CN108446471B - Mountain area electromagnetic field prediction technique based on three-dimensional moment method and two-dimentional Fast Multiple Method - Google Patents
Mountain area electromagnetic field prediction technique based on three-dimensional moment method and two-dimentional Fast Multiple Method Download PDFInfo
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Abstract
The mountain area electromagnetic field prediction technique based on three-dimensional moment method and two-dimentional Fast Multiple Method that the invention proposes a kind of, under the premise of being meant to ensure that computational accuracy, reduce computing resource consumption, and efficiently near field electromagnetic field distribution of the emulation mountain area under electromagnet source radiation event, realize step are as follows: establish mountain model；Obtain Gauss integration sample point coordinate；Construct fritter massif three-dimensional simulation model；Calculate the scattering electric field and fringe magnetic field of the scattering electric field and fringe magnetic field and magnetic distribution region to be predicted site at the incidence field excitation of massif D difference simulation model；Obtain in-field of the massif D difference simulation model in TE wave and when TM wave；Calculate the scattering electric field and fringe magnetic field of massif D difference simulation model region site to be predicted in TE wave；Calculate the scattering electric field and fringe magnetic field of massif D difference simulation model region site to be predicted in TM wave；Mountain three-dimensional model is obtained in site field distribution in region to be predicted and Distribution of Magnetic Field.
Description
Technical Field
The invention belongs to the technical field of electromagnetic fields and microwaves, relates to a mountainous area near-field electromagnetic field prediction method, and particularly relates to a mountainous area near-field electromagnetic field prediction method of a three-dimensional moment method mixed two-dimensional fast multipole algorithm, which can be used for providing reasonable suggestions for the erection of short-wave antennas and base stations.
Background
China is a multi-mountain country, and the mountain area accounts for 69.1 percent of the total national soil area. The mountainous area is more susceptible to various disasters, traffic interruption is often caused by the occurrence of the disasters, information transmission and command of emergency rescue and relief work can only depend on a communication system, and the research on the distribution of electromagnetic fields in the mountainous area has a particularly important significance on disaster prevention and reduction in the mountainous area.
The existing main method for detecting the near-field electromagnetic field in the mountainous area has field measurement and numerical simulation, wherein the field measurement refers to predicting the electromagnetic field distribution condition of the mountainous area in a measuring mode under the condition of short-wave antenna or base station radiation, firstly, the method cannot eliminate the interference of measuring personnel and a test probe to the electromagnetic field, and secondly, the method needs a large amount of manpower, material resources and financial resources and cannot meet the increasing requirements. The numerical simulation means that the distribution of the electromagnetic field in the mountainous area is simulated by using a computer according to a specific model, for example, a full wave method, namely a three-dimensional moment method (MoM) is combined with a high-performance computing technology to perform numerical calculation simulation, wherein the moment method is a method for discretizing a continuous equation into an algebraic equation set and is a classic electromagnetic field numerical simulation algorithm. In the prior art, when the mountain electromagnetic field is predicted, a mountain three-dimensional model is established, simulation parameters are set, a three-dimensional moment method is used for generating a dense matrix equation, a dense matrix equation solver is used for solving the dense matrix equation, and then an electric field and a magnetic field of a required point are solved, so that a large amount of time, memory and computing resources are consumed in the process, and when the electric size of the mountain three-dimensional model is increased, the time, the memory and the computing resources required by simulation are rapidly increased, so that the ever-increasing requirements cannot be met by adopting a computer cluster.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a mountainous area electromagnetic field prediction method based on a three-dimensional moment method and two-dimensional rapid multipole, and aims to reduce the consumption of computing resources and efficiently simulate the near-field electromagnetic field distribution of mountainous areas under the condition of electromagnetic source radiation on the premise of ensuring the computing precision.
The technical idea of the invention is that a concrete mountain model is obtained by a field measurement or geographic information system, a radiation source and a small mountain in a certain range with the radiation source as the center are integrally used as a new radiation source, three-dimensional modeling is used, a three-dimensional moment method is used for simulation calculation on the new radiation source, a mountain exceeding the new radiation source uses two-dimensional modeling according to a selected surface and uses two-dimensional fast multipole for solving, the key point of combination is that an incident field required by the two-dimensional fast multipole simulation is given by the three-dimensional moment method, and finally, a scattering field on the selected surface is given by the three-dimensional moment method and is superposed with a scattering field given by the two-dimensional fast multipole to obtain a final total field.
