿{\mathrm{\Φ}}_S\left(r\right)+\mathrm{i\ω}{A}_V\left(r\right)+\▿{\mathrm{\Φ}}_V\left(r\right)]}_{\tan }---\left(19\right)$

Wherein, D (r) is electric displacement vector, E ^incfor incident electric fields, for incident electric fields tangential component.

Adopt Galerkin method to test above formula (18) and (19), and use fast multipole techniques acceleration matrix vector to take advantage of, solve the induction current containing metal surface in cavity configuration and dielectric polarization current.

Step 5, obtained the electric field value of various discrete point needed for parabolic equation on cavity hatch face by the induction current of metal surface in target with open cavity cavity and medium endosome polarization current, concrete steps are as follows:

Step 5.1, carried out in cavity hatch face discrete at equal intervals, discrete size is not more than 0.1 incident wave wavelength, obtains the coordinate figure of each discrete point;

Step 5.2, application Green's function integral solve the electric field of each discrete point on opening surface.

The electric field that the induction current obtaining metal surface in chamber produces at opening surface place, chamber.In hypothesis space, a known current source J (r') is distributed on the metallic object V that a border is S, then the scattering electric field that in space, any point produces can by dyadic Green's function be expressed as compactly:

$E_S^{\mathrm{sca}}\left(\stackrel{\→}{r}\right)=-\frac{\mathrm{i\ω\μ}}{4\mathrm{\π}}{\∫}_s\stackrel{\→}{\stackrel{\→}{G}}(r,r^{\text{'}})\·J(r\text{'})\mathrm{dS}---\left(20\right)$

Wherein, J (r') represents the current source in space, represent the scattering electric field of any point in space, represent dyadic Green's function.

Obtain the electric field that chamber medium endosome polarization current produces at opening surface place, chamber equally.In hypothesis space, a known current source J (r') is distributed on the dielectric V that a border is S, then the scattering electric field that in space, any point produces can by dyadic Green's function be expressed as compactly:

$E_V^{\mathrm{sca}}\left(r\right)=-\frac{\mathrm{i\ω\μ}}{4\mathrm{\π}}{\∫}_V\stackrel{\→}{\stackrel{\→}{G}}(r,r\text{'})\·J(r\text{'})\mathrm{dS}---\left(21\right)$

Wherein, represent the scattering electric field of any point in space.

The face of chamber opening part is carried out discrete at equal intervals, draw the coordinate of each point, coordinate information is substituted into respectively in formula (20) lattice and formula (21) Green's function integral formula, the electric field that two parts produce is superposed, solve the electric field value at each discrete point place of chamber opening part, as Fig. 5.

Step 6, aftertreatment is carried out to the electric field on last tangent plane, electric field on the cavity hatch face of step 5 gained is replaced the electric field of the former target cavity opening part of step 3 gained, carry out far to field transformation to the near field electric field value of gained and solve Radar Cross Section, concrete steps are as follows:

Electric field in step 6.1, the cavity hatch face step 5 obtained is multiplied by e ^-ikx, replace by the electric field of the cavity hatch of mesh free para-curve gained;

Step 6.2, to process after last tangent plane on electric field release far field by near field, according to the electric field value determination Radar Cross Section in far field.

Under three-dimensional system of coordinate, the dual station RCS in (θ, φ) direction is:

$\mathrm{\σ}(\mathrm{\θ},\mathrm{\φ})=\underset{r\→\∞}{\lim }{4\mathrm{\πr}}^2\frac{{\left|E^s(x,y,z)\right|}^2}{{\left|E^i(x,y,z)\right|}^2}---\left(22\right)$

Wherein E ^sand E ⁱrepresent the electric field component of scattered field and incident field respectively, represent the distance between field source point.

Finally solve the dual station RCS of target with open cavity, when the present invention analyzes the electromagnetic scattering of Electrically large size object, computing velocity is fast, consumes internal memory few, has very high using value.

