A moM-po electromagnetic scattering hybrid method based on matrix dimension reduction

Abstract

The application discloses a MoM-PO electromagnetic scattering hybrid method based on matrix dimension reduction, according to the region division of a target into an original region and a dimension reduction region, impedance matrices in a method of moments (MoM) are divided into blocks, and then two transfer matrices are constructed to establish an expression of unknowns between the two regions; through simple operation of the matrix blocks, the high-dimensional impedance matrix is changed into a low-dimensional impedance matrix, so that the complexity of matrix element filling and subsequent equation solving and calculation can be effectively reduced; and through the introduction of an electric dipole model, the calculation process of matrix element filling is further simplified.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electromagnetic scattering, and particularly relates to a MoM-PO electromagnetic scattering hybrid method. BACKGROUND

[0002] The method of moment (MoM) is a numerical method based on discrete integral equation, which is widely used to calculate arbitrary three-dimensional geometries with small electrical size. By decomposing sub-regions and using basis functions, an impedance matrix is constructed to solve the current calculation. However, when the unknown quantity increases, the memory and time consumption are huge, the calculation efficiency is low, and it cannot be used to calculate electrically large size targets. For electrically large size targets, high frequency algorithm is a commonly used calculation method and is efficient in calculation, but it cannot handle complex structure targets.

[0003] Therefore, the method of moment is often combined with the physical optics method to form a hybrid algorithm, which divides the target into a method of moment area containing fine and complex structures, and a physical optics (PO) area containing large size smooth structures, in order to balance the accuracy and efficiency of the two algorithms. However, when calculating the impedance matrix element filling of the method of moment area and considering the mutual coupling between the method of moment area and the physical optics area, the calculation complexity of the matrix element is high, which leads to a large occupation of solving time and a reduction of calculation efficiency. Although some improved algorithms have been proposed, they all have certain defects. For example, the high-order hybrid algorithm and the adaptive integration method cannot accurately model and simulate arbitrary three-dimensional complex targets, resulting in that these methods are not flexible and applicable. The iterative hybrid algorithm has a large amount of iteration between the two areas when facing the electrically large size method of moment area on the electrically large object, which leads to a large calculation cost of the matrix calculation of the method of moment area.

[0004] Therefore, it is necessary to further study the hybrid algorithm to reduce the calculation amount and improve the applicability of the algorithm. SUMMARY

[0005] In order to overcome the deficiencies of the prior art, the application provides a MoM-PO electromagnetic scattering hybrid method based on matrix dimension reduction (Hybrid Dimension Reduction Algorithm, HDRA), which divides the target into original regions and dimension reduction regions according to the region division, blocks the impedance matrix in the method of moment, and then uses two constructed transfer matrices to establish the expression of unknowns between the two regions. Through simple operation of the matrix block, the high-dimensional impedance matrix is changed into a low-dimensional impedance matrix, which can effectively reduce the complexity of matrix element filling and subsequent equation solving calculation. At the same time, by introducing the electric dipole model, the calculation process of matrix element filling is further simplified.

[0006] The technical solution adopted by the application to solve the technical problems comprises the following steps:

[0007] Step 1: Discretely expand the surface current of the target using RWG basis functions, and the X surface current expansion coefficients after discretization of the surface current are X unknowns to be solved; construct an impedance matrix equation ZI = V by the method of moments, where X × X dimensional Z is the known impedance matrix, X × 1 dimensional I is the column vector composed of X unknown surface current expansion coefficients; X × 1 dimensional V is the known excitation column vector;

[0008] Step 1-1: Divide the target surface into an original region and a reduced dimension region, so as to divide the X unknown surface current expansion coefficients into two parts, which are M surface current expansion coefficients of the original region and N surface current expansion coefficients of the reduced dimension region, and M + N = X; therefore, in the impedance matrix equation, the column vector I to be solved is divided into two parts, which are M × 1 dimensional column vector I composed of M surface current expansion coefficients of the original region and N × 1 dimensional column vector I composed of N surface current expansion coefficients of the reduced dimension region; at the same time, the impedance matrix Z is divided into four matrix blocks, which are M × M dimensional self-coupling matrix Z1 of the original region, M × N dimensional coupling action matrix Z2 of the reduced dimension region on the original region, N × M dimensional coupling action matrix Z3 of the original region on the reduced dimension region, and N × N dimensional self-coupling matrix Z4 of the reduced dimension region; the excitation column vector V is also divided into M × 1 dimensional excitation action vector V on the original region and N × 1 dimensional excitation action vector V on the reduced dimension region. M N M N As shown in equation (1)