According to the technical idea, the technical scheme adopted by the invention comprises the following steps:
(1) building a mountain model:
(1a) obtaining mountain three-dimensional information and dielectric medium information by using a field measurement or geographic information system, constructing a mountain three-dimensional model, and constructing a small mountain three-dimensional model which is contained in a mountain and takes a radiation source as a center;
(1b) subtracting a small mountain three-dimensional model from the mountain three-dimensional model to obtain a mountain three-dimensional difference model, and cutting the mountain three-dimensional difference model through a preset plane where an electromagnetic field to be predicted is located to obtain a mountain two-dimensional difference model containing height;
(2) acquiring the Gauss integral sampling point coordinates required by excitation of an incident field of a mountain two-dimensional difference simulation model:
(2a) setting the frequency of a radiation source of the mountain two-dimensional difference model, adding the radiation source into the mountain two-dimensional difference model, and setting the dielectric constant, the conductivity and the permeability of the mountain two-dimensional difference model with the radiation source added to obtain a mountain two-dimensional difference simulation model;
(2b) pre-simulating the mountain two-dimensional difference simulation model to obtain Gaussian integral sampling point coordinates required by excitation of an incident field of the mountain two-dimensional difference simulation model;
(3) constructing a three-dimensional simulation model of the small mountain:
setting the frequency of a radiation source of the small mountain three-dimensional model, adding the radiation source into the small mountain three-dimensional model, and then setting the dielectric constant, the conductivity and the permeability of the small mountain three-dimensional model with the radiation source added to obtain a small mountain three-dimensional simulation model, wherein the frequency of the radiation source of the small mountain three-dimensional model is the same as the frequency of the radiation source of the mountain two-dimensional difference model, and the dielectric constant, the conductivity and the permeability of the small mountain three-dimensional model are the same as the dielectric constant, the conductivity and the permeability of the mountain two-dimensional difference model;
(4) calculating scattering electric field E at excitation position of incident field of mountain two-dimensional difference simulation model by using three-dimensional moment methodS-GAnd a scattered magnetic field HS-GAnd the scattered electric field E at the field point of the electromagnetic field distribution region to be predictedS-IAnd a scattered magnetic field HS-I：
(4a) Calculating an electromagnetic flow basis function coefficient vector X:
calculating an impedance matrix A and a voltage matrix B of a small mountain three-dimensional simulation model by using a three-dimensional moment method, constructing a dense matrix equation AX-B by using the impedance matrix A and the voltage matrix B, and solving the dense matrix equation to obtain an electromagnetic flow basis function coefficient vector X, wherein the electromagnetic flow basis function coefficient vector X is obtainedInAs a vector of current basis function coefficients, MnIs a magnetic flow basis function coefficient vector;
(4b) calculating current J and magnetic current M on each curved surface of the small mountain three-dimensional simulation model:
according to the vector of the electromagnetic flow basis function coefficientCalculating current J and magnetic current M on each curved surface of the small mountain three-dimensional simulation model;
(4c) calculating scattering electric field E on Gaussian integral sampling point coordinateS-GAnd a scattered magnetic field HS-GAnd scattering electric field E at field points of the electromagnetic field distribution region to be predicted in the small-mountain three-dimensional simulation modelS-IAnd a scattered magnetic field HS-I：
Calculating by adopting an integral equation through the current J and the magnetic current M on each curved surface in the small mountain three-dimensional simulation modelScattering electric field E on Gaussian integral sampling point coordinateS-GAnd a scattered magnetic field HS-GAnd scattering electric field E of the small mountain three-dimensional simulation model at the field point of the electromagnetic field distribution region to be predictedS-IAnd a scattered magnetic field HS-I；
(5) Obtaining an incident field in a TE wave and an incident field in a TM wave of a mountain two-dimensional difference simulation model:
(5a) using xoy plane as reference plane, and collecting scattered electric field ES-GExtracting x-direction component ExAnd y-direction component EyWhile simultaneously deriving from the scattered magnetic field HS-GExtracting z-direction component HzAnd E isx、EyAnd HzThe combination of (1) is set as an incident field when a mountain two-dimensional difference simulation model TE wave;
(5b) using xoy plane as reference plane, and collecting scattered electric field ES-GExtracting the z-direction component EzWhile simultaneously deriving from the scattered magnetic field HS-GExtracting x-direction component HxAnd y-direction component HyAnd E isz、HxAnd HyThe combination of (1) is set as an incident field of a mountain two-dimensional difference simulation model TM wave;
(6) calculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predicted by adopting a two-dimensional fast multipole algorithmS-TEAnd a scattered magnetic field HS-TE：
(6a) Calculating an electromagnetic flow basis function vector X when the incident field excitation type of the mountain two-dimensional difference simulation model is TE waveFTE：