Embodiment 1

The present embodiment has carried out the exemplary simulation with the electromagnetic scattering of medium target with open cavity, emulation realizes on the personal computer of dominant frequency 2.83GHz, internal memory 3.5GB, with the metal cuboid length of side for 6m, the cavity segment length of side is 3m cube, a face coating thickness in chamber is 0.2m's, relative dielectric constant be 2.0 medium be example, Fig. 6 is its x, z cross sectional representation plane, it is incident that ripple faces chamber opening part, under observing different frequency, and the RCS of central spot on the opening surface of chamber, incident wave line of propagation θ=0 ° discrete interval on x-axis direction is 0.1 wavelength, in order to verify the correctness of the inventive method, using honorable integral equation simulation result as reference.Fig. 7 is the inventive method RCS value at back scattering point place and comparing result of honorable integral equation at respective frequencies, can find out the correctness of context of methods from the curve figure.Fig. 8 is the result of this example dual station RCS under the frequency of 320MHz, can find out that the inventive method can calculate the dual station RCS in backward 15 ° of target with open cavity accurately, illustrate that this method can the Electromagnetic Scattering Characteristics of express-analysis complex appearance metal target with open cavity.

In sum, the invention solves traditional mesh free para-curve method cannot accurate Calculation containing the defect of cavity configuration, the cavity segment honorable integral Equation Methods that quick multistage sub-technology is accelerated calculates, remaining part is used as solid metal mesh free para-curve and is solved, it realizes process flexible freely, has important practical engineering application and is worth.

Claims (7)

1. cavity is containing a dielectric object electromagnetic scattering hybrid analysis, and it is characterized in that, step is as follows:

Step 1, the cavity portion of target with open cavity is filled to solid metal, set up the discrete model of target after filling, determine that the axial direction of parabolic equation is as x-axis, the relation between adjacent two tangent planes of CN difference scheme acquisition is used in x-axis direction, RPIM is all adopted to construct shape function and space derivative in y-axis, z-axis direction, and introduce scatterer boundary condition, construct matrix equation;

Step 2, successively Recursive Solution is carried out to the node electric field value on each tangent plane, solved the electric field value of various discrete Nodes on next tangent plane by the right vector of the information and equation of constantly updating frontier point;

Step 3, the electric field value of last tangent plane to be revised, solve the matrix equation of last tangent plane, obtain the electric field value at discrete nodes place, and this electric field value is carried out the correction of phase place;

Step 4, cavity portion in target to be solved with honorable integral equation separately, by metal covering in cavity and the discrete sub-scatterer grouping obtained of dielectric, adopt diverse ways computing impedance matrix element according to the position relationship of any two sub-scatterer place groups, adopt quick multistage submethod to solve induction current and the medium endosome polarization current of metal surface in cavity;

Step 5, obtained the electric field value of various discrete point needed for parabolic equation on cavity hatch face by the induction current of metal surface in target with open cavity cavity and medium endosome polarization current;

Step 6, aftertreatment is carried out to the electric field on last tangent plane, electric field on the cavity hatch face of step 5 gained is replaced the electric field of the former target cavity opening part of step 3 gained, far to field transformation is carried out to the near field electric field value of gained and solves Radar Cross Section.

2. cavity is containing dielectric object electromagnetic scattering hybrid analysis according to claim 1, and it is characterized in that, the equation of structural matrix described in step 1, specifically comprises the following steps:

Step 1.1, the cavity portion of target with open cavity is filled to solid metal, it is discrete the metal Scattering Targets obtained to be carried out square grid, forms several tangent planes perpendicular to x-axis direction, and finds out the frontier point of solid metal Scattering Targets on each tangent plane;

Step 1.2, geometric relationship according to target, determine to fill the discrete nodes of rear Scattering Targets inside, borderline discrete nodes, the discrete nodes of air layer and the discrete nodes of PML layer correspondence;

Step 1.3, determine that the axial direction of parabolic equation is as x-axis, under three-dimensional situation, normal vector parabolic equation is expressed as:

$\left\{\begin{array}{c}\frac{{\∂}^2{u}_x^s}{{\∂y}^2}(x,y,z)+\frac{{\∂}^2{u}_x^s}{{\∂z}^2}(x,y,z)+2\mathrm{ik}\frac{{\∂u}_x^s}{\∂x}(x,y,z)=0\\ \frac{{\∂}^2{u}_y^s}{{\∂y}^2}(x,y,z)+\frac{{\∂}^2{u}_y^s}{{\∂z}^2}(x,y,z)+2\mathrm{ik}\frac{{\∂u}_y^s}{\∂x}(x,y,z)=0\\ \frac{{\∂}^2{u}_z^s}{{\∂y}^2}(x,y,z)+\frac{{\∂}^2{u}_z^s}{{\∂z}^2}(x,y,z)+2\mathrm{ik}\frac{{\∂u}_z^s}{\∂x}(x,y,z)=0\end{array}\right.---\left(1\right)$

