CN113158517A - CN-FDTD simulation method and device based on system matrix combination and related components - Google Patents

CN-FDTD simulation method and device based on system matrix combination and related components Download PDF

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CN113158517A
CN113158517A CN202110350679.7A CN202110350679A CN113158517A CN 113158517 A CN113158517 A CN 113158517A CN 202110350679 A CN202110350679 A CN 202110350679A CN 113158517 A CN113158517 A CN 113158517A
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冯乃星
张玉贤
汪国平
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Shenzhen University
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Abstract

The invention discloses a CN-FDTD simulation method, a device, computer equipment and a storage medium based on system matrix combination, wherein the method comprises the following steps: respectively establishing an electromagnetic parameter distribution model and a 3D geometric model for a material to be simulated; assigning corresponding electromagnetic material properties to the 3D geometric model; setting corresponding initial conditions and boundary conditions; combining the initial condition and the boundary condition, and subdividing the 3D geometric model by utilizing a uniform grid; obliquely incident plane electromagnetic waves to the split 3D geometric model; and recording each time step of the three-dimensional time domain electromagnetic field quantity in the simulation calculation process through a simulation calculation process based on a CN-FDTD method combined by a system matrix, and acquiring the three-dimensional frequency domain electromagnetic field quantity by adopting discrete Fourier transform to realize a three-dimensional full-wave electromagnetic simulation process. The embodiment of the invention can quickly acquire the three-dimensional time domain electromagnetic field quantity distribution and realize corresponding accurate simulation of lower-frequency electromagnetic problems.

Description

CN-FDTD simulation method and device based on system matrix combination and related components
Technical Field
The invention relates to the technical field of an electromagnetic wave time domain finite difference method, in particular to a CN-FDTD simulation method, a device and related components based on system matrix combination.
Background
Electromagnetic scattering is a natural phenomenon that occurs at any time, such as a dazzling aurora, a sky blue, a red sunset, and the like. Finite Difference Time Domain (FDTD) has been used as an important tool for electromagnetic scattering research and has been deeply introduced into various electromagnetic problems. Electromagnetic scattering is a progressive process in time. One of the greatest advantages of the finite difference time domain method is that far-field variations of electromagnetic scattering at different frequency points can be obtained with time-domain broadband pulses. Far-field distribution information of radar scattering cross section (RCS) can be obtained using the FDTD method.
It is well known that FDTD is traditionally subject to Courant-Friedrichs-Lewy (CFL) stability conditions. In order to break through the condition limitation of CFL, an alternating direction implicit (ADI-) FDTD method is proposed in 1999, and a set of ADI-FDTD based on the iterative theory of a system matrix, which is called as a system combining (SC-) ADI-FDTD method for short, is reestablished in 2019, so that the time domain electromagnetic calculation process is further accelerated. In 2004, the numerical discrete format of Crank-Nicolson (CN, a finite difference method) was also applied to the CFL stability condition breaking through the FDTD method, which is collectively called CN-FDTD, but the implementation method has only stayed on the current technical level.
Therefore, how to completely construct a system-integrated CN-FDTD method (SC-CN-FDTD) through an iterative theory of a system matrix so as to effectively solve the specific problem of three-dimensional electromagnetic scattering on the premise of sufficient spatial sampling rate is a problem to be solved by those skilled in the art.
Disclosure of Invention
The embodiment of the invention provides a CN-FDTD simulation method, a CN-FDTD simulation device and related components based on system matrix combination, and aims to improve the simulation precision of three-dimensional electromagnetic scattering.
