CN106446470B - A kind of non-uniform dielectric finite difference frequency domain method of efficient parallel - Google Patents
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Abstract
The present invention relates to a kind of non-uniform dielectric finite difference frequency domain methods of efficient parallel, include: S1, geometric shape, dimensional parameters and the medium parameter for obtaining inhomogeneous dielectric object；S2, region division is carried out to inhomogeneous dielectric object as multiple subdomains；S3, using Octree subdivision algorithm to carry out square volume mesh to each subdomain uniformly discrete, and defines electromagnetic current on square volume mesh；S4, frequency domain finite difference matrix equation is established on each subdomain, electromagnetic current matrix equation is established according to the boundary condition of each subdomain and excitation condition；S5, calculating is iterated to the electromagnetic current matrix equation on each subdomain using Gmres algorithm, and carries out the coupling of the boundary between adjacent subdomain；Iteration, until the electromagnetic current variation in each subdomain is respectively less than convergence threshold.The present invention realizes the accurate acquisition of the electromagnetic property data of inhomogeneous dielectric object, adaptable, calculate that simple, computational accuracy is high, is greatly expanded the electromagnetism computing capability of inhomogeneous dielectric object.
Description
Technical field
The present invention relates to the non-homogeneous of a kind of non-uniform dielectric finite difference frequency domain method, in particular to a kind of efficient parallel
Medium finite difference frequency domain method belongs to the quick computing technique of electromagnetic characteristic of scattering.
Background technique
In non-uniform dielectric body electromagnetic field inducing characteristic for electromagnetism stealth technology, antenna house design, inhale wave screen and set
Meter, underground objects detection technology and Electromagnetic Modeling of organism etc. all have great importance, and carry out inhomogeneous interphase electricity
The research of magnetic field induction characteristic is to understanding in Electromagnetic Wave Propagation mechanism in dielectric, dielectric electromagnetic response and non-uniform dielectric body
Electromagnet phenomenon etc. all there is important value.
The method of present analysis scattering non-uniform dielectric electromagnetic property mainly has method based on the differential equation and based on product
Divide the method for equation.Wherein the method based on integral equation is needed target entirety subdivision, and the matrix equation formed is full rank
, computing capability is strictly dependent on computer hardware resource, and even complexity also reaches O under efficient accelerating algorithm
(NlogN), it is unable to satisfy the demand of growing electrically large sizes.And the finite-difference algorithm based on the differential equation, it imitates
It is true to calculate in strict accordance with electromagnetic current Distribution Principle, electric current and magnetic current cross-distribution, and the matrix equation formed be it is sparse, passing through
Its computation complexity can reach O (N) after crossing Region Decomposition, have efficient computing capability.
Wang Wenbo, Xu Jin equality were published in the document on national microwave and millimeter wave proceeding in 2011 in 2011
In " being based on the quick analyzing three-dimensional inhomogeneous interphase scattering properties of improved VIE-MoM/MLFMA ", propose using improved
Quickly the multistage sub- three-dimensional non-uniform dielectric Electromagnetic Scattering Characteristics of technology solution are quickly analyzed for integral equation moment method and multilayer, are utilized
The dielectric property of SWG basic function unit improves the solution formula of the near field impedance element of traditional VIE-MoM/MLFMA, knot
Compress technique is closed, the calculation amount and memory requirements of analysis non-uniform dielectric material are reduced.But this method SWG basic function number with
Target size is that index power is incremented by three times, and impedance matrix is full rank, and computing capability is still limited, is not enough to carry out
Electrically large size object Analysis of Electromagnetic Character.
Document " the quickly analysis that Zhao Bo, Gong Shuxi, Wang Xing etc. were published on Xian Electronics Science and Technology University's journal in 2015
Inhomogeneous interphase is fastly with the algorithm of scattering properties " in, it proposes a kind of progressive waveform evaluation of utilization and solves non-homogeneous Jie
The algorithm of the Wide band scattering characteristic of matter target derives the higher derivative with computing impedance matrix and excitation vectors, then given
Dielectric (flux) density is unfolded in frequency point, is approached with pade and further spreads out bandwidth, to realize any in rapid Estimation frequency band
The dielectric (flux) density of frequency point obtains the Wide band scattering characteristic of inhomogeneous interphase.But this method is still the volume based on MoM point side
Journey solves, and computing capability is severely limited to computer hardware resource.