In formula, be respectively the component of wave function in x-axis, y-axis, z-axis direction, be respectively the component of electric field in x-axis, y-axis, z-axis direction, k is wave number, and i is imaginary number;

In PML medium, vector parabolic equation is expressed as:

$\left\{\begin{array}{c}{\left(\frac{1}{1-\mathrm{i\σ}\left(y\right)}\right)}^2\frac{{\∂}^2{u}_x^s(x,y,z)}{{\∂y}^2}+\frac{{2\mathrm{i\σ}}_{0}y}{{(1-\mathrm{i\σ}\left(y\right))}^3{\mathrm{\δ}}^2}\frac{{\∂u}_x^s(x,y,z)}{\∂y}+{\left(\frac{1}{1-\mathrm{i\σ}\left(z\right)}\right)}^2\frac{{\∂}^2{u}_x^s(x,y,z)}{{\∂z}^2}\\ +\frac{{2\mathrm{i\σ}}_{0}z}{{(1-\mathrm{i\σ}\left(z\right))}^3{\mathrm{\δ}}^2}\frac{{\∂u}_x^s(x,y,z)}{\∂z}+2\mathrm{ik}\frac{{\∂u}_x^s(x,y,z)}{\∂x}=0\\ \left(\frac{1}{1-\mathrm{i\σ}\left(y\right)}\right)2^{}\frac{{\∂}^2{u}_y^s(x,y,z)}{{\∂y}^2}+\frac{{2\mathrm{i\σ}}_{0}y}{{(1-\mathrm{i\σ}\left(y\right))}^3{\mathrm{\δ}}^2}\frac{{\∂u}_y^s(x,y,z)}{\∂y}+{\left(\frac{1}{1-\mathrm{i\σ}\left(z\right)}\right)}^2\frac{{\∂}^2{u}_y^s(x,y,z)}{{\∂z}^2}\\ +\frac{{2\mathrm{i\σ}}_{0}z}{{(1-\mathrm{i\σ}\left(z\right))}^3{\mathrm{\δ}}^2}\frac{{\∂u}_y^s(x,y,z)}{\∂z}+2\mathrm{ik}\frac{{\∂u}_y^s(x,y,z)}{\∂x}=0\\ \left(\frac{1}{1-\mathrm{i\σ}\left(y\right)}\right)2^{}\frac{{\∂}^2{u}_z^s(x,y,z)}{{\∂y}^2}+\frac{{2\mathrm{i\σ}}_{0}y}{{(1-\mathrm{i\σ}\left(y\right))}^3{\mathrm{\δ}}^2}\frac{{\∂u}_z^s(x,y,z)}{\∂y}+{\left(\frac{1}{1-\mathrm{i\σ}\left(z\right)}\right)}^2\frac{{\∂}^2{u}_z^s(x,y,z)}{{\∂z}^2}\\ +\frac{{2\mathrm{i\σ}}_{0}z}{{(1-\mathrm{i\σ}\left(z\right))}^3{\mathrm{\δ}}^2}\frac{{\∂u}_z^s(x,y,z)}{\∂z}+2\mathrm{ik}\frac{{\∂u}_z^s(x,y,z)}{\∂x}=0\end{array}\right.---\left(2\right)$

In formula, σ () represents the function of electrical loss, σ ₀represent the coefficient of electrical loss, δ represents the coefficient of skin depth;

Use the relation between adjacent two tangent planes of CN difference scheme acquisition in x-axis direction, all adopt RPIM to construct shape function and space derivative in y-axis, z-axis direction, electric field u (x, y, z) is launched by shape function, is shown below:

u(x,y,z)＝Φ(x,y,z)U _S(x,y,z) (3)