In a first aspect, an embodiment of the present invention provides a CN-FDTD simulation method based on system matrix combination, including:
respectively establishing an electromagnetic parameter distribution model and a 3D geometric model for a material to be simulated;
assigning corresponding electromagnetic material properties to the 3D geometric model based on the electromagnetic parameter distribution model;
setting corresponding initial conditions and boundary conditions based on the 3D geometric model;
combining the initial condition and the boundary condition, and utilizing a uniform grid to divide the 3D geometric model;
utilizing the plane electromagnetic wave to obliquely enter the subdivided 3D geometric model to obtain the distribution condition of the three-dimensional time domain electromagnetic field quantity;
and recording each time step of the three-dimensional time domain electromagnetic field quantity in the simulation calculation process through a simulation calculation process based on a CN-FDTD method combined by a system matrix, and acquiring the three-dimensional frequency domain electromagnetic field quantity by adopting discrete Fourier transform to realize a three-dimensional full-wave electromagnetic simulation process.
In a second aspect, an embodiment of the present invention provides a CN-FDTD simulation apparatus based on system matrix combination, including:
the device comprises a first establishing unit, a second establishing unit and a third establishing unit, wherein the first establishing unit is used for respectively establishing an electromagnetic parameter distribution model and a 3D geometric model for a material to be simulated;
an attribute assigning unit, configured to assign corresponding electromagnetic material attributes to the 3D geometric model based on the electromagnetic parameter distribution model;
a condition setting unit for setting corresponding initial conditions and boundary conditions based on the 3D geometric model;
the subdivision unit is used for dividing the 3D geometric model by utilizing a uniform grid in combination with the initial condition and the boundary condition;
the distribution acquisition unit is used for acquiring the distribution condition of the three-dimensional time domain electromagnetic field quantity by utilizing the oblique incidence of the plane electromagnetic wave to the subdivided 3D geometric model;
and the simulation realization unit is used for recording each time step of the three-dimensional time domain electromagnetic field quantity in the simulation calculation process through the simulation calculation process of a CN-FDTD method based on system matrix combination, and acquiring the three-dimensional frequency domain electromagnetic field quantity by adopting discrete Fourier transform to realize the three-dimensional full-wave electromagnetic simulation process.
In a third aspect, an embodiment of the present invention provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor, when executing the computer program, implements the CN-FDTD simulation method based on system matrix combination according to the first aspect.
In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the CN-FDTD simulation method based on system matrix combination according to the first aspect is implemented.
The embodiment of the invention provides a CN-FDTD simulation method, a device, computer equipment and a storage medium based on system matrix combination, wherein the method comprises the following steps: respectively establishing an electromagnetic parameter distribution model and a 3D geometric model for a material to be simulated; assigning corresponding electromagnetic material properties to the 3D geometric model based on the electromagnetic parameter distribution model; setting corresponding initial conditions and boundary conditions based on the 3D geometric model; combining the initial condition and the boundary condition, and subdividing the 3D geometric model by utilizing a uniform grid; utilizing the plane electromagnetic wave to be obliquely incident to the subdivided 3D geometric model to obtain the distribution condition of the three-dimensional time domain electromagnetic field quantity; and recording each time step of the three-dimensional time domain electromagnetic field quantity in the simulation calculation process through a simulation calculation process based on a CN-FDTD method combined by a system matrix, and acquiring the three-dimensional frequency domain electromagnetic field quantity by adopting discrete Fourier transform to realize a three-dimensional full-wave electromagnetic simulation process. According to the embodiment of the invention, the three-dimensional time domain electromagnetic field quantity distribution can be rapidly obtained by establishing the 3D geometric model and subdividing and obliquely projecting the 3D geometric model and the plane electromagnetic wave, namely, the time domain field, the frequency domain field and the far field information distribution of electromagnetic scattering can be rapidly obtained, and the corresponding accurate simulation of the electromagnetic problem with lower frequency can be realized based on a CN-FDTD method combined with a system matrix.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a schematic flow diagram of a CN-FDTD simulation method based on system matrix combination according to an embodiment of the present invention;
fig. 2 is a system structure diagram of a CN-FDTD simulation method based on system matrix combination according to an embodiment of the present invention;
fig. 3 is a structural model diagram of a planar electromagnetic wave oblique incidence 3D geometric model in a CN-FDTD simulation method based on system matrix combination according to an embodiment of the present invention;
FIG. 4 is a time domain electric field intensity E at the center of the structural model diagram shown in FIG. 3yA comparative graph of (a);
FIG. 5a and FIG. 5b are the electric field intensity E in the frequency domain at the center of the structural model diagram of FIG. 3yReal part versus imaginary part of graph;
fig. 6a, fig. 6b and fig. 6c are schematic diagrams of radar scattering cross-section distributions in the xOy, xOz and yOz directions of the structural model diagram of fig. 3, respectively;
fig. 7 is a schematic block diagram of a CN-FDTD simulation apparatus based on system matrix combination according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without any inventive step, are within the scope of the present invention.