[0009]

[0010] Step 1-2: Construct a linear expression between the N unknown surface current expansion coefficients of the reduced dimension region and the M unknown surface current expansion coefficients of the original region, and write it in matrix form as shown in equation (2):

[0011] I N = TI M + P (2)

[0012] Wherein, the matrix T is a coupling transfer matrix of N × M dimension, and the matrix P is an excitation transfer matrix of N × 1 dimension;

[0013] Step 1-3: Take the first M rows of the impedance matrix Z to construct a new matrix equation, and reduce the number of unknowns from X to M by the linear relationship between I N and I M , that is, only I M is retained, and the X × X dimensional matrix equation shown in equation (1) in step 1-1 is reduced to a M × M dimensional matrix equation by transformation and simplification of the matrix equation:

[0014] [Z′][I​​​M ] = [V'] (3)

[0015] where [V'] = [V M ] - [Z2][P] is the new M-dimensional excitation column vector, [Z'] = [Z1] + [Z2][T] is the new M x M-dimensional impedance matrix;

[0016] Step 2: fill the coupling effect of the i-th pair of surface elements in the original region at the midpoint of the common edge of the j-th pair of surface elements in the reduced dimension region into the corresponding element T ji in the matrix T, and fill the excitation effect of the incident wave at the midpoint of the j-th common edge in the reduced dimension region into the corresponding element P j in the matrix P; in the process of filling the matrix T, an infinitesimal dipole model with equivalent dipole moment is used to replace the current distribution on a group of triangular surface elements in the original region by using the equivalent dipole method;

[0017] Step 3: solve the M-dimensional matrix equation of formula (3) in steps 1-3 to obtain I M , to obtain the M unknown surface current expansion coefficients in the original region; then solve I N in formula (2) in steps 1-2 to obtain the N unknown surface current expansion coefficients in the reduced dimension region, so as to obtain all X surface current expansion coefficients.

[0018] The beneficial effects of the present application are as follows:

[0019] 1. The method of the present application can calculate the electromagnetic scattering problem of a three-dimensional electrically large target with complex and fine structures of any shape, and has universality.

[0020] 2. Compared with the traditional moment method, the method of the present application reduces the number of elements required to be filled in the impedance matrix, thereby reducing the calculation time and improving the calculation efficiency.

[0021] 3. The method of the present application uses an electric dipole equivalent model, avoids the double integration solution of the radiation field in the traditional moment method, and reduces the calculation amount of the matrix element filling in the mutual coupling effect matrix.

[0022] 4. Compared with the traditional moment method, the method of the present application reduces the dimension of the impedance matrix, avoids the solution calculation of the high-order matrix equation, and reduces the complexity of the operation in the solution process.

[0023] 5. Compared with the traditional moment method, the method of the present application reduces the occupation of the computer storage space required in the calculation process by reducing the dimension of the impedance matrix.

[0024] 6. Compared with the traditional physical optics method, the method of the present application has better accuracy of the calculation result through the analysis and calculation of the fine structure and the complete physical meaning in the calculation process. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 Flow chart of matrix dimension reduction hybrid algorithm based on equivalent model of electric dipole of the present application.

[0026] Figure 2 Combined body calculation model schematic diagram of matrix dimension reduction hybrid algorithm of the embodiment of the present application, (a) front view, (b) side view.

[0027] Figure 3 Different algorithm single station electromagnetic scattering cross section result comparison schematic diagram of the embodiment of the present application. DETAILED DESCRIPTION

[0028] The present application is further illustrated below in conjunction with the drawings and embodiments.

[0029] The present application is based on the block and transformation of matrix, the impedance matrix is blocked according to the dimension reduction region and the original region, the coupling transfer matrix and the excitation transfer matrix are constructed to establish the linear relationship of the current between the two regions, so as to reduce the dimension of the impedance matrix equation by transforming the matrix equation. The dimension of the impedance matrix is reduced to the dimension of the self-coupling matrix block of the moment region. Generally speaking, the moment region is often some small and fine parts, and the number of unknown quantities is small, so the dimension of the self-coupling matrix block is small, which greatly reduces the complexity of subsequent equation solving. At the same time, the element filling of the high-dimensional impedance matrix is converted to the element filling of the low-dimensional matrix block and the simple operation between small matrix blocks. In order to further simplify and accelerate the calculation of the matrix block, the equivalent dipole method is introduced, which regards the basis function as a dipole model, avoiding the calculation of double integral when filling the matrix block. The calculation of each matrix block in the method has a clear physical meaning, and also guarantees the continuity of the surface current between the moment region and the physical optics region, thereby ensuring the accuracy of the calculation result.

