CN113935157A - Cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method - Google Patents

Cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method Download PDF

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CN113935157A
CN113935157A CN202111138380.1A CN202111138380A CN113935157A CN 113935157 A CN113935157 A CN 113935157A CN 202111138380 A CN202111138380 A CN 202111138380A CN 113935157 A CN113935157 A CN 113935157A
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韩兴斌
刘阳
刘春恒
侯进永
魏斌斌
臧晴
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32802 Troops Of People's Liberation Army Of China
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Abstract

The invention belongs to the technical field of electronics, and particularly relates to a cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method. The invention comprises the following steps: step 1, modeling a typical platform; step 2: self-adaptive mesh generation based on a bilinear patch aiming at a platform model; and step 3: solving the electromagnetic disturbance coupling numerical value of the cross-scale multi-mechanism complex structure: and (3) performing electromagnetic disturbance coupling numerical solution of the complex structure cross-scale multi-mechanism on the bilinear patches segmented in the step (2) by adopting a parallel high-order moment method based on regional decomposition, namely a HOMOM-MLFMA mixed algorithm. According to the invention, through rough subdivision of a smooth structure of a typical platform and fine subdivision of a complex fine structure, adaptive grid modeling of the typical platform can be realized, and on the basis, accurate electromagnetic modeling is realized by using a self-adaptive high-order moment method.

Description

Cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method
Technical Field
The invention belongs to the technical field of electronics, and particularly relates to a cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method.
Background
Complex targets often contain a variety of physical structures, such as cavities, dihedral angles, cubes, cylinders, spheres, etc., with different physical structures having different electromagnetic scattering properties. The RCS of a complex target generally has no analytical solution, and a numerical calculation method is generally required to solve the RCS value of the target. Generally, the surface of a complex object is divided into patches, the RCS value of each patch is calculated, and then the calculated RCS of the patches is synthesized. The calculation method employed needs to balance the contradiction between the calculation accuracy and the calculation amount. The conventional methods such as geometric optics method and physical optics method have huge calculation amount, and can be used for RCS calculation of complex targets only by correcting.
A complex target is planed, a traditional MoM usually adopts a triangle (surface mesh) to carry out geometric modeling, the number of triangle meshes required by the geometric modeling is very large, and the model precision is not high, so that the precision of an electromagnetic calculation result is reduced due to geometric modeling errors.
Disclosure of Invention
The invention aims to:
the invention provides a cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method, which realizes self-adaptive grid modeling of a typical platform by roughly dividing a smooth structure of the typical platform and finely dividing a complex fine structure, and realizes accurate electromagnetic modeling by using a self-adaptive high-order moment method on the basis.
The technical scheme adopted by the invention is as follows:
a cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method comprises the following steps: step 1, modeling a typical platform; step 2: self-adaptive mesh generation based on a bilinear patch aiming at a platform model; and step 3: solving the electromagnetic disturbance coupling numerical value of the cross-scale multi-mechanism complex structure: and (3) performing electromagnetic disturbance coupling numerical solution of the complex structure cross-scale multi-mechanism on the bilinear patches segmented in the step (2) by adopting a parallel high-order moment method based on regional decomposition, namely a HOMOM-MLFMA mixed algorithm.
In step 2, a bilinear patch is a non-planar curvilinear quadrilateral defined by four space vectors, which is used to define a flat or long and narrow surface.
In the curve quadrangle, the parameter equation is as follows:
Figure BDA0003283104140000021
wherein, p and s are defined as original coordinates of a certain position of the complex object, r11，r12，r21And r22Is a position vector of four vertices, and after transformation, the equation can be expressed as:
r(p,s)＝rc+rpp+rss+rpsps (2)
wherein:
Figure BDA0003283104140000022
Figure BDA0003283104140000023
Figure BDA0003283104140000024
Figure BDA0003283104140000031
the step 3 comprises the following steps:
step 3.1: determining an application scene of a HOMOM-MLFMA hybrid algorithm; step 3.2: calculating principle of HOMOM-MLFMA hybrid algorithm; step 3.3: computational solution
Figure BDA0003283104140000033
And
Figure BDA0003283104140000034
step (ii) of3.4: solving RCS of complex structures
In step 3.1, the homo m-MLFMA mixing algorithm includes: multilayer fast multipole method, i.e. MLFMA, high order basis function moment method, i.e. homo in combination with LU decomposition method.