It will be understood that the terms "comprises" and/or "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.
Referring to fig. 1, fig. 1 is a schematic flow chart of a CN-FDTD simulation method based on system matrix combination according to an embodiment of the present invention, which specifically includes: steps S101 to S106.
S101, respectively establishing an electromagnetic parameter distribution model and a 3D geometric model for a material to be simulated;
s102, endowing the 3D geometric model with corresponding electromagnetic material properties based on the electromagnetic parameter distribution model;
s103, setting corresponding initial conditions and boundary conditions based on the 3D geometric model;
s104, dividing the 3D geometric model by utilizing a uniform grid in combination with the initial condition and the boundary condition;
s105, obtaining the distribution condition of the three-dimensional time domain electromagnetic field quantity by utilizing the oblique incidence of the plane electromagnetic wave to the split 3D geometric model;
s106, recording each time step of the three-dimensional time domain electromagnetic field quantity in the simulation calculation process through a simulation calculation process based on a CN-FDTD method combined by a system matrix, and acquiring the three-dimensional frequency domain electromagnetic field quantity by adopting discrete Fourier transform to realize a three-dimensional full-wave electromagnetic simulation process.
In this embodiment, an electromagnetic parameter distribution model and a 3D geometric model of a multilayer spherical model are established for a material to be simulated, and corresponding electromagnetic material attributes, initial conditions, and boundary conditions are given. And (3) carrying out initialization subdivision on the multilayer spherical model (namely the 3D geometric model) by using the uniform grid as a background unit. And then, the plane electromagnetic wave is obliquely incident to the 3D geometric model to obtain the distribution condition of the three-dimensional time domain electromagnetic field quantity, then, the three-dimensional time domain electromagnetic field quantity is recorded in each time step through the simulation calculation process of a CN-FDTD method based on system matrix combination, and the three-dimensional frequency domain electromagnetic field quantity is obtained by adopting discrete Fourier transform, so that the three-dimensional full-wave electromagnetic simulation process can be realized.
According to the embodiment, the time domain field, the frequency domain field and the far field information distribution of electromagnetic scattering can be rapidly acquired, and corresponding accurate simulation can be realized on low-frequency electromagnetic problems.
In an embodiment, the electromagnetic material properties comprise permittivity, permeability, conductivity.
In this embodiment, when the electromagnetic material attribute is given to the 3D geometric model based on the electromagnetic parameter distribution model, specifically, a dielectric constant attribute, a magnetic permeability attribute, an electric conductivity attribute, and the like may be given to the 3D geometric model. Of course, in order to enrich the 3D geometric model, it is also possible to assign more electromagnetic parameter distribution models thereto, such as magnetic field strength and magnetic susceptibility, and so on.
In one embodiment, the step S104 includes:
based on the initial condition, carrying out initialization subdivision on the 3D geometric model by using a uniform grid;
and taking the boundary condition as a calculation truncation boundary of the subdivided 3D geometric model.
In this embodiment, the initial condition is used in the process of building the 3D geometric model, and the boundary condition is used as a truncation boundary in the subsequent calculation process.