[0030] As shown in Figure 1 A MoM-PO electromagnetic scattering hybrid method based on matrix dimension reduction, comprising the following steps:

[0031] Step 1: Discretely expand the surface current of the target using RWG basis function, and the X surface current expansion coefficients after discretization of the surface current are X unknown quantities to be solved; construct the impedance matrix equation ZI = V by moment method, wherein X X dimension Z is the known impedance matrix, X 1 dimension I is the column vector composed of X unknown surface current expansion coefficients; X 1 dimension V is the known excitation column vector.

[0032] Step 1-1: The target surface is divided into a primary region and a reduced dimension region, so that the unknown X surface current expansion coefficients can be divided into two parts, M surface current expansion coefficients of the primary region and N surface current expansion coefficients of the reduced dimension region, and M+N=X. Therefore, in the impedance matrix equation, the column vector I to be solved can also be divided into two parts, M surface current expansion coefficients of the primary region form an M×1 dimension column vector I M and N surface current expansion coefficients of the reduced dimension region form an N×1 dimension column vector I N ; At the same time, the impedance matrix Z is divided into four matrix blocks, M×M dimension self-coupling matrix Z1 of the primary region, M×N dimension coupling effect matrix Z2 of the reduced dimension region to the primary region, N×M dimension coupling effect matrix Z3 of the primary region to the reduced dimension region, and N×N dimension self-coupling matrix Z4 of the reduced dimension region; The excitation column vector V is also divided into M×1 dimension excitation effect vector V M of the primary region and N×1 dimension excitation effect vector V N , as shown in equation (1):

[0033]

[0034] Step 1-2: Linear expression between N unknown surface current expansion coefficients of the reduced dimension region and M unknown surface current expansion coefficients of the primary region is constructed, written in matrix form as shown in equation (2):

[0035] I N =TI M +P (2)

[0036] Wherein, the matrix T is an N×M dimension coupling transfer matrix, and the matrix P is an N×1 dimension excitation transfer matrix;

[0037] Step 1-3: The first M rows of the impedance matrix Z are taken to form a new matrix equation, and the number of unknowns is reduced to M from the linear relationship between I N and I M , that is, only I M is retained, and the X×X dimension matrix equation shown in equation (1) in step 1-1 is reduced to an M×M dimension matrix equation through matrix equation transformation and simplification:

[0038] Z′I M =V′ (3)

[0039] Wherein, V′=V M -Z2P is a new M dimension excitation column vector, and Z′=Z1+Z2T is a new M×M dimension impedance matrix;

[0040] Step 2: Physically-optically approximating the current in the reduced dimension region, ignoring the self-coupling effect of the reduced dimension region, the influencing factor of the surface current is the original region surface current and the far field electromagnetic wave effect; the coupling effect of the i-th facet pair in the original region at the midpoint of the public edge of the j-th facet pair in the reduced dimension region is filled into the corresponding element T ji in the matrix T, the excitation effect of the incident wave at the midpoint of the j-th public edge in the reduced dimension region is filled into the corresponding element P j in the matrix P; in the process of filling the matrix T, the equivalent dipole method is used to replace the current distribution on a group of triangular facets in the original region with an infinitesimal dipole model having an equivalent dipole moment;

[0041] Step 3: solving the M-dimensional matrix equation of formula (3) in steps 1-3 to obtain I M , obtaining the M unknown surface current expansion coefficients in the original region; then solving I N in formula (2) in steps 1-2 to obtain the N unknown surface current expansion coefficients in the reduced dimension region, thereby obtaining all X unknown surface current expansion coefficients.