LiuJun, Zhao Zhi such as admire at document " the dispersive medium FDTD based on OpenMP that was published in electronics technology in 2015
Parallel Programming " analyze dispersive medium Fdtd Method model, and given point for unmagnetized plasma
Layer line recursive convolution algorithm, describes the basic model of OpenMP Parallel Design, and applies it to unmagnetized plasma
Calculating in.By the wave transparent property verification correctness of algorithm, parallel efficiency is 98% or more.But this method is base
In Model in Time Domain, computing capability is severely limited to target size, and algorithm stability is poor.
Summary of the invention
The purpose of the present invention is to provide a kind of non-uniform dielectric finite difference frequency domain methods of efficient parallel, are non-homogeneous
The accurate acquisitions of the electromagnetic property data of dielectric object provides technological means, it is adaptable, code migrating is high, it is simple to calculate,
Computational accuracy is high, is greatly expanded the electromagnetism computing capability of inhomogeneous dielectric object, is easy to Project Realization.
In order to achieve the above object, the present invention provides a kind of non-uniform dielectric finite difference frequency domain method of efficient parallel,
It comprises the steps of:
S1, geometric shape, dimensional parameters and the medium parameter that inhomogeneous dielectric object is obtained by mapping；
S2, inhomogeneous dielectric object progress region division is decomposed according to geometric shape, dimensional parameters and medium parameter
Multiple subdomains are formed, the electromagnetic parameter information of entire inhomogeneous dielectric object is constructed by the electromagnetic parameter on each subdomain；
S3, to each subdomain, be utilized respectively Octree subdivision algorithm and carry out subdivision, carried out just according to electromagnetic wave medium wavelength
Cube grid is uniformly discrete, and defines electromagnetic current on discrete obtained square volume mesh；
S4, according to electromagnetic field partial differential equation, frequency domain finite difference matrix equation is established on each subdomain, according to each
The boundary condition and excitation condition of subdomain establish electromagnetic current matrix equation；
S5, calculating is iterated to the electromagnetic current matrix equation on each subdomain using Gmres algorithm, on each subdomain
Iterative calculation result is the electromagnetic current induction field of each subdomain, and carries out the coupling of the boundary between adjacent subdomain；Repeat
Iterative calculation completes the frequency of entire inhomogeneous dielectric object until the electromagnetic current variation in each subdomain is respectively less than convergence threshold
The effective difference electromagnetism in domain calculates.
In the S1, the geometric shape of inhomogeneous dielectric object is cuboid；The medium parameter is respectively ε1=
3.24-j0.02 ε2=1.3-j0.2, ε3=4-j0.9.
In the S2, when inhomogeneous dielectric object is resolved into multiple subdomains, in each subdomain for being decomposed to form
Medium parameter is identical, and the subdivision length of each subdomain is medium wavelength.
In the S3, the square volume mesh in each subdomain is equally distributed, the square volume mesh in different subdomains
It need not be identical.
In the S3, to each subdomain, Octree subdivision algorithm use the discrete electromagnetic current of Yee cellular format, comprising with
Lower step:
S31, the maximum cuboid box for surrounding single subdomain profile is calculated, as father's layer cube；
S32, by described father's layer cube to 8 pieces of sublayer cubes are divided into, calculate the center of each sublayer cube
Angle between the vector and subdomain outside direction of minimum range and corresponding minimum range between subdomain profile；
If the minimum range between the center and subdomain profile of S33, each sublayer cube is less than current sublayer cube
Body side lengthTimes, or currently sublayer cube is located inside subdomain, then retains the sublayer cube, otherwise give up；
S34, using the sublayer cube retained in S33 as next round iteration father layer cube, repeat S32~S33,
Until the sublayer cube size currently retained reaches the size needs of discrete square volume mesh, then the sublayer currently retained is vertical
Cube can be used as the square volume mesh for defining electromagnetic current.
In the S3, incident electromagnetic wave frequency point is 1.0GHz, and the length of square volume mesh is the 1/15 of incident electromagnetic wave
Wavelength.
In the S4, comprising the following steps:
S41, according to frequency domain Maxwell (Maxwell) equation group, have:
Wherein, ε and μ is complex dielectric constant and magnetic conductivity respectively；Using square volume mesh to sub- domain carry out it is discrete after, it is right
The H answeredx、Hy、Hz、Ex、Ey、EzThe differential equation of each component are as follows:
It is S42, amount arrangement in field unknown on each square grid node is as follows:
[x1..., xN-1, xN]T；
Obtain following electromagnetic current Matrix division:
In the S5, calculating is iterated using electromagnetic current matrix equation of the Gmres algorithm to each subdomain, it is only necessary to benefit
Interative computation can be completed with a matrix vector multiplication, and the electromagnetic current iterative calculation in each subdomain is parallel.