In one embodiment, the step S105 includes:
taking the plane electromagnetic wave as an excitation source, and performing radiation calculation on the subdivided 3D geometric model;
and generating electromagnetic absorption and electromagnetic scattering phenomena on the split 3D geometric model of the planar electromagnetic wave so as to obtain the distribution condition of the three-dimensional time domain electromagnetic field quantity.
In this embodiment, when the planar electromagnetic wave is obliquely incident to the subdivided 3D geometric model, the planar electromagnetic wave is used as an excitation source to perform radiation calculation on the subdivided 3D geometric model, and electromagnetic absorption, electromagnetic scattering and other phenomena are generated on the 3D geometric model by the planar electromagnetic wave, so that the distribution condition of the corresponding three-dimensional time domain electromagnetic field quantity can be obtained in the radiation calculation process.
In one embodiment, the step S106 includes:
determining the antisymmetric tensor C of the electromagnetic wave through a Maxwell rotation equation system:
Figure BDA0003002298880000061
and combining the antisymmetric tensor C, and obtaining a system matrix by using a CN discrete method in the time direction:
Figure BDA0003002298880000062
Figure BDA0003002298880000063
in the formula (I), the compound is shown in the specification,
Figure BDA0003002298880000064
and En+1Is an uncertain variable at time step n +1,
Figure BDA0003002298880000065
and EnIs a known variable at the nth time step;
decomposing the antisymmetric tensor C into a first differential tensor A and a second differential tensor B, wherein C is A-B:
Figure BDA0003002298880000066
and according to the first differential tensor A and the second differential tensor B, unfolding the CN-FDTD:
(CHEA-CHEB)En+1+Hn+1/2＝CHHHn-1/2-(CHEA-CHEB)En
En+1-(CEHA-CEHB)Hn+1/2＝CEEEn+(CEHA-CEHB)Hn-1/2；
and combining the expansion of the CN-FDTD to obtain a unified formula of the system matrix:
(I6×6-P)(I6×6-Q)un+1＝(R6×6+P+Q+PQ)un
in the formula I6×6R, P, Q respectively represent 6 × 6 identity matrixes, unIs represented by the electric field strength EnAnd magnetic field strength
Figure BDA0003002298880000067
N-th time step of formation, un+1Is represented by the electric field strength En+1And the intensity of the magnetic field
Figure BDA0003002298880000068
The (n + 1) th time step;
and carrying out simulation calculation by using a unified formula of the system matrix, and recording each time step of the three-dimensional time domain electromagnetic field quantity in the simulation calculation process.
In this embodiment, when the numerical calculation of the time domain electromagnetic field is adopted, the necessary conditions of the electromagnetic wave can be better represented by using maxwell rotation equation system:
Figure BDA0003002298880000069
Figure BDA00030022988800000610
in the formula, vectors E and H respectively represent electric field intensity and magnetic field intensity, and medium parameters epsilon, mu and sigmaeAnd σmThe tensor can be well represented, representing permittivity, permeability, conductivity and equivalent magnetic loss, respectively. Calculator
Figure BDA0003002298880000071
The specific features that represent the spatially varying relationship can be expressed as the antisymmetric tensor C:
Figure BDA0003002298880000072
using the Crank-Nicolson discretization method in the time direction, the maxwell rotation equation set can be expressed as follows:
Figure BDA0003002298880000073
Figure BDA0003002298880000074
wherein the iteration matrixes can be respectively expressed as
CHH＝(μΔt-1+0.5σm)-1(μΔt-1-0.5σm)
CHEC＝0.5CHEC＝0.5(μΔt-1+0.5σm)-1C
CEE＝(εΔt-1+0.5σe)-1(εΔt-1-0.5σe)
CEHC＝0.5CEHC＝0.5(εΔt-1+0.5σe)-1C
As can be seen,
Figure BDA0003002298880000075
and En+1Is an uncertain variable of a new time step, and
Figure BDA0003002298880000076
and EnIs a known variable for the current time step. Thus, the expression for CN-FDTD can be as follows:
Figure BDA0003002298880000077
Figure BDA0003002298880000078
further, the antisymmetric tensor C can be decomposed into two different tensors and expressed as: c is A-B;
wherein the differential tensor can be expressed as:
Figure BDA0003002298880000079
wherein
Figure BDA00030022988800000710
Representing a differential operator in a certain spatial direction.