Inputting the incident field of the TE wave obtained in the step (5a) into a two-dimensional fast multipole algorithm program to be used as the incident field of the mountain two-dimensional difference simulation model at the moment, and calculating an impedance matrix A of the mountain two-dimensional difference simulation model by using a two-dimensional fast multipole algorithmFTEAnd voltage matrix BFTEReuse of the impedance matrix AFTEAnd voltage matrix BFTEConstruction of matrix equation AFTE·XFTE＝BFTEThen solving the matrix equation to obtain the electromagnetic flow basis function coefficient vector XFTEWherein Is a vector of coefficients of a basis function of the current,is a magnetic flow basis function coefficient vector;
(6b) calculating the current J on each line section grid in the mountain two-dimensional difference simulation modelFTEAnd magnetic current MFTE：
According to the vector of the electromagnetic flow basis function coefficientCalculating the current J on each line section grid in the mountain two-dimensional difference simulation modelFTEAnd magnetic current MFTE；
(6c) Calculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predictedS-TEAnd a scattered magnetic field HS-TE：
Adopting an integral equation to simulate the current J on each line section grid in the mountain two-dimensional difference simulation modelFTEAnd magnetic current MFTECalculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predictedS-TEAnd a scattered magnetic field HS-TE；
(7) Calculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predicted by adopting a two-dimensional fast multipole algorithmS-TMAnd a scattered magnetic field HS-TM：
(7a) Calculating an electromagnetic flow basis function vector X when the incident field excitation type of the mountain two-dimensional difference simulation model is TM waveFTM：
Inputting the incident field of the TM wave obtained in the step (5b) into a two-dimensional fast multipole algorithm program to serve as the incident field of the mountain two-dimensional difference simulation model at the moment, and calculating an impedance matrix A of the mountain two-dimensional difference simulation model by using a two-dimensional fast multipole algorithmFTMAnd voltage matrix BFTMReuse of the impedance matrix AFTMAnd voltage matrix BFTMConstruction of matrix equation AFTM·XFTM＝BFTMThen solving the matrix equation to obtain the electromagnetic flow basis function coefficient vector XFTMWherein Is a vector of coefficients of a basis function of the current,is a magnetic flow basis function coefficient vector;
(7b) calculating the current J on each line section grid in the mountain two-dimensional difference simulation modelFTMAnd magnetic current MFTM：
According to electric field basis function coefficient vectorCalculating the current J on each line section grid in the mountain two-dimensional difference simulation modelFTMAnd magnetic current MFTM；
(7c) Calculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predictedS-TMAnd a scattered magnetic field HS-TM：
Adopting an integral equation to simulate the current J on each line section grid in the mountain two-dimensional difference simulation modelFTMAnd magnetic current MFTMCalculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predictedS-TMAnd a scattered magnetic field HS-TM；
(8) Obtaining the electric field distribution E of the mountain three-dimensional model at the field point of the region to be predictedTOTAnd magnetic field distribution HTOT：
Will ES-I、ES-TEAnd ES-TMSuperposing to obtain the electric field distribution E of the mountain three-dimensional model at the field point of the area to be predictedTOT：ETOT＝ES-I+ES-TE+ES-TMIs prepared from HS-I、HS-TEAnd HS-TMSuperposing to obtain the magnetic field distribution H of the mountain three-dimensional model at the field point of the region to be predictedTOT：HTOT＝HS-I+HS-TE+HS-TM。
Compared with the prior art, the invention has the following advantages:
the invention fully utilizes the precision of a three-dimensional moment method in processing complex targets and the capability of two-dimensional rapid multipole in processing ultra-large targets or environments; compared with the prior art, the method has the advantages of less consumption of computing resources and higher efficiency on the premise of ensuring the computing precision.
Drawings
FIG. 1 is a block diagram of an implementation flow of the present invention;
FIG. 2 is a three-dimensional model of a mountain of the present invention;
FIG. 3 is a three-dimensional model of a small mountain of the present invention;
FIG. 4 is a geometric relationship between a three-dimensional model of a hill and a three-dimensional model of a hill block according to the present invention;
FIG. 5 is a mountain two-dimensional difference model of the present invention including altitude;
FIG. 6 is a comparison of electric field results of the method of integrating and solving the mountain three-dimensional model obtained by the prior art, wherein E is the value in FIG. 6(a)yComparison of the results of the real part component of (1), FIG. 6(b) is EyComparing the results of the imaginary components;
FIG. 7 is a comparison of the global solution of the three-dimensional model of a mountain obtained using the prior art and the electric field results of the present invention, wherein FIG. 7(a) is EzComparison of the results of the real part component of (1), FIG. 7(b) is EzThe results of the imaginary components of (a) are compared.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, a method for predicting a mountain electromagnetic field based on a three-dimensional moment method and a two-dimensional fast multipole comprises the following steps:
step 1) building a mountain model:
step 1a) obtaining mountain three-dimensional information and dielectric medium information by using a field measurement or geographic information system, and constructing a mountain three-dimensional model by using software GID (graphic identification), wherein the position of the mountain three-dimensional model on a coordinate axis is an x axis as shown in figure 2: 1420m-2020m, y-axis: 1350m-1950m, z-axis: 45m-200m, and simultaneously constructing a small mountain three-dimensional model with (1720,1820,150) as the center, which is contained in the mountain, by using the software GID, wherein the position of the small mountain on the coordinate axis is the x axis as shown in FIG. 3: 1570m-1870m, y-axis: 1500m-1800m, z-axis: 71m-200m, wherein the relationship between the mountain model and the small mountain model is shown in figure 4, and the small mountain model is in the mountain model;