In the step 3.2, the step of the method,
the computational model is divided into a homo region and a MLFMA region, so the matrix equation ZI ═ V is written as follows:
Figure BDA0003283104140000032
wherein Z isMMAnd ZFFSelf-impedance matrices, Z, representing HOMOM and MLFMA, respectivelyFMAnd ZMFRespectively, the mutual impedance matrix between HOMOM and MLFMA, IMAnd IFFor unknown electromagnetic current coefficient, VMAnd VFVoltage matrices, HOMOM and MLFMA, respectively;
the HOMOM region directly solves the impedance matrix equation by LU decomposition, so that the problem of slow convergence or non-convergence is avoided, and the MLFMA region can only be solved by an iteration method;
considering that the solution methods of the basis functions and the matrix equations in the two regions are different, the matrix equations are conveniently solved in an iterative voltage mode, and the coupling effect between the two regions is calculated through the iterative voltage and is external iteration.
The outer iteration is realized by modifying a voltage matrix, and the matrix equation (3) is rewritten as:
Figure BDA0003283104140000041
wherein
Figure BDA0003283104140000042
And
Figure BDA0003283104140000043
representing the correction to the voltage matrix at the i-th outer iteration, the matrix vector being multiplied
Figure BDA0003283104140000044
And
Figure BDA0003283104140000045
the method is realized by two steps: first calculating coupling near field, then checking the near field with corresponding weight function, and then obtaining
Figure BDA0003283104140000046
And
Figure BDA0003283104140000047
substituting equation (4) to obtain
Figure BDA0003283104140000048
And
Figure BDA0003283104140000049
judging whether convergence occurs or not through an equation (5), if not, continuing the iteration, and if so, stopping the iteration, wherein epsilon is an allowable error.
||Ii+1-Ii||2/||Ii||2＜ε (5)。
In the above-mentioned step 3.3,
computing
Figure BDA00032831041400000410
Calculating near fields E and H on the surface of the MLFMA region, the near fields being generated by surface electromagnetic flows J and M of the HOMOM region, expressed as follows:
E(J,M)＝ηL(J)-K(M) (6)
Figure BDA00032831041400000411
wherein, the operators L and K are defined as follows:
Figure BDA00032831041400000412
Figure BDA00032831041400000413
wherein X represents an equivalent current J or an equivalent magnetic current M,
Figure BDA00032831041400000414
for the wave impedance of free space, the green function G (r, r') in free space is defined as follows:
Figure BDA00032831041400000415
where r' is the position vector of the source point and r is the position vector of the field point. Divergence operator
Figure BDA00032831041400000416
Acting on r', gradient operators
Figure BDA0003283104140000051
Acting on r, and applying the weight function w of the obtained near field and MLFMA regionm(m ═ 1,2, 3.) assay, yielding:
Figure BDA0003283104140000052
where α is the combining factor of the CFIE, η is the wave impedance in free space,
Figure BDA0003283104140000053
is the outer normal unit vector of the MLFMA region surface,
Figure BDA0003283104140000054
is calculated like
Figure BDA0003283104140000055
In the above-mentioned step 3.4,
the steps 3.2 and 3.3 are repeated to obtain the I meeting the precision requirementMAnd IFFrom IMAnd IFFurther, the scattered field and RCS of a complex structure can be obtained.
Ensuring the communication stability in the LU decomposition process, adopting a binary tree principal component selection strategy and considering both high performance and autonomous controllability; for a panel column A, selecting principal elements in a binary tree protocol mode, wherein each local decomposition is a node of the binary tree, each communication combination is a binary tree protocol, the local decomposition is a process for processing local data by a process, and no communication exists in the process; the communication combination is a process of combining two processes into one group and exchanging local decomposition results, and communication is concentrated in the process.