Therefore, the expansion processing of the expression of the CN-FDTD results in:
(CHEA-CHEB)En+1+Hn+1/2＝CHHHn-12-(CHEA-CHEB)En
En+1-(CEHA-CEHB)Hn+1/2＝CEEEn+(CEHA-CEHB)Hn-1/2
so far, in conjunction with fig. 2, in conjunction with the above expansion, one can obtain:
(I6×6-P-Q)un+1＝(R6×6+P+Q)un
in the formula I6×6Representing a 6 × 6 identity matrix, the other 6 × 6 matrices are as followsThe following steps:
Figure BDA00030022988800000711
the vector u formed by the electric field strength E and the magnetic field strength H is represented as:
Figure BDA00030022988800000712
further finishing to obtain:
(I6×6-P)(I6×6-Q)un+1＝(R6×6+P+Q+PQ)un+PQ(un+1-un)
wherein PQ (u)n+1-un) As a high-order infinite item, since there is enough time sampling rate in the numerical calculation, it can be defined as zero, so the expression of the CN-FDTD (i.e. the unified formula of the system matrix of the joint CN-FDTD) can be rewritten as:
(I6×6-P)(I6×6-Q)un+1＝(R6×6+P+Q+PQ)un
it can be seen that the system matrix (SC) combining scheme is incorporated into the CN-FDTD method, namely, SC-CN-FDTD, which can represent the whole calculation process by a system diagram, as shown in fig. 2. After the preprocessing shown by the dashed box in fig. 2, the repeated vector PQu at each time step can be effectively avoidedn。
In an embodiment, the CN-FDTD simulation method based on system matrix combination further includes:
importing the 3D geometric model after subdivision into a simulation calculation process of a CN-FDTD method based on system matrix combination;
and performing time domain electromagnetic scattering calculation on the subdivided 3D geometric model by utilizing the simulation calculation process.
In this embodiment, after the 3D geometric model is initially subdivided according to the uniform grid, the obtained 3D geometric model is a discretized 3D geometric model, and the discretized 3D geometric model is imported into a computation process of SC-CN-FDTD (i.e., the CN-FDTD method based on system matrix combination), so that time-domain electromagnetic scattering computation can be directly performed on the discretized 3D geometric model by using a simulation computation process.
In an embodiment, the performing time-domain electromagnetic scattering calculation on the subdivided 3D geometric model by using the simulation calculation process includes:
vector u in the system matrixnSeparation into electric field intensity EnAnd the intensity of the magnetic field
Figure BDA0003002298880000084
Determining a vector v from the system matrixnWherein v isn＝(R6×6+P+Q+PQ)un；
For vector vnPerforming expansion processing, and combining the system matrix to obtain a tri-diagonal matrix phi1＝I3×3-CEHACHEB；
And performing time domain electromagnetic scattering calculation on the subdivided 3D geometric model by using the three-diagonal matrix.
In this embodiment, in the process of performing time-domain electromagnetic scattering calculation on the discretized 3D geometric model by using the simulation calculation process, the matrix pseudo code of the nth time step in the SC-CN-FDTD method is represented as follows:
the vector u is re-split into the electric field strength E and the magnetic field strength H, followed by the vector QunCan be expressed as:
Figure BDA0003002298880000081
Figure BDA0003002298880000082
further, the vector v may be expanded as:
Figure BDA0003002298880000083
Figure BDA0003002298880000091
will be provided with
Figure BDA0003002298880000092
Performing development treatment:
Figure BDA0003002298880000093
taking into account implicit terms
Figure BDA0003002298880000094
It is possible to obtain:
Figure BDA0003002298880000095
Figure BDA0003002298880000096
wherein the tri-diagonal matrix is represented as Φ1＝I3×3-CEHACHEB。
Further, the same processing mode is used for solving the problem
Figure BDA0003002298880000097
It is possible to obtain:
Figure BDA0003002298880000098
consider the implicit term as En+1It is possible to obtain:
Figure BDA0003002298880000099
Figure BDA00030022988800000910
wherein the tri-diagonal matrix is represented as Φ2＝I3×3-CEHBCHEA。
And further realizing efficient time domain electromagnetic scattering calculation according to the iterative process of the SC-CN-FDTD method.