In formula, U _s(x, y, z) is electric field coefficient to be asked, Φ (x, y, z)=[Φ ₁(x, y, z), Φ ₂(x, y, z) ..., Φ _n(x, y, z)] be shape function, N is the number of discrete nodes in supporting domain, passes through to realize Φ (x, y, z) differentiate to the differentiate of u (x, y, z);

Step 1.4, introducing scatterer boundary condition, construct matrix equation: for object boundary point, suppose that P is the point on scatterer surface, n=(n _x, n _y, n _z) be the normal orientation of P point, n × E=0 on the surface of pure conductor, that is:

n(P)×E ^s(P)=-n(P)×E ⁱ(P) (4)

In formula, E ⁱrepresent incident electric fields, E ^srepresent scattered field; Three corresponding equations are obtained by formula (4):

$\left\{\begin{array}{c}{n}_x{E}_y\left(P\right)-n_y{E}_x\left(P\right)=0\\ n_x{E}_z\left(P\right)-n_z{E}_x\left(P\right)=0\\ n_y{E}_z\left(P\right)-n_z{E}_y\left(P\right)=0\end{array}\right.---\left(5\right)$

Formula (5) is transformed to:

$\left\{\begin{array}{c}{n}_x{u}_y^s\left(P\right)-n_y{u}_x^s\left(P\right)=-e^{-\mathrm{ikx}}(n_x{E}_y^i\left(P\right)-n_y{E}_x^i\left(P\right))\\ n_x{u}_z^s\left(P\right)-n_z{u}_x^s\left(P\right)=-e^{-\mathrm{ikx}}(n_x{E}_z^i\left(P\right)-n_z{E}_x^i\left(P\right))\\ n_y{u}_z^s\left(P\right)-n_z{u}_y^s\left(P\right)=-e^{-\mathrm{ikx}}(n_y{E}_z^i\left(P\right)-n_z{E}_y^i\left(P\right))\end{array}\right.---\left(6\right)$

In formula, represent the component of incident electric fields on x-axis, y-axis, z-axis direction respectively, represent the component of wave function on x-axis, y-axis, z-axis direction respectively;

By electric field u (x, y, z) by shape function u (x, y, z)=Φ (x, y, z) U _s(x, y, z) launches, U _s(x, y, z) is electric field coefficient to be asked, Φ (x, y, z)=[Φ ₁(x, y, z), Φ ₂(x, y, z) ..., Φ _n(x, y, z)] be shape function, N is the number of discrete nodes in supporting domain, and above formula is expressed as following form:

$\left\{\begin{array}{c}{n}_s\mathrm{\Φ}\left(P\right)U_{S,y}\left(P\right)-n_y\mathrm{\Φ}\left(p\right)U_{S,x}\left(P\right)=-e^{-\mathrm{ikx}}(n_x{E}_y^i\left(P\right)-n_y{E}_x^i\left(P\right))\\ n_s\mathrm{\Φ}\left(P\right)U_{S,z}\left(P\right)-n_z\mathrm{\Φ}\left(p\right)U_{S,x}\left(P\right)=-e^{-\mathrm{ikx}}(n_x{E}_z^i\left(P\right)-n_z{E}_x^i\left(P\right))\\ n_y\mathrm{\Φ}\left(P\right)U_{S,z}\left(P\right)-n_z\mathrm{\Φ}\left(p\right)U_{S,y}\left(P\right)=-e^{-\mathrm{ikx}}(n_y{E}_z^i\left(P\right)-n_z{E}_y^i\left(P\right))\end{array}\right.---\left(7\right)$

Wherein, U _s,x(x, y, z), U _s,y(x, y, z), U _s,z(x, y, z) is electric field coefficient the to be asked component on x-axis, y-axis, z-axis direction; Divergence equation under the three-dimensional coordinate of P point is transformed to:

$\frac{i}{2k}(\frac{{\∂}^2{u}_x^s}{{\∂y}^2}\left(P\right)+\frac{{\∂}^2{u}_x^s}{{\∂z}^2}\left(P\right))+{\mathrm{iku}}_x^s\left(P\right)+\frac{{\∂u}_y^s}{\∂y}\left(P\right)+\frac{{\∂u}_z^s}{\∂z}\left(P\right)=0---\left(8\right)$