The invention has the beneficial effects that:
(1) according to the cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method provided by the invention, the integrated modeling only needs a few patches to finely simulate the complex target.
(2) The invention provides a cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method, which is characterized in that a complex fine structure and platform integrated modeling technology and an adaptive order basis function moment method are adopted, the adaptive grid modeling of a typical platform is realized by roughly dividing a smooth structure of the typical platform and finely dividing the complex fine structure, and the accurate electromagnetic modeling is realized by using an adaptive high-order moment method on the basis.
(3) The invention provides a cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method, which provides a region decomposition moment method, an Adaptive Integration (AIM) algorithm and an Adaptive Integration (AIM) algorithm based on region decomposition aiming at the problem that the traditional full-wave method is difficult to solve the cross-scale multi-mechanism electromagnetic scattering.
Drawings
FIG. 1 is a flow chart of a cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method provided by the invention;
fig. 2 is a schematic diagram of adaptive mesh generation based on bilinear patches.
Detailed Description
The cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method provided by the invention is further described in detail with reference to the accompanying drawings and specific embodiments.
The invention solves the problem of electromagnetic disturbance coupling numerical values of different mechanisms between a cross-scale macroscopic whole body and microscopic details by taking wavelength as a scale under the condition of a complex structure, and has the difficulty of calculating the cross-scale multi-mechanism coupling electromagnetic disturbance under the condition of a space electromagnetic environment. A method of typical platform modeling, self-adaptive mesh generation of platform modeling, a hybrid algorithm, a fast solver, parallel computing and the like is adopted to develop a self-adaptive mesh generation fast layering hybrid solver algorithm based on parallel computing. Based on the above, the invention provides a cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method, which comprises the following steps:
step 1, modeling of typical platform
Aiming at typical target geometric structure modeling, the stealth performance of the stealth aircraft mainly depends on the appearance design, and the surface wave-absorbing material is adopted. Accurate geometric modeling of the flying target is therefore important. However, after the three-dimensional structure of the flying target is obtained, the simulation cannot be directly performed, and the continuous curved surface needs to be subdivided by using a triangular mesh so as to be discretized. We model the geometry of the complex structure of a typical flying target.
Step 2: adaptive mesh generation based on bilinear patches for platform model
Aiming at the problem that meshes can change along with frequency in electromagnetic simulation of a broadband typical platform, adaptive mesh subdivision modeling based on bilinear patches is adopted for a complex target, one bilinear patch is a non-planar curvilinear quadrangle defined by four space vectors, and a flat or long and narrow face is defined by the bilinear patch.
The parametric equation for this quadrilateral is:
Figure BDA0003283104140000071
wherein, p and s are defined as original coordinates of a certain position of the complex object, r11，r12，r21And r22Is a position vector of four vertices, and after transformation, the equation can be expressed as:
r(p,s)＝rc+rpp+rss+rpsps (2)
wherein:
Figure BDA0003283104140000072
Figure BDA0003283104140000075
Figure BDA0003283104140000073
Figure BDA0003283104140000074
the maximum length allowed by the longest side of the bilinear patch is the wavelength of two electromagnetic waves, the current distribution on the patch can be well approximated by a global polynomial at the moment, and self-adaptive mesh modeling based on the bilinear patch is realized according to different wavelengths under the condition of a broadband background.
And step 3: electromagnetic disturbance coupling numerical solution of complex structure cross-scale multi-mechanism
And (3) performing electromagnetic disturbance coupling numerical solution of the complex structure cross-scale multi-mechanism on the bilinear patches segmented in the step (2) by adopting a parallel high-order moment method based on regional decomposition.