In the S5, the convergence threshold of each subdomain is 0.05.
In conclusion the non-uniform dielectric finite difference frequency domain method of efficient parallel provided by the invention, solves existing skill
The problem of the high-speed simulation Modeling Calculation of inhomogeneous dielectric object electromagnetic property in art is the electromagnetic property of inhomogeneous dielectric object
The accurate acquisition of data provides technological means, and adaptable, code migrating height calculates simple, computational accuracy height, greatly opens up
The electromagnetism computing capability for having opened up inhomogeneous dielectric object, is easy to Project Realization.
Detailed description of the invention
Fig. 1 is the flow chart of the non-uniform dielectric finite difference frequency domain method of the efficient parallel in the present invention；
Fig. 2 is that the subdomain of the inhomogeneous dielectric object in the present invention divides schematic diagram；
Fig. 3 is to carry out the discrete schematic diagram of square volume mesh using Octree subdivision algorithm in the present invention；
Fig. 4 powers on the distribution schematic diagram of magnetic current for the square volume mesh in the present invention；
Fig. 5 is that the non-uniform dielectric in the present invention passes through the near-field scattering electric field value obtained after iteration convergence and conventional method
Contrast schematic diagram.
Specific embodiment
Below in conjunction with FIG. 1 to FIG. 5, the preferred embodiment that the present invention will be described in detail.
As shown in Figure 1, the non-uniform dielectric finite difference frequency domain method of efficient parallel of the present invention, includes following step
It is rapid:
S1, geometric shape, dimensional parameters and the medium parameter that inhomogeneous dielectric object is obtained by mapping；
S2, inhomogeneous dielectric object progress region division is decomposed according to geometric shape, dimensional parameters and medium parameter
Multiple subdomains are formed, the electromagnetic parameter information of entire inhomogeneous dielectric object is constructed by the electromagnetic parameter on each subdomain；
S3, to each subdomain, be utilized respectively Octree subdivision algorithm and carry out subdivision, carried out just according to electromagnetic wave medium wavelength
Cube grid is uniformly discrete, and defines electromagnetic current on discrete obtained square volume mesh；
S4, according to electromagnetic field partial differential equation, frequency domain finite difference matrix equation is established on each subdomain, according to each
The boundary condition and excitation condition of subdomain establish electromagnetic current matrix equation；
S5, it is changed using Gmres algorithm (broad sense minimum margin algorithm) to the electromagnetic current matrix equation on each subdomain
In generation, calculates, and the iterative calculation result on each subdomain is the electromagnetic current induction field of each subdomain, and carries out between adjacent subdomain
Boundary coupling；Repeat to iterate to calculate, until the electromagnetic current variation in each subdomain is respectively less than convergence threshold, complete entire
The effective difference electromagnetism of the frequency domain of inhomogeneous dielectric object calculates.
In the present embodiment, in the S1, the geometric shape of inhomogeneous dielectric object is cuboid, dimensional parameters be 3m ×
2m×1m；The medium parameter shares three groups, respectively ε1=3.24-j0.02, ε2=1.3-j0.2, ε3=4-j0.9.
In the S2, when inhomogeneous dielectric object is resolved into multiple subdomains, it need to guarantee that medium is joined in each subdomain
The size of several continuity and each subdomain is suitable；Under normal circumstances, the medium ginseng in each subdomain being decomposed to form
Number is identical, and the subdivision length of each subdomain is medium wavelength.In the present embodiment, as shown in Fig. 2, by non-uniform dielectric mesh
Mark is decomposed into E1, E2 and E3 totally 3 subdomains together with boundary.
In the S3, the square volume mesh in each subdomain is equally distributed, the square volume mesh in different subdomains
It need not be identical.
In the S3, as shown in figure 3, the core of Octree subdivision algorithm is constantly lookup cube to each subdomain
Positional relationship between body center and subzone boundaries, using the discrete electromagnetic current of Yee cellular format comprising the steps of:
S31, the maximum cuboid box for surrounding single subdomain profile is calculated, as father's layer cube；
S32, by described father's layer cube to 8 pieces of sublayer cubes are divided into, calculate the center of each sublayer cube
Angle between the vector and subdomain outside direction of minimum range and corresponding minimum range between subdomain profile；
If the minimum range between the center and subdomain profile of S33, each sublayer cube is less than current sublayer cube
Body side lengthTimes, or currently sublayer cube is located inside subdomain, then retains the sublayer cube, otherwise give up；
S34, using the sublayer cube retained in S33 as next round iteration father layer cube, repeat S32~S33,
Until the sublayer cube size currently retained reaches the size needs of discrete square volume mesh, then the sublayer currently retained is vertical
Cube can be used as the square volume mesh for defining electromagnetic current.