In a specific embodiment, in order to perform numerical verification between the CN-FDTD simulation method based on system matrix combination and the conventional FDTD method provided in the embodiments of the present invention, a multilayer sphere model with different electromagnetic parameters shown in fig. 3 is combined, where a circle center is point in fig. 3 and an incident angle θ is an angle of incidenceinc＝80°，
Figure RE-GDA00030840139100000910
On four-layer spheres with radii of 100mm, 75mm, 50mm, 20mm and relative dielectric constants of 4, 9, 16, 25, respectively, a maximum frequency of 0.1GHz and a spatial separation Δ w of 5.0mm are initialized, respectively, from the outside to the inside. The entire grid number is (77 × 77 × 77) in the x, y, and z directions. In the multilayer sphere model, the maximum CFL factor s can be obtained when the minimum spatial sampling density is 120PPWmax9.4298. Compared with the conventional FDTD with the CFL factor s being 1, the method provided by the present embodiment has the CFL factors s being 1, 5 and smaxNear field E at observation point (0,0,0)yThe time domain field results are plotted as shown in FIG. 4, near field EyThe frequency domain field results are plotted as shown in fig. 5a and 5b, and in the plane polar coordinate system of xOy, xOz and yOz, as shown in fig. 6a, 6b and 6c, the 0.1GHz radar scattering cross section of the far field can be displayed by the CFL factor s ═ smaxTo (3).
In another embodiment, a computer performance ratio of the CN-FDTD simulation method based on system matrix combination provided in the embodiment of the present invention is shown in table 1, and it is obvious that the CFL factor is smaxWhen the frequency is 9.4298, SC-CN-FDTD can be superior to the computer execution efficiency.
Figure BDA0003002298880000101
TABLE 1
Fig. 7 is a schematic block diagram of a CN-FDTD simulation apparatus 700 based on system matrix combination according to an embodiment of the present invention, where the apparatus 700 includes:
the first establishing unit 701 is used for respectively establishing an electromagnetic parameter distribution model and a 3D geometric model for a material to be simulated;
an attribute assigning unit 702 for assigning a corresponding electromagnetic material attribute to the 3D geometric model based on the electromagnetic parameter distribution model;
a condition setting unit 703, configured to set corresponding initial conditions and boundary conditions based on the 3D geometric model;
a subdivision unit 704, configured to divide the 3D geometric model by using a uniform mesh in combination with the initial condition and the boundary condition;
the distribution acquisition unit 705 is configured to acquire the distribution of the three-dimensional time domain electromagnetic field quantity by using the 3D geometric model after the planar electromagnetic wave is obliquely incident to the subdivision;
the simulation implementation unit 706 is configured to record each time step of the three-dimensional time domain electromagnetic field quantity in the simulation calculation process through a simulation calculation process based on a CN-FDTD method combined by a system matrix, and obtain a three-dimensional frequency domain electromagnetic field quantity by using a discrete fourier transform, so as to implement a three-dimensional full-wave electromagnetic simulation process.
In an embodiment, the electromagnetic material properties comprise permittivity, permeability, conductivity.
In an embodiment, the dividing unit 704 includes:
the initialization subdivision unit is used for performing initialization subdivision on the 3D geometric model by using a uniform grid based on the initial condition;
and the boundary setting unit is used for taking the boundary condition as a calculation truncation boundary of the subdivided 3D geometric model.