Step 3.1: HOMOM-MLFMA mixed algorithm application scene
For typical structural platforms with fine structures such as blades of engine intakes, propellers on airplanes, antennas on platforms, etc., it is considered that these parts usually contain fine structures and metal medium mixed materials. Moreover, the discretized geometric models of the parts usually comprise non-uniform grids, the condition number of the matrix is deteriorated due to the factors, and the problem of slow convergence or even non-convergence exists when an iterative solution is adopted to solve a matrix equation, so that a multilayer fast multipole method (MLFMA) is not suitable for calculating the fine structures, and the parts need to be calculated by combining a high-order basis function moment method (HOMOM) with an LU decomposition method. On the other hand, the typical structure platform is generally a metal conductor with a simpler appearance, the matrix condition number is better, and the MLFMA calculation is suitable. Namely, the platform and the integrated model of the fine structure are divided into two regions of the fine structure and the platform, different electromagnetic algorithms are respectively selected for different regions, and a HOMOM-MLFMA hybrid algorithm is formed.
Step 3.2: HOMOM-MLFMA hybrid algorithm calculation principle
The computational model is divided into a homo region and a MLFMA region, so the matrix equation ZI ═ V can be written in the form:
Figure BDA0003283104140000081
wherein Z isMMAnd ZFFSelf-impedance matrices, Z, representing HOMOM and MLFMA, respectivelyFMAnd ZMFRepresenting the mutual impedance matrix between the homo m and MLFMA, respectively. Higher order basis functions reduce Z compared to RWG basis functionsMM，ZFMAnd ZMFThereby reducing the amount of computation and memory requirements. I isMAnd IFFor unknown electromagnetic current coefficient, VMAnd VFVoltage matrices for homo m and MLFMA, respectively.
The HOMOM region directly solves the impedance matrix equation by LU decomposition, so that the problem of slow convergence or non-convergence is avoided, and the MLFMA region can only be solved by an iteration method. Considering that the basis functions and the matrix equation solving method are different in the two regions, it is convenient to solve the matrix equation in an iterative voltage manner. The coupling between the two regions is calculated by iterating the voltages, which we call the process outer iteration. Since the integrated model of the stage and the fine structure is divided into two regions of the fine structure and the stage, the coupling ratio between the two regions is weak. At this point, the outer iteration may converge quickly. The outer iteration is realized by modifying the voltage matrix, and the matrix equation (3) can be rewritten as:
Figure BDA0003283104140000091
wherein
Figure BDA0003283104140000092
And
Figure BDA0003283104140000093
representing the correction to the voltage matrix at the ith outer iteration. Matrix vector multiplication
Figure BDA0003283104140000094
And
Figure BDA0003283104140000095
the method is realized by two steps: the coupled near field is first calculated and then verified with the corresponding weight function. Then the obtained
Figure BDA0003283104140000096
And
Figure BDA0003283104140000097
substituting equation (4) to obtain
Figure BDA0003283104140000098
And
Figure BDA0003283104140000099
judging whether convergence occurs or not through the formula (5), if not, continuing the iteration, and if so, stopping the iteration. Where ε is the allowable error.
||Ii+1-Ii||2/||Ii||2＜ε (5)
Step 3.3: computational solution
Figure BDA00032831041400000910
And
Figure BDA00032831041400000911
to be provided with
Figure BDA00032831041400000912
For example, near fields E and H on the surface of the MLFMA region are calculated, which are generated by the surface electromagnetic flows J and M of the HOMOM region, and are expressed as follows:
E(J,M)＝ηL(J)-K(M) (6)
Figure BDA0003283104140000101
wherein, the operators L and K are defined as follows:
Figure BDA0003283104140000102
Figure BDA0003283104140000103
wherein X represents an equivalent current J or an equivalent magnetic current M,
Figure BDA0003283104140000104
is the wave impedance in free space. The green function G (r, r') in free space is defined as follows:
Figure BDA0003283104140000105
where r' is the position vector of the source point and r is the position vector of the field point. Divergence operator
Figure BDA0003283104140000106
Acting on r', gradient operators
Figure BDA0003283104140000107
Acts on r. Then, the weight function w of the obtained near field and MLFMA region is calculatedm(m ═ 1,2, 3.) assay, yielding:
Figure BDA0003283104140000108
where α is the combining factor of the CFIE, η is the wave impedance in free space,
Figure BDA0003283104140000109
is the outer normal unit vector of the MLFMA domain surface. The above process does not require the matrix Z to be stored in memoryMFAnd ZFMThis can significantly reduce memory consumption.