In the present embodiment, in the S3, set incident electromagnetic wave frequency point as 1.0GHz, incident angle be (theta,
Phi)=(0 °, 0 °) motivates for horizontal polarization；And the length of the square volume mesh is 1/15 wavelength of incident electromagnetic wave.
In the S3, electromagnetic current is defined on the square volume mesh obtained using Octree subdivision algorithm, such as Fig. 4 institute
Show, according to Theory of Electromagnetic Field, electric field node and magnetic field node be it is interlaced, electric field node be located at around mutually hangs down therewith
The center of straight magnetic field node, magnetic field node are also equally that magnetic field node is located at electric field node perpendicular around
Center.
In the S4, corresponding matrix equation is established using frequency domain finite difference algorithm, by solving on Yee cellular
Electromagnetic current induction coefficient obtains target induction field, comprising the following steps:
S41, according to frequency domain Maxwell (Maxwell) equation group, have:
Wherein, ε and μ is complex dielectric constant and magnetic conductivity respectively；Using square volume mesh to sub- domain carry out it is discrete after, it is right
The H answeredx、Hy、Hz、Ex、Ey、EzThe differential equation of each component are as follows:
It is S42, amount arrangement in field unknown on each square grid node is as follows:
[x1..., xN-1, xN]T；
Obtain following electromagnetic current Matrix division:
In the S5, Gmres algorithm is to solve for a kind of efficient iterative method of asymmetric high level matrix, and it was calculated
Journey largely can adapt to parallel computation；What it was used, which restarts skill and pretreatment skill, greatly improves
When the efficiency, especially each interative computation that matrix iteration solves, only makees a matrix vector and be multiplied, greatly improve calculating
Efficiency.
In the S5, to Asymmetric Electric magnetic current matrix equation Ax=b, the specific implementation steps are as follows:
S51, setting arbitrary initial solution x0, obtain surplus r0, note β=| | r0||2, v1=r0/ β, then have:
r0=b-Ax0；
S52, definition (m+1) × m rank matrixIf
S53, calculating:
If h is calculatedj+1,j=0, then m=j is set, and jump and execute S54；Otherwise, it calculates:
vj+1=wj/hj+1,j；
S54, solutionCalculate ym, and xm=x0+Vmym；
S55, the above-mentioned S51~S54 of circulation, can be obtained minimum margin function, realize and most preferably approach what is really solved.It should
It points out, the selection for restarting thresholding m is most important to the number of iterations, selects suitable m that can greatly improve iterative calculation efficiency.
The comparing result of obtained near-field scattering electric field value and conventional method after the iteration convergence of non-uniform dielectric by the method for the invention
As shown in Figure 5.
In the S5, calculating is iterated using electromagnetic current matrix equation of the Gmres algorithm to each subdomain, it is only necessary to benefit
Interative computation can be completed with the multiplication of matrix vector, and the electromagnetic current iterative calculation in each subdomain be can be parallel
, parallel efficiency reaches 98% or more.
In the present embodiment, in the S5, the convergence threshold of each subdomain is 0.05.
In conclusion the non-uniform dielectric finite difference frequency domain method of efficient parallel provided by the present invention, with existing skill
Art is compared, and is had the advantage that
1, using Subdomain method, it is convenient, fast to ensure that the electromagnetic field in each subdomain solves；Due to each subdomain
In electromagnetism Scattering Calculation can individually carry out, interactive quantity is less in parallel procedure, and parallel efficiency is higher；
2, subdivision is carried out to subdomain using the uniform Yee cellular of Octree subdivision algorithm, it is easy to accomplish without by it
His subdivision tool is convenient for the Automation Design；
3, the impedance matrix that frequency domain finite difference matrix equation is formed is sparse, and amount of storage is small, can reach higher
Computational efficiency.
It is discussed in detail although the contents of the present invention have passed through above preferred embodiment, but it should be appreciated that above-mentioned
Description is not considered as limitation of the present invention.After those skilled in the art have read above content, for of the invention
A variety of modifications and substitutions all will be apparent.Therefore, protection scope of the present invention should be limited to the appended claims.