[0042] Step 4: obtaining the surface current expansion coefficients, calculating the scattering field, radar scattering cross section and other problems of the target according to the RWG basis function and application requirements. Specific embodiments:

[0044] The following further describes the present application by taking a preferred combination model as a specific implementation example. The combination calculation model is shown in Figure 2 , (a) and (b) are the front view and side view of the calculation model, respectively. The model is composed of an electrically large conductor sphere, a circular cone and a cube, wherein the sphere center coordinates are (0, 0, 0.7), the circular cone bottom radius is 0.1 meters and is parallel to the XOY plane, the bottom center coordinates are (0, 0, 2.02), the height of the circular cone is 0.2 meters, the side length of the cube is 0.1 meters, and the cube center coordinates are (1.3, 0.1, 0.1). The calculation frequency is 1.5 GHz, wherein the incident wave is θ polarization, the incident direction changes from 0° to 180° along the θ direction, and the φ angle always remains 0°.

[0045] The specific steps are as follows:

[0046] Step 1: discretely expanding the surface current of the target by using the RWG basis function to obtain X surface current expansion coefficients of the target, that is, X unknown quantities to be solved; obtaining the impedance matrix equation ZI = V by using the moment method, wherein Z is an X × X dimensional impedance matrix, I is an X × 1 dimensional surface current coefficient matrix to be solved, and V is an X × 1 dimensional excitation column vector.

[0047] In the preferred embodiment, the total number of unknowns X of the model is 141174. The impedance matrix Z is a 141174x141174 matrix, I is a 141174x1 matrix of unknown surface current expansion coefficients; V is a 141174x1 excitation column vector.

[0048] Step 1-1: The target surface is divided into a primary region and a reduced dimension region, so that the X surface current expansion coefficients are divided into two parts, M surface current expansion coefficients of the primary region and N surface current expansion coefficients of the reduced dimension region, and M+N=X. Therefore, in the impedance matrix equation, the matrix I is divided into two parts, an Mx1 column vector I of M surface current expansion coefficients of the primary region M and an Nx1 column vector I of N surface current expansion coefficients of the reduced dimension region N ; at the same time, the impedance matrix Z is divided into four matrix blocks, an MxM self-coupling matrix Z1 of the primary region, an MxN coupling matrix Z2 of the reduced dimension region to the primary region, an NXM coupling matrix Z3 of the primary region to the reduced dimension region, and an NxN self-coupling matrix Z4 of the reduced dimension region; the excitation column vector V is also divided into an Mx1 excitation vector V M to the primary region and an Nx1 excitation vector V N to the reduced dimension region, as shown in equation (1):

[0049]

[0050] In the preferred embodiment, the cone and cube parts are set as the primary region, and the conductor sphere part is set as the reduced dimension region. The number of unknowns M of the cone and cube parts is 1113, and the number of unknowns N of the conductor sphere part is 140061. Z1 is a 1113x1113 self-coupling matrix of the cone and cube parts, Z2 is a 1113x140061 mutual coupling matrix of the conductor sphere to the cone and cube parts, Z3 is a 140061x1113 mutual coupling matrix of the cone and cube parts to the conductor sphere, and Z4 is a 140061x140061 self-coupling matrix of the conductor sphere.

[0051] Step 1-2: A linear expression between the 140061 unknown surface current expansion coefficients I N of the conductor sphere part and the 1113 unknown surface current expansion coefficients I M of the cone and cube parts is constructed, as shown in equation (2):

[0052] I N = TI M +P (2)

[0053] Wherein, the matrix T is a 140061*1113 dimensional coupling transfer matrix, and the matrix P is a 140061*1 dimensional excitation transfer matrix;

[0054] Step 1-3: taking the first M=1113 rows of the impedance matrix Z to constitute a new matrix equation, that is, I N and I M The linear relationship of the unknown number is reduced to 1113, that is, only I M , and the 141174*141174 dimensional matrix equation shown in formula (1) in step 1-1 is reduced to a 1113*1113 dimensional matrix equation through transformation and simplification of the matrix equation:

[0055] Z′I M =V′ (3)

[0056] Wherein, V′=V M -Z2P is a new 1113 dimensional excitation column vector, and Z′=Z1+Z2T is a new 1113*1113 dimensional impedance matrix;

[0057] Step 2: physically and optically approximating the surface current of the conductor sphere, ignoring the self-coupling effect of the conductor sphere, and the influencing factors of the surface current are the surface currents of the cone and the cube part and the far-field electromagnetic wave effect. The coupling effect of the i-th face element pair in the cone and the cube part at the midpoint of the common edge of the j-th face element pair on the conductor sphere is filled into the corresponding element T ji of the matrix T, and the excitation effect of the incident wave at the midpoint of the j-th common edge on the conductor sphere is filled into the corresponding element P j of the matrix P. In the process of filling the matrix T, the equivalent dipole method is used, and an infinitesimal dipole model with equivalent dipole moment is used to replace the current distribution on a group of triangular face elements in the original area.