step 1b) subtracting a small mountain three-dimensional model from a mountain three-dimensional model by using boolean operation of software GID, where the boolean operation is a digital symbolic logic deduction method, including union, intersection, and subtraction, and is commonly used for processing graphs in three-dimensional modeling software to obtain a mountain three-dimensional difference model, and selecting x 1720m as a plane where an electromagnetic field to be predicted is located, cutting the mountain three-dimensional difference model to obtain a yz section of the mountain three-dimensional difference model at x 1720m, as shown in fig. 5, that is, a mountain two-dimensional difference model including height, selecting a point (1720,1820,150) to a point (1720,1820,270) on a plane at 1720m as an electromagnetic field distribution area point to be predicted, and the position of the mountain two-dimensional difference model is shown in fig. 5;
step 2) acquiring Gaussian integral sampling point coordinates required by excitation of an incident field of a mountain two-dimensional difference simulation model:
step 2a), setting the type of a radiation source of the mountain two-dimensional difference model as a point source, setting the coordinate of the radiation source as (1650,210) and the frequency of the radiation source as 10MHz, adding the radiation source into the mountain two-dimensional difference model, and setting the relative dielectric constant of the mountain two-dimensional difference model with the added radiation source as 4, the electrical conductivity as 0.001 and the relative magnetic conductivity as 1 to obtain a mountain two-dimensional difference simulation model;
step 2b) pre-simulating the mountain two-dimensional difference simulation model to obtain a Gaussian integral sampling point coordinate (y) required by excitation of an incident field of the mountain two-dimensional difference simulation modelk,zk) K represents the kth sample point;
pre-simulation refers to running an existing simulation model once and outputting a required value, and here refers to running a mountain two-dimensional difference simulation model once by using two-dimensional rapid multipole;
step 3), constructing a three-dimensional simulation model of the small mountain body:
setting the type of a radiation source of the small mountain three-dimensional model as a half-wave symmetrical oscillator, wherein the center coordinate is (1720,1650,210), the frequency is 10MHz, adding the radiation source into the small mountain three-dimensional model, and setting the relative dielectric constant of the small mountain three-dimensional model with the added radiation source as 4, the electrical conductivity as 0.001 and the relative magnetic conductivity as 1 to obtain the small mountain three-dimensional simulation model;
step 4) calculating a scattering electric field E at the excitation position of the incident field of the mountain two-dimensional difference simulation model by using a three-dimensional moment methodS-GAnd a scattered magnetic field HS-GAnd the scattered electric field E at the field point of the electromagnetic field distribution region to be predictedS-IAnd a scattered magnetic field HS-I：
Step 4a) calculating an electromagnetic flow basis function coefficient vector X:
calculating an impedance matrix A and a voltage matrix B of the small mountain three-dimensional simulation model by using a three-dimensional moment method, constructing a dense matrix equation AX (equal to B) by using the impedance matrix A and the voltage matrix B, and solving the dense matrix equation to obtain an electromagnetic flow basis function coefficient vector X;
step 4b), calculating current J and magnetic current M on each curved surface of the small mountain three-dimensional simulation model:
according to the vector of the electromagnetic flow basis function coefficient
Using the formula
Calculating the current J and the magnetic current M on each curved surface, wherein fn(r) is a basis function, η0Is the wave impedance in free space;
step (ii) of4c) Complementing the coordinates of the Gaussian integral sampling points obtained in the step 2) into three-dimensional coordinates according to the tangent plane, wherein the coordinates of the Gaussian integral sampling points obtained in the step 2) are two-dimensional coordinates, and the type of the coordinates required by the three-dimensional moment method is three-dimensional coordinates, so that the two-dimensional coordinates are complemented into the three-dimensional coordinates required by the three-dimensional moment method according to the cut plane, namely coordinates (y) in the three-dimensional coordinatesk,zk) The complement is (1720, y)k,zk)，
Using integral equations
Wherein J is the current on each curved surface, M is the magnetic current on each curved surface, J is the imaginary unit, k is the wave number in the medium space, eta0Is free space wave impedance, R' is the coordinates of a source point, R is the distance from a field point to the source point, and G (R) is a free space Green function;
calculating Gaussian integral sampling point coordinates (1720, y) through current J and magnetic current M on each curved surface in the small mountain three-dimensional simulation modelk,zk) Upper scattering electric field ES-GAnd a scattered magnetic field HS-GAnd scattering electric field E of the three-dimensional simulation model of the small mountain from point (1720,1820,150) to point (1720,1820,270)S-IAnd a scattered magnetic field HS-I；
Step 5) obtaining an incident field in a TE wave and an incident field in a TM wave of the mountain two-dimensional difference simulation model:
step 5a) with the xoy plane as the reference plane, from the scattered electric field ES-GExtracting x-direction component ExAnd the y-direction componentEyWhile simultaneously deriving from the scattered magnetic field HS-GExtracting z-direction component HzAnd E isx、EyAnd HzThe combination of (1) is set as an incident field when a mountain two-dimensional difference simulation model TE wave;