Claims (7)
1. a kind of non-uniform dielectric finite difference frequency domain method of efficient parallel, characterized by comprising:
S1, geometric shape, dimensional parameters and the medium parameter that inhomogeneous dielectric object is obtained by mapping；
S2, inhomogeneous dielectric object progress region division is decomposed to form according to geometric shape, dimensional parameters and medium parameter
Multiple subdomains construct the electromagnetic parameter information of entire inhomogeneous dielectric object by the electromagnetic parameter on each subdomain；
S3, to each subdomain, be utilized respectively Octree subdivision algorithm and carry out subdivision, square is carried out according to electromagnetic wave medium wavelength
Grid is uniformly discrete, and defines electromagnetic current on discrete obtained square volume mesh；
S4, according to electromagnetic field partial differential equation, frequency domain finite difference matrix equation is established on each subdomain, according to each subdomain
Boundary condition and excitation condition establish electromagnetic current matrix equation；
S5, calculating is iterated to the electromagnetic current matrix equation on each subdomain using Gmres algorithm, the iteration on each subdomain
Calculated result is the electromagnetic current induction field of each subdomain, and carries out the coupling of the boundary between adjacent subdomain；Repeat iteration
It calculates, until the electromagnetic current variation in each subdomain is respectively less than convergence threshold, the frequency domain for completing entire inhomogeneous dielectric object has
Difference electromagnetism is imitated to calculate；
In the S3, to each subdomain, Octree subdivision algorithm uses the discrete electromagnetic current of Yee cellular format, includes following step
It is rapid:
S31, the maximum cuboid box for surrounding single subdomain profile is calculated, as father's layer cube；
S32, by described father's layer cube to 8 pieces of sublayer cubes are divided into, calculate center and the son of each sublayer cube
Minimum range between the profile of domain and the angle between the vector and subdomain outside direction of corresponding minimum range；
If the minimum range between the center and subdomain profile of S33, each sublayer cube is less than current sublayer cube side
LongTimes, or currently sublayer cube is located inside subdomain, then retains the sublayer cube, otherwise give up；
S34, using the sublayer cube retained in S33 as next round iteration father layer cube, repeat S32~S33, until
The sublayer cube size currently retained reaches the size needs of discrete square volume mesh, then the sublayer cube currently retained
It can be used as the square volume mesh for defining electromagnetic current；
In the S4, comprising the following steps:
S41, according to frequency domain Maxwell (Maxwell) equation group, have:
Wherein, ε and μ is complex dielectric constant and magnetic conductivity respectively；Using square volume mesh to sub- domain carry out it is discrete after, it is corresponding
Hx、Hy、Hz、Ex、Ey、EzThe differential equation of each component are as follows:
It is S42, amount arrangement in field unknown on each square grid node is as follows:
[x1..., xN-1, xN]T；
Obtain following electromagnetic current Matrix division:
2. the non-uniform dielectric finite difference frequency domain method of efficient parallel as described in claim 1, which is characterized in that described
In S1, the geometric shape of inhomogeneous dielectric object is cuboid；Medium parameter is respectively ε1=3.24-j0.02, ε2=1.3-
J0.2, ε3=4-j0.9.
3. the non-uniform dielectric finite difference frequency domain method of efficient parallel as claimed in claim 2, which is characterized in that described
In S2, when inhomogeneous dielectric object is resolved into multiple subdomains, the medium parameter in each subdomain being decomposed to form is identical
, and the subdivision length of each subdomain is medium wavelength.
4. the non-uniform dielectric finite difference frequency domain method of efficient parallel as claimed in claim 3, which is characterized in that described
In S3, the square volume mesh in each subdomain be it is equally distributed, the square volume mesh in different subdomains need not be identical.
5. the non-uniform dielectric finite difference frequency domain method of efficient parallel as claimed in claim 4, which is characterized in that described
In S3, incident electromagnetic wave frequency point is 1.0GHz, and the length of square volume mesh is 1/15 wavelength of incident electromagnetic wave.
6. the non-uniform dielectric finite difference frequency domain method of efficient parallel as claimed in claim 5, which is characterized in that described
In S5, calculating is iterated using electromagnetic current matrix equation of the Gmres algorithm to each subdomain, it is only necessary to utilize a matrix vector
Interative computation can be completed in multiplication, and the electromagnetic current iterative calculation in each subdomain is parallel.
7. the non-uniform dielectric finite difference frequency domain method of efficient parallel as claimed in claim 5, which is characterized in that described
In S5, the convergence threshold of each subdomain is 0.05.
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