To electric field u _x(x, y, z), u _y(x, y, z), u _z(x, y, z) adopts RPIM to construct shape function and space derivative, and pass through to realize shape function Φ (x, y, z) differentiate about the differentiate of y-axis and z-axis to electric field u (x, y, z), formula (8) is discrete is:

$\frac{i}{2k}(\frac{{\∂}^2}{{\∂y}^2}+\frac{{\∂}^2}{{\∂z}^2})\mathrm{\Φ}\left(P\right)U_{S,x}\left(P\right)+\mathrm{ik\Φ}\left(P\right)U_{S,x}\left(P\right)+\frac{\∂\mathrm{\Φ}\left(P\right)}{\∂y}{U}_{S,y}\left(P\right)+\frac{\∂\mathrm{\Φ}\left(P\right)}{\∂z}{U}_{S,z}\left(P\right)=0---\left(9\right)$

Formula (7) and formula (9) simultaneous are constructed system of linear equations, coupled relation is filled in matrix equation, the interpolation of nonhomogeneous boundary condition can be completed, construct final matrix equation.

3. cavity contains dielectric object electromagnetic scattering hybrid analysis according to claim 1, it is characterized in that, successively Recursive Solution is carried out to the node electric field value on each tangent plane described in step 2, solved the electric field value of various discrete Nodes on next tangent plane by the right vector of the information and equation of constantly updating frontier point, specifically comprise the following steps:

Step 2.1, the right vector when the electric field value of previous tangent plane various discrete node is solved as current tangent plane;

Step 2.2, at the determined frontier point place of current tangent plane, add tangential component be 0 and divergence be the boundary condition of 0, the node electric field value assignment being in interior of articles is 0, formed current tangent plane upgrade after matrix equation;

Matrix equation after step 2.3, solution procedure 2.2 upgrade, obtains the electric field value of the node of current tangent plane various discrete.

4. cavity is containing dielectric object electromagnetic scattering hybrid analysis according to claim 1, and it is characterized in that, revise the electric field value of last tangent plane described in step 3, detailed process is as follows:

Because the incident electric fields of parabolic equation method differs a phase place relative to the incident electric fields of honorable integral Equation Methods, so the electric field of the scattered field of finally trying to achieve is also by difference phase place, this phase place is compensated, the electric field that parabolic equation method is determined is multiplied by as the electric field value required for final parabolic equation method, wherein θ is incident wave and x-axis angle, for incident wave and y-axis angle.

5. cavity is containing dielectric object electromagnetic scattering hybrid analysis according to claim 1, and it is characterized in that, adopt quick multistage submethod to solve induction current and the medium endosome polarization current of metal surface in cavity described in step 4, detailed process is as follows:

Step 4.1, the metallic member surface triangles of cavity is carried out subdivision, obtain the numbering of each triangular element, the coordinate of point, normal vector; Media fraction tetrahedron carries out subdivision, obtains the unit normal vector in each tetrahedral numbering, tessarace coordinate, four faces;

Step 4.2, use honorable integral equation, do the gold test of gal the Liao Dynasty, and accelerate solution procedure by quick multistage sub-technology, obtain induction current and the medium endosome polarization current of metal surface in cavity.

6. cavity contains dielectric object electromagnetic scattering hybrid analysis according to claim 1, it is characterized in that, obtained the electric field value of various discrete point needed for parabolic equation on cavity hatch face by the induction current of metal surface in target with open cavity cavity and medium endosome polarization current described in step 5, be specially: cavity hatch face is carried out discrete at equal intervals, discrete size is not more than 0.1 incident wave wavelength, obtain the coordinate figure of each discrete point, application Green's function integral solves the electric field of each discrete point on opening surface.

7. cavity is containing dielectric object electromagnetic scattering hybrid analysis according to claim 1, and it is characterized in that, carry out far to field transformation to the near field electric field value of gained described in step 6 and solve Radar Cross Section, step is as follows:

Step 6.1, the electric field on cavity hatch face is multiplied by e ^-ikx, replace by the electric field of the cavity hatch of mesh free para-curve gained;

Step 6.2, to process after last tangent plane on electric field release far field by near field, according to the electric field value determination Radar Cross Section in far field.