step 5b) using the xoy plane as a reference plane and scattering the electric field ES-GExtracting the z-direction component EzWhile simultaneously deriving from the scattered magnetic field HS-GExtracting x-direction component HxAnd y-direction component HyAnd E isz、HxAnd HyThe combination of (1) is set as an incident field of a mountain two-dimensional difference simulation model TM wave;
step 6) calculating the scattering electric field E of the mountain two-dimensional difference simulation model from point (1820,150) to point (1820,270) by adopting a two-dimensional fast multipole algorithmS-TEAnd a scattered magnetic field HS-TE：
Step 6a) calculating an electric field basis function vector X when the incident field excitation type of the mountain two-dimensional difference simulation model is TE waveFTE：
Inputting the incident field of the TE wave obtained in the step 5a) into a two-dimensional fast multipole algorithm program to be used as the incident field of the mountain two-dimensional difference simulation model at the moment, and calculating an impedance matrix A of the mountain two-dimensional difference simulation model by using a two-dimensional fast multipole algorithmFTEAnd voltage matrix BFTEReuse of the impedance matrix AFTEAnd voltage matrix BFTEConstruction of matrix equation AFTE·XFTE＝BFTEThen solving the matrix equation to obtain the electromagnetic flow basis function coefficient vector XFTE；
Step 6b) calculating the current J on each line section grid in the mountain two-dimensional difference simulation modelFTEAnd magnetic current MFTE：
According to the vector of the electromagnetic flow basis function coefficient
Using the formula
Calculating the current J on each line section gridFTEAnd magnetic current MFTE，Is a basis function, η0Is the wave impedance in free space;
step 6c) calculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predictedS-TEAnd a scattered magnetic field HS-TE：
Using integral equations
Wherein,JFTEfor the current on the grid of the line segments, MFTEIs the magnetic current on each line segment grid, j is an imaginary unit, k is the free space wave number, eta0Is free space wave impedance, rho' is the source point coordinate, rho is the field point coordinate,is a second class of zeroth order hank functions;
through the current J on each line section grid in the mountain two-dimensional difference simulation modelFTEAnd magnetic current MFTECalculating the scattering electric field E of the mountain two-dimensional difference simulation model from point (1820,150) to point (1820,270)S-TEAnd a scattered magnetic field HS-TE；
Step 7) calculating the scattering electric field E of the mountain two-dimensional difference simulation model from the point (1820,150) to the point (1820,270) by adopting a two-dimensional fast multipole algorithmS-TMAnd a scattered magnetic field HS-TM：
Step 7a) calculating an electromagnetic flow basis function vector X when the incident field excitation type of the mountain two-dimensional difference simulation model is TM waveFTM：
Inputting the incident field of the TM wave obtained in the step (5b) into a two-dimensional fast multipole algorithm program to serve as the incident field of the mountain two-dimensional difference simulation model at the moment, and calculating an impedance matrix A of the mountain two-dimensional difference simulation model by using a two-dimensional fast multipole algorithmFTMAnd voltage matrix BFTMReuse of the impedance matrix AFTMAnd voltage matrix BFTMConstruction of matrix equation AFTM·XFTM＝BFTMThen solving the matrix equation to obtain the electromagnetic flow basis function coefficient vector XFTM；
Step 7b) calculating the current J on each line section grid in the mountain two-dimensional difference simulation modelFTMAnd magnetic current MFTM：
According to electric field basis function coefficient vector
Using the formula
Calculating the current J on each line section gridFTMAnd magnetic current MFTMWherein Is a basis function, η0Is the wave impedance in free space;
step 7c) calculating the scattering electric field E of the mountain two-dimensional difference simulation model from point (1820,150) to point (1820,270)S-TMAnd a scattered magnetic field HS-TM：
Using integral equations
Wherein,JFTMfor the current on the grid of the line segments, MFTMIs the magnetic current on each line segment grid, j is an imaginary unit, k is the free space wave number, eta0Is free space wave impedance, rho' is the source point coordinate, rho is the field point coordinate,is a second class of zeroth order hank functions;
through the current J on each line section grid in the mountain two-dimensional difference simulation modelFTMAnd magnetic current MFTMCalculating the scattering electric field E of the mountain two-dimensional difference simulation model from point (1820,150) to point (1820,270)S-TMAnd a scattered magnetic field HS-TM；
Step 8) obtaining the electric field distribution E of the mountain three-dimensional model from point (1720,1820,150) to point (1720,1820,270)TOTAnd magnetic field distribution HTOT：
Original ES-TE、ES-TM、HS-TEAnd HS-TMThe scattering electric field and the scattering magnetic field of the mountain two-dimensional difference simulation model from the point (1820,150) to the point (1820,270) are obtained, and because the cut plane is a yz plane with x being 1720m, the scattering field is also the scattering field of the corresponding mountain three-dimensional model from the point (1720,1820,150) to the point (1720,1820,270); will ES-I、ES-TEAnd ES-TMThe superposition is carried out to obtain the electric field distribution E of the mountain three-dimensional model from the point (1720,1820,150) to the point (1720,1820,270)TOT：ETOT＝ES-I+ES-TE+ES-TMIs prepared from HS-I、HS-TEAnd HS-TMThe superposition is carried out to obtain the magnetic field distribution H of the mountain three-dimensional model from the point (1720,1820,150) to the point (1720,1820,270)TOT：HTOT＝HS-I+HS-TE+HS-TM。
The technical effects of the present invention are further described below in conjunction with simulation experiments:
1. simulation conditions and content