In an embodiment, the distribution obtaining unit 705 includes:
the radiation calculation unit is used for performing radiation calculation on the split 3D geometric model by taking the plane electromagnetic wave as an excitation source;
and the phenomenon generation unit is used for generating electromagnetic absorption and electromagnetic scattering phenomena on the split 3D geometric model of the planar electromagnetic wave so as to acquire the distribution condition of the three-dimensional time domain electromagnetic field quantity.
In an embodiment, the simulation implementation unit 706 includes:
the antisymmetric tensor determining unit is used for determining the antisymmetric tensor C of the electromagnetic wave through a Maxwell rotation equation set:
Figure BDA0003002298880000111
a combining unit, configured to combine the antisymmetric tensor C and obtain a system matrix by using a CN discretization method in a time direction:
Figure BDA0003002298880000112
Figure BDA0003002298880000113
in the formula (I), the compound is shown in the specification,
Figure BDA0003002298880000114
and En+1Is an uncertain variable at time step n +1,
Figure BDA0003002298880000115
and EnIs a known variable at the nth time step;
a decomposition unit configured to decompose the antisymmetric tensor C into a first differential tensor A and a second differential tensor B, where C is A-B:
Figure BDA0003002298880000116
a matrix expansion unit configured to expand the CN-FDTD according to the first differential tensor a and the second differential tensor B:
(CHEA-CHEB)En+1+Hn+1/2＝CHHHn-1/2-(CHEA-CHEB)En
En+1-(CEHA-CEHB)Hn+1/2＝CEEEn+(CEHA-CEHB)Hn-1/2；
a combination unit, configured to combine the CN-FDTD expansion to obtain a unified formula of the system matrix:
(I6×6-P)(I6×6-Q)un+1＝(R6×6+P+Q+PQ)un
in the formula I6×6R, P, Q respectively represent 6 × 6 identity matrixes, unIs represented by the electric field strength EnAnd magnetic field strength
Figure BDA0003002298880000117
N-th time step of formation, un+1Is represented by the electric field strength En+1And the intensity of the magnetic field
Figure BDA0003002298880000118
The (n + 1) th time step;
and the recording unit is used for carrying out simulation calculation by utilizing the unified formula of the system matrix and recording each time step of the three-dimensional time domain electromagnetic field quantity in the simulation calculation process.
In an embodiment, the simulation apparatus 700 further includes:
the importing unit is used for importing the split 3D geometric model into a simulation calculation process of a CN-FDTD method based on system matrix combination;
and the first time domain electromagnetic scattering calculation is used for performing time domain electromagnetic scattering calculation on the subdivided 3D geometric model by utilizing the simulation calculation process.
In an embodiment, the first time domain electromagnetic scattering calculation comprises:
a separation unit for separating the vectors u in the system matrixnSeparation into electric field intensity EnAnd the intensity of the magnetic field
Figure BDA0003002298880000121
A vector determination unit for determining a vector v from the system matrixnWherein v isn＝(R6×6+P+Q+PQ)un；
A vector expansion unit for expanding the vector vnsPerforming expansion processing, and combining the system matrix to obtain a tri-diagonal matrix phi1＝I3×3-CEHACHEB；
And calculating the second time domain electromagnetic scattering, which is used for performing time domain electromagnetic scattering calculation on the subdivided 3D geometric model by using the three diagonal matrixes.
Since the embodiment of the apparatus portion and the embodiment of the method portion correspond to each other, please refer to the description of the embodiment of the method portion for the embodiment of the apparatus portion, which is not repeated here.
Embodiments of the present invention also provide a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed, the steps provided by the above embodiments can be implemented. The storage medium may include: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
The embodiment of the present invention further provides a computer device, which may include a memory and a processor, where the memory stores a computer program, and the processor may implement the steps provided in the foregoing embodiments when calling the computer program in the memory. Of course, the computer device may also include various network interfaces, power supplies, and the like.