[0058] Step 3: solving the 1113 dimensional matrix equation of formula (3) in step 1-3 to solve I M , obtaining 1113 unknown surface current coefficients of the cone and the cube part; and solving I N from formula (2) in step 1-2, obtaining 140061 unknown surface current coefficients of the conductor sphere. Thus, all 141174 unknown surface current coefficients are obtained.

[0059] Step 4: solving the obtained target surface current, and calculating the target scattering field, radar scattering cross section and other problems according to the application requirements. Figure 3Compared with the results of the single station RCS calculated by the matrix reduction hybrid algorithm, the method of moments and the traditional physical optics algorithm, the time of the method of moments is 6 hours, and the time of the matrix reduction hybrid algorithm is 94 minutes, which can save 73.89% of time. At the same time, it can be seen that the matrix reduction hybrid algorithm is more accurate than the traditional physical optics method, and closer to the accurate solution of the method of moments, that is, the accuracy is higher.

Claims

1. A MoM-PO electromagnetic scattering mixing method based on matrix dimensionality reduction, characterized in that, Includes the following steps: Step 1: Discretize the surface current of the target using RWG basis functions. The X surface current expansion coefficients after discretization are the X unknowns to be determined. Construct the impedance matrix equation ZI = V using the method of moments, where the X×X dimension Z is the known impedance matrix, the X×1 dimension I is the column vector composed of the X unknown surface current expansion coefficients, and the X×1 dimension V is the known excitation column vector. Step 1-1: Divide the target surface into an original region and a reduced-dimensional region, thus dividing the unknown X surface current expansion coefficients into two parts: M surface current expansion coefficients in the original region and N surface current expansion coefficients in the reduced-dimensional region, with M + N = X. Therefore, in the impedance matrix equation, the column vector I to be determined is divided into two parts: an M×1 dimensional column vector I formed by the M surface current expansion coefficients in the original region. M The N×1 column vector I formed by the N surface current expansion coefficients in the dimension reduction region. N Simultaneously, the impedance matrix Z is divided into four matrix blocks: an M×M dimensional self-coupling matrix Z1 of the original region, an M×N dimensional coupling matrix Z2 of the reduced region to the original region, an N×M dimensional coupling matrix Z3 of the original region to the reduced region, and an N×N dimensional self-coupling matrix Z4 of the reduced region; the excitation column vector V is also divided into an M×1 dimensional excitation vector V_excitation_to_the_original_region. M The effect vector V of the N×1 dimensional excitation on the dimensionality reduction region N As shown in equation (1) Step 1-2: Construct a linear expression between the N unknown surface current expansion coefficients in the dimension reduction region and the M unknown surface current expansion coefficients in the original region, written in matrix form, as shown in equation (2): AND N =YOU M +P (2) Wherein, matrix T is an N×M dimensional coupling transfer matrix, and matrix P is an N×1 dimensional excitation transfer matrix; Steps 1-3: Take the first M rows of the impedance matrix Z to construct a new matrix equation, from I N and I M The linear relationship reduces the number of unknowns to M, that is, only I is retained. M Furthermore, by transforming and simplifying the matrix equation, the X×X dimensional matrix equation shown in equation (1) of step 1-1 is reduced to an M×M dimensional matrix equation: [Z′][I M ]=[V′] (3) Where, [V′]=[V M [Z2][P] is the new M-dimensional excitation column vector, and [Z′] = [Z1] + [Z2][T] is the new M×M-dimensional impedance matrix; Step 2: Fill the corresponding element T in matrix T with the coupling effect of the i-th face pair in the original region at the midpoint of the common edge of the j-th face pair in the reduced region. ji At the point where the excitation effect of the incident wave at the midpoint of the j-th common edge in the dimension-reduced region is located, the corresponding element P in matrix P is filled. j In the process of filling matrix T, the equivalent dipole method is used, and an infinitesimal dipole model with equivalent dipole moments is used to replace the current distribution on a set of triangular elements in the original region. Step 3: Solve the M-dimensional matrix equation of equation (3) in Step 1-3 to obtain I. M We obtain the M unknown surface current expansion coefficients in the original region; then we solve I using equation (2) from step 1-2. N We obtain the N unknown surface current expansion coefficients in the dimension-reduced region, and thus obtain all X surface current expansion coefficients.

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