In the prior art, a computer cluster is used for calculating the distribution of an electric field and a magnetic field of a mountain three-dimensional simulation model from a point (1720,1820,150) to a point (1720,1820,270) by using a three-dimensional moment method, wherein the simulation parameter setting of the mountain three-dimensional simulation model is consistent with the simulation parameters of a small mountain three-dimensional model and is used for comparison and verification of the result of a combination method; the method comprises the steps that a computer cluster is used for calculating the distribution of an electric field and a magnetic field of a small mountain three-dimensional simulation model from a point (1720,1820,150) to a point (1720,1820,270) by using a three-dimensional moment method, and the electric field and the magnetic field of a Gaussian integral sampling point required by excitation of an incident field of a two-dimensional difference simulation model; and calculating the electric field and magnetic field distribution of the two-dimensional difference simulation model from point (1820,150) to point (1820,270) by using a computer and utilizing the two-dimensional fast multipole; each node is provided with two Xeon E5-269212 cores of a central processing unit 64GB DDR3 memory and a plurality of hard disks.
2. And (3) simulation result analysis:
the following table shows the comparison between the memory and CPU core count used and the calculation time in the prior art and the present invention, respectively, in the specific examples:
as can be seen from the data in the table above, the invention greatly reduces the computing resources and greatly improves the simulation efficiency;
referring to FIG. 6, FIGS. 6(a), 6(b) are the electric fields E on point (1720,1820,150) to point (1720,1820,270) for the present invention and the prior art, respectivelyyReal and imaginary components;
referring to FIG. 7, FIGS. 7(a), 7(b) are the electric fields E on point (1720,1820,150) to point (1720,1820,270) for the present invention and the prior art, respectivelyzReal and imaginary components;
as can be seen from fig. 6 and 7, the results of the present invention and the prior art are well matched, so the simulation verifies the accuracy of the present invention.
Claims (8)
1. A mountain area electromagnetic field prediction method based on a three-dimensional moment method and a two-dimensional fast multipole is characterized by comprising the following steps:
(1) building a mountain model:
(1a) obtaining mountain three-dimensional information and dielectric medium information by using a field measurement or geographic information system, constructing a mountain three-dimensional model, and constructing a small mountain three-dimensional model which is contained in a mountain and takes a radiation source as a center;
(1b) subtracting a small mountain three-dimensional model from the mountain three-dimensional model to obtain a mountain three-dimensional difference model, and cutting the mountain three-dimensional difference model through a preset plane where an electromagnetic field to be predicted is located to obtain a mountain two-dimensional difference model containing height;
(2) acquiring the Gauss integral sampling point coordinates required by excitation of an incident field of a mountain two-dimensional difference simulation model:
(2a) setting the frequency of a radiation source of the mountain two-dimensional difference model, adding the radiation source into the mountain two-dimensional difference model, and setting the dielectric constant, the conductivity and the permeability of the mountain two-dimensional difference model with the radiation source added to obtain a mountain two-dimensional difference simulation model;
(2b) pre-simulating the mountain two-dimensional difference simulation model to obtain Gaussian integral sampling point coordinates required by excitation of an incident field of the mountain two-dimensional difference simulation model;
(3) constructing a three-dimensional simulation model of the small mountain:
setting the frequency of a radiation source of the small mountain three-dimensional model, adding the radiation source into the small mountain three-dimensional model, and then setting the dielectric constant, the conductivity and the permeability of the small mountain three-dimensional model with the radiation source added to obtain a small mountain three-dimensional simulation model, wherein the frequency of the radiation source of the small mountain three-dimensional model is the same as the frequency of the radiation source of the mountain two-dimensional difference model, and the dielectric constant, the conductivity and the permeability of the small mountain three-dimensional model are the same as the dielectric constant, the conductivity and the permeability of the mountain two-dimensional difference model;
(4) calculating scattering electric field E at excitation position of incident field of mountain two-dimensional difference simulation model by using three-dimensional moment methodS-GAnd a scattered magnetic field HS-GAnd the scattered electric field E at the field point of the electromagnetic field distribution region to be predictedS-IAnd a scattered magnetic field HS-I：
(4a) Calculating an electromagnetic flow basis function coefficient vector X:
calculating an impedance matrix A and a voltage matrix B of a small mountain three-dimensional simulation model by using a three-dimensional moment method, constructing a dense matrix equation AX-B by using the impedance matrix A and the voltage matrix B, and solving the dense matrix equation to obtain an electromagnetic flow basis function coefficient vector X, wherein the electromagnetic flow basis function coefficient vector X is obtainedInAs a vector of current basis function coefficients, MnIs a magnetic flow basis function coefficient vector;
(4b) calculating current J and magnetic current M on each curved surface of the small mountain three-dimensional simulation model:
according to the vector of the electromagnetic flow basis function coefficientCalculating current J and magnetic current M on each curved surface of the small mountain three-dimensional simulation model;