Figure BDA00032831041400001010
Is calculated like
Figure BDA00032831041400001011
Step 3.4: solving RCS of complex structures
The steps 3.2 and 3.3 are repeated to obtain the I meeting the precision requirementMAnd IFFrom IMAnd IFFurther, the scattered field and RCS of a complex structure can be obtained.
The parallel high-order moment method is a core, wherein matrix parallel filling accounts for about 5-10% of the total time, parallel solution of a matrix equation accounts for about more than 90% of the total time, therefore, redundant calculation in and among processes is eliminated as far as possible, filling efficiency is improved, and an efficient parallel matrix filling scheme is realized by adopting optimized grid numbering.
The communication stability in the LU decomposition process is ensured as much as possible, a binary tree principal component selection strategy is adopted, high performance and autonomous controllability are considered, and a schematic diagram of the principle is shown in the following figure 1. And aiming at a panel column A, selecting principal elements in a binary tree protocol mode, wherein each local decomposition is a node of the binary tree, and each communication combination is a binary tree protocol. The local decomposition is a process for processing local data by a process, and no communication exists in the process; the communication combination is a process of combining two processes into one group and exchanging local decomposition results, and communication is concentrated in the process. The strategy introduces a redundant calculation process of 'local decomposition', concentrates data which needs to be communicated immediately originally and delays the data until necessary, thereby reducing communication traffic and communication times.
When the electromagnetic problem is very large in scale, it is still difficult to meet the simulation requirements even with parallel computing techniques. According to the thought of 'divide and conquer' the problem to be solved is divided into a plurality of sub-problems, each sub-problem is solved independently, and the coupling relation between the sub-problems is considered, and finally the solution of the complete problem is obtained.
The region decomposition includes two types, i.e., an overlapping type and a non-overlapping type: the overlapped region decomposition ensures the continuity of current by extending to the buffer region of the adjacent sub-region, the algorithm is easy to understand and realize, but the introduction of the buffer region brings trouble to modeling, the calculated amount is correspondingly increased, and the size of the equation region can also influence the calculation precision; the non-overlapping region decomposition has higher flexibility in modeling and solving. Fig. 2 below shows a schematic diagram of non-overlapped and overlapped region decomposition, wherein the non-overlapped region uses a virtual electromagnetic current surface to ensure the current continuity between regions, and the overlapped region decomposition uses a buffer region to ensure the current continuity between regions.
For different areas, different electromagnetic algorithms can be adopted for solving, and the algorithm adopts a high-order moment method and a mixed algorithm of multilayer fast multipole:
firstly, the fine structure of the electrical large size can be calculated by adopting a high-order moment method based on an EFIE + PMHW equation, and the electrical large size platform can be calculated by utilizing an MLFMA based on CFIE;
secondly, the computational model is divided into regions of homo and MLFMA, so the matrix equation ZI ═ V can be written in the form,
Figure BDA0003283104140000121
wherein Z isMMAnd ZFFSelf-impedance matrices, Z, representing HOMOM and MLFMA, respectivelyFMAnd ZMFRepresenting the mutual impedance matrix between the homo m and MLFMA, respectively. I isMAnd IFFor unknown electromagnetic current coefficient, VMAnd VFVoltage matrices for homo m and MLFMA, respectively.
The HOMOM region directly solves the impedance matrix equation by LU decomposition, so that the problem of slow convergence or non-convergence is avoided, and the MLFMA region can only be solved by an iteration method. Considering that the basis functions and the matrix equation solving method are different in the two regions, it is convenient to solve the matrix equation in an iterative voltage manner. The coupling between the two regions is calculated by iterating the voltages, which we call the process outer iteration. We refer to the iterations inside the MLFMA as inner iterations, as distinguished from outer iterations. In practical engineering, a large antenna array is usually mounted at a fixed height on a platform, so that the coupling ratio between the two areas is weak. At this point, the outer iteration may converge quickly.