(4c) calculating scattering electric field E on Gaussian integral sampling point coordinateS-GAnd a scattered magnetic field HS-GAnd scattering electric field E at field points of the electromagnetic field distribution region to be predicted in the small-mountain three-dimensional simulation modelS-IAnd a scattered magnetic field HS-I：
Calculating a scattering electric field E on a Gaussian integral sampling point coordinate through the current J and the magnetic current M on each curved surface in the small mountain three-dimensional simulation model by adopting an integral equationS-GAnd a scattered magnetic field HS-GAnd scattering electric field E of the small mountain three-dimensional simulation model at the field point of the electromagnetic field distribution region to be predictedS-IAnd a scattered magnetic field HS-I；
(5) Obtaining an incident field in a TE wave and an incident field in a TM wave of a mountain two-dimensional difference simulation model:
(5a) using xoy plane as reference plane, and collecting scattered electric field ES-GExtracting x-direction component ExAnd y-direction component EyWhile simultaneously deriving from the scattered magnetic field HS-GExtracting z-direction component HzAnd E isx、EyAnd HzThe combination of (1) is set as an incident field when a mountain two-dimensional difference simulation model TE wave;
(5b) using xoy plane as reference plane, and collecting scattered electric field ES-GExtracting the z-direction component EzWhile simultaneously deriving from the scattered magnetic field HS-GExtracting x-direction component HxAnd y-direction component HyAnd E isz、HxAnd HyThe combination of (1) is set as an incident field of a mountain two-dimensional difference simulation model TM wave;
(6) calculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predicted by adopting a two-dimensional fast multipole algorithmS-TEAnd a scattered magnetic field HS-TE：
(6a) Calculating an electromagnetic flow basis function vector X when the incident field excitation type of the mountain two-dimensional difference simulation model is TE waveFTE：
Inputting the incident field of the TE wave obtained in the step (5a) into a two-dimensional fast multipole algorithm program to be used as the incident field of the mountain two-dimensional difference simulation model at the moment, and calculating an impedance matrix A of the mountain two-dimensional difference simulation model by using a two-dimensional fast multipole algorithmFTEAnd voltage matrix BFTEReuse of the impedance matrix AFTEAnd voltage matrix BFTEConstruction of matrix equation AFTE·XFTE＝BFTEThen solving the matrix equation to obtain the electromagnetic flow basis function coefficient vector XFTEWherein Is a vector of coefficients of a basis function of the current,is a magnetic flow basis function coefficient vector;
(6b) calculating the current J on each line section grid in the mountain two-dimensional difference simulation modelFTEAnd magnetic current MFTE：
According to the vector of the electromagnetic flow basis function coefficientCalculating the current J on each line section grid in the mountain two-dimensional difference simulation modelFTEAnd magnetic current MFTE；
(6c) Calculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predictedS-TEAnd a scattered magnetic field HS-TE：
Adopting an integral equation to simulate the current J on each line section grid in the mountain two-dimensional difference simulation modelFTEAnd magnetic current MFTECalculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predictedS-TEAnd a scattered magnetic field HS-TE；
(7) Calculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predicted by adopting a two-dimensional fast multipole algorithmS-TMAnd a scattered magnetic field HS-TM：
(7a) Calculating an electromagnetic flow basis function vector X when the incident field excitation type of the mountain two-dimensional difference simulation model is TM waveFTM：
Inputting the incident field of the TM wave obtained in the step (5b) into a two-dimensional fast multipole algorithm program to serve as the incident field of the mountain two-dimensional difference simulation model at the moment, and calculating an impedance matrix A of the mountain two-dimensional difference simulation model by using a two-dimensional fast multipole algorithmFTMAnd voltage matrix BFTMReuse of the impedance matrix AFTMAnd voltage matrix BFTMConstruction of matrix equation AFTM·XFTM＝BFTMThen solving the matrix equation to obtain the electromagnetic flow basis function coefficient vector XFTMWherein Is a vector of coefficients of a basis function of the current,is a magnetic flow basis function coefficient vector;
(7b) calculating the current J on each line section grid in the mountain two-dimensional difference simulation modelFTMAnd magnetic current MFTM：
According to electric field basis function coefficient vectorCalculating the current J on each line section grid in the mountain two-dimensional difference simulation modelFTMAnd magnetic current MFTM；
(7c) Calculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predictedS-TMAnd a scattered magnetic field HS-TM：
Adopting an integral equation to simulate the current J on each line section grid in the mountain two-dimensional difference simulation modelFTMAnd magnetic current MFTMCalculating the scattering electric field E of the mountain two-dimensional difference simulation model at the field point of the region to be predictedS-TMAnd a scattered magnetic field HS-TM；
(8) Obtaining the electric field distribution E of the mountain three-dimensional model at the field point of the region to be predictedTOTAnd magnetic field distribution HTOT：
Will ES-I、ES-TEAnd ES-TMSuperposing to obtain the electric field distribution E of the mountain three-dimensional model at the field point of the area to be predictedTOT：ETOT＝ES-I+ES-TE+ES-TMIs prepared from HS-I、HS-TEAnd HS-TMSuperposing to obtain the magnetic field distribution H of the mountain three-dimensional model at the field point of the region to be predictedTOT：HTOT＝HS-I+HS-TE+HS-TM。
2. The method for predicting the electromagnetic field in the mountainous area based on the three-dimensional moment method and the two-dimensional fast multipole as claimed in claim 1, wherein the step (4a) of solving the dense matrix equation adopts a dense matrix solver.