The external iteration is realized by correcting a voltage matrix, and the matrix equation can be rewritten as
Figure BDA0003283104140000131
Wherein
Figure BDA0003283104140000132
And
Figure BDA0003283104140000133
representing the correction to the voltage matrix at the ith outer iteration. Matrix vector multiplication
Figure BDA0003283104140000134
And
Figure BDA0003283104140000135
the method is realized by two steps: the coupled near field is first calculated and then verified with the corresponding weight function. To be provided with
Figure BDA0003283104140000136
For example, near fields E and H on the surface of the MLFMA region are calculated, which are generated by the surface electromagnetic flows J and M of the HOMOM region, and are expressed as follows:
E(J,M)＝ηL(J)-K(M) (14)
Figure BDA0003283104140000137
wherein the operators L and K are defined as follows
Figure BDA0003283104140000138
Figure BDA0003283104140000139
Wherein X represents an equivalent current J or an equivalent magnetic current M,
Figure BDA00032831041400001310
is the wave impedance in free space. G (r, r ') is the Green's function in free space. Divergence operator
Figure BDA00032831041400001311
Acting on r', gradient operators
Figure BDA00032831041400001312
Acts on r. Then, the weight function w of the obtained near field and MLFMA region is calculatedm(m 1,2, 3.) to obtain
Figure BDA00032831041400001313
Where α is the combining factor of the CFIE, η is the wave impedance in free space,
Figure BDA00032831041400001314
is the outer normal unit vector of the MLFMA domain surface. The above process does not require the matrix Z to be stored in memoryMFAnd ZFMThis can significantly reduce memory consumption.
Figure BDA00032831041400001315
Is calculated like
Figure BDA00032831041400001316
And is omitted here.
When solving the first equation in the above equation, the LU decomposition needs to be performed only once, and the result can be reused to speed up the outer iteration. When the second equation of the above formula is solved by MLFMA, the equation is taken
Figure BDA0003283104140000141
As
Figure BDA0003283104140000142
May reduce the number of inner iteration steps.

Claims (10)

1. A cross-scale multi-mechanism fusion electromagnetic scattering numerical solving method is characterized by comprising the following steps: the method comprises the following steps: step (1), modeling a typical platform; step (2): self-adaptive mesh generation based on a bilinear patch aiming at a platform model; and (3): solving the electromagnetic disturbance coupling numerical value of the cross-scale multi-mechanism complex structure: and (3) performing electromagnetic disturbance coupling numerical solution of a complex structure cross-scale multi-mechanism on the bilinear patches segmented in the step (2) by adopting a parallel high-order moment method based on regional decomposition, namely a HOMOM-MLFMA mixed algorithm.
2. The method for solving the cross-scale multi-mechanism fusion electromagnetic scattering numerical value according to claim 1, characterized in that: in the step (2), a bilinear patch is a non-planar curvilinear quadrilateral defined by four space vectors, and is used for defining a flat or long and narrow surface.
3. The method for solving the cross-scale multi-mechanism fusion electromagnetic scattering numerical value according to claim 2, characterized in that: in the curve quadrangle, the parameter equation is as follows:
Figure FDA0003283104130000011
wherein, p and s are defined as original coordinates of a certain position of the complex object, r11，r12，r21And r22Is a position vector of four vertices, and after transformation, the equation can be expressed as:
r(p,s)＝rc+rpp+rss+rpsps (2)
wherein:
Figure FDA0003283104130000012
Figure FDA0003283104130000013
Figure FDA0003283104130000021
Figure FDA0003283104130000022
4. the method according to claim 3, wherein the method comprises the following steps: the step (3) comprises the following steps:
step (3.1): determining an application scene of a HOMOM-MLFMA hybrid algorithm; step (3.2): calculating principle of HOMOM-MLFMA hybrid algorithm; step (3.3): computational solution
Figure FDA0003283104130000023
And
Figure FDA0003283104130000024
step (3.4): and solving the RCS of the complex structure.
5. The method according to claim 4, wherein the method comprises the following steps: in the step (3.1), the homo m-MLFMA mixing algorithm includes: multilayer fast multipole method, i.e. MLFMA, high order basis function moment method, i.e. homo in combination with LU decomposition method.
6. The method according to claim 5, wherein the method comprises the following steps: in the step (3.2), the step (c),
the computational model is divided into a homo region and a MLFMA region, so the matrix equation ZI ═ V is written as follows:
Figure FDA0003283104130000025
wherein Z isMMAnd ZFFSelf-impedance matrices, Z, representing HOMOM and MLFMA, respectivelyFMAnd ZMFRespectively, the mutual impedance matrix between HOMOM and MLFMA, IMAnd IFFor unknown electromagnetic current coefficient, VMAnd VFVoltage matrices, HOMOM and MLFMA, respectively;
the HOMOM region directly solves the impedance matrix equation by LU decomposition, so that the problem of slow convergence or non-convergence is avoided, and the MLFMA region can only be solved by an iteration method;
considering that the solution methods of the basis functions and the matrix equations in the two regions are different, the matrix equations are conveniently solved in an iterative voltage mode, and the coupling effect between the two regions is calculated through the iterative voltage and is external iteration.
7. The method of claim 6, wherein the method comprises the following steps: the outer iteration is realized by modifying a voltage matrix, and the matrix equation (3) is rewritten as:
Figure FDA0003283104130000031
wherein
Figure FDA0003283104130000032
And
Figure FDA0003283104130000033
representing the correction to the voltage matrix at the i-th outer iteration, the matrix vector being multiplied
Figure FDA0003283104130000034
And
Figure FDA0003283104130000035
the method is realized by two steps: first calculating coupling near field, then checking the near field with corresponding weight function, and then obtaining
Figure FDA0003283104130000036
And
Figure FDA0003283104130000037
substituting equation (4) to obtain
Figure FDA0003283104130000038
And
Figure FDA0003283104130000039
judging whether convergence occurs or not through an equation (5), if not, continuing the iteration, and if so, stopping the iteration, wherein epsilon is an allowable error.
||Ii+1-Ii||2/||Ii||2＜ε (5)。
8. The method according to claim 7, wherein the method comprises the following steps: in the step (3.3), the step (c),
computing
Figure FDA00032831041300000310
Calculating near fields E and H on the surface of the MLFMA region, the near fields being generated by surface electromagnetic flows J and M of the HOMOM region, expressed as follows:
E(J,M)＝ηL(J)-K(M) (6)
Figure FDA00032831041300000311
wherein, the operators L and K are defined as follows:
Figure FDA0003283104130000041
Figure FDA0003283104130000042
wherein X represents an equivalent current J or an equivalent magnetic current M,
Figure FDA0003283104130000043
for the wave impedance of free space, the green function G (r, r') in free space is defined as follows:
Figure FDA0003283104130000044
where r' is the position vector of the source point and r is the position vector of the field point. Divergence operator
Figure FDA0003283104130000045
Acting on r', gradient operators
Figure FDA0003283104130000046
Acting on r, and applying the weight function w of the obtained near field and MLFMA regionm(m ═ 1,2, 3.) assay, yielding:
Figure FDA0003283104130000047
where α is the combining factor of the CFIE, η is the wave impedance in free space,
Figure FDA0003283104130000048
is the outer normal unit vector of the MLFMA region surface,
Figure FDA0003283104130000049
is calculated like
Figure FDA00032831041300000410
9. The method according to claim 8, wherein the method comprises the following steps: in the step (3.4), the step of,
the steps (3.2) and (3.3) are repeated to obtain the I meeting the precision requirementMAnd IFFrom IMAnd IFFurther, the scattered field and RCS of a complex structure can be obtained.
10. The method according to claim 9, wherein the method comprises the following steps:
ensuring the communication stability in the LU decomposition process, adopting a binary tree principal component selection strategy and considering both high performance and autonomous controllability; for a panel column A, selecting principal elements in a binary tree protocol mode, wherein each local decomposition is a node of the binary tree, each communication combination is a binary tree protocol, the local decomposition is a process for processing local data by a process, and no communication exists in the process; the communication combination is a process of combining two processes into one group and exchanging local decomposition results, and communication is concentrated in the process.
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