3. The mountain area electromagnetic field prediction method based on the three-dimensional moment method and the two-dimensional fast multipole as claimed in claim 1, wherein the step (4b) of calculating the current J and the magnetic current M on each curved surface of the small mountain three-dimensional simulation model comprises the following calculation formulas:
wherein f isn(r) is a basis function, η0Is the wave impedance in free space, InAs a vector of current basis function coefficients, MnIs a magnetic flow basis function coefficient vector.
4. The method for predicting the electromagnetic field in the mountainous area based on the three-dimensional moment method and the two-dimensional fast multipole as claimed in claim 1, wherein the step (4c) of calculating the scattering electric field E on the Gaussian integral sampling point coordinatesS-GAnd a scattered magnetic field HS-GAnd the scattered electric field E at the field point of the electromagnetic field distribution region to be predictedS-IAnd a scattered magnetic field HS-IThe calculation formulas are respectively as follows:
wherein J is the current on each curved surface, M is the magnetic current on each curved surface, J is the imaginary unit, k is the wave number in the medium space, eta0For free space wave impedance, R 'is the source point coordinate, R is the field point to source point distance, and G (R) is the free space Green's function.
5. The method for predicting the electromagnetic field in the mountainous area based on the three-dimensional moment method and the two-dimensional fast multipole as claimed in claim 1, wherein the step (6b) of calculating the current J on each line segment grid in the two-dimensional difference simulation model of the mountainsFTEAnd magnetic current MFTEThe calculation formulas are respectively as follows:
wherein f isn (fm)(p) is the basis function, η0Is the wave impedance in free space,is a vector of coefficients of a basis function of the current,is a magnetic flow basis function coefficient vector.
6. The method for predicting the electromagnetic field in the mountainous area based on the three-dimensional moment method and the two-dimensional fast multipole as claimed in claim 1, wherein the step (6c) of calculating the scattering electric field E of the two-dimensional difference simulation model of the mountains at the field point of the area to be predictedS-TEAnd a scattered magnetic field HS-TEThe calculation formulas are respectively as follows:
wherein,JFTEfor the current on the grid of the line segments, MFTEIs the magnetic current on each line segment grid, j is an imaginary unit, k is the free space wave number, eta0Is free space wave impedance, rho' is the source point coordinate, rho is the field point coordinate,is a second class of zeroth-order hank functions.
7. The method for predicting the electromagnetic field in the mountainous area based on the three-dimensional moment method and the two-dimensional fast multipole as claimed in claim 1, wherein the step (7b) of calculating the current J on each line segment grid in the two-dimensional difference simulation model of the mountainsFTMAnd magnetic current MFTMThe calculation formulas are respectively as follows:
wherein f isn (fm)(p) is the basis function, η0Is the wave impedance in free space,is a vector of coefficients of a basis function of the current,is made of magnetismA vector of flow basis function coefficients.
8. The method for predicting the electromagnetic field in the mountainous area based on the three-dimensional moment method and the two-dimensional fast multipole as claimed in claim 1, wherein the step (7c) of calculating the scattering electric field E of the two-dimensional difference simulation model of the mountains at the field point of the area to be predictedS-TMAnd a scattered magnetic field HS-TMThe calculation formulas are respectively as follows:
wherein,JFTMfor the current on the grid of the line segments, MFTMIs the magnetic current on each line segment grid, j is an imaginary unit, k is the free space wave number, eta0Is free space wave impedance, rho' is the source point coordinate, rho is the field point coordinate,is a second class of zeroth-order hank functions.
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