The embodiments in the specification are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the method disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description. It should be noted that, for those skilled in the art, without departing from the principle of the present application, several improvements and modifications can be made to the present application, and these improvements and modifications also fall into the protection scope of the claims of the present application.
It is further noted that, in the present specification, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.

Claims (10)

1. A CN-FDTD simulation method based on system matrix combination is characterized by comprising the following steps:
respectively establishing an electromagnetic parameter distribution model and a 3D geometric model for a material to be simulated;
assigning corresponding electromagnetic material properties to the 3D geometric model based on the electromagnetic parameter distribution model;
setting corresponding initial conditions and boundary conditions based on the 3D geometric model;
combining the initial condition and the boundary condition, and subdividing the 3D geometric model by utilizing a uniform grid;
utilizing the plane electromagnetic wave to obliquely enter the subdivided 3D geometric model to obtain the distribution condition of the three-dimensional time domain electromagnetic field quantity;
and recording each time step of the three-dimensional time domain electromagnetic field quantity in the simulation calculation process through a simulation calculation process based on a CN-FDTD method combined by a system matrix, and acquiring the three-dimensional frequency domain electromagnetic field quantity by adopting discrete Fourier transform to realize a three-dimensional full-wave electromagnetic simulation process.
2. The system matrix integration based CN-FDTD simulation method according to claim 1, wherein the electromagnetic material properties comprise permittivity, permeability, conductivity.
3. The system matrix combination-based CN-FDTD simulation method according to claim 1, wherein the combination of the initial condition and the boundary condition and the subdivision of the 3D geometric model by using a uniform grid comprises:
based on the initial condition, carrying out initialization subdivision on the 3D geometric model by using a uniform grid;
and taking the boundary condition as a calculation truncation boundary of the subdivided 3D geometric model.
4. The CN-FDTD simulation method based on system matrix combination according to claim 1, wherein the obtaining of the distribution of the three-dimensional time domain electromagnetic field quantity by using the oblique incidence of the planar electromagnetic wave to the subdivided 3D geometric model comprises:
taking the plane electromagnetic wave as an excitation source, and performing radiation calculation on the subdivided 3D geometric model;
and generating electromagnetic absorption and electromagnetic scattering phenomena on the split 3D geometric model of the planar electromagnetic wave so as to obtain the distribution condition of the three-dimensional time domain electromagnetic field quantity.
5. The system matrix combination based CN-FDTD simulation method according to claim 1, wherein the recording of the three-dimensional time domain electromagnetic field quantity at each time step in the simulation calculation process through the simulation calculation process of the system matrix combination based CN-FDTD method comprises:
determining the antisymmetric tensor C of the electromagnetic wave through a Maxwell rotation equation system:
Figure FDA0003002298870000021
and combining the antisymmetric tensor C, and obtaining a system matrix by using a CN discrete method in the time direction:
Figure FDA0003002298870000022
Figure FDA0003002298870000023
in the formula (I), the compound is shown in the specification,
Figure FDA0003002298870000024
and En+1Is an uncertain variable at time step n +1,
Figure FDA0003002298870000025
and EnIs a known variable at the nth time step;
decomposing the antisymmetric tensor C into a first differential tensor A and a second differential tensor B, wherein C is A-B:
Figure FDA0003002298870000026
and according to the first differential tensor A and the second differential tensor B, unfolding the CN-FDTD:
(CHEA-CHEB)En+1+Hn+1/2＝CHHHn-1/2-(CHEA-CHEB)En
En+1-(CEHA-CEHB)Hn+1/2＝CEEEn+(CEHA-CEHB)Hn-1/2；
and combining the expansion of the CN-FDTD to obtain a unified formula of the system matrix:
(I6×6-P)(I6×6-Q)un+1＝(R6×6+P+Q+PQ)un
in the formula I6×6R, P, Q respectively represent 6 × 6 identity matrixes, unIs represented by the electric field strength EnAnd the intensity of the magnetic field
Figure FDA0003002298870000027
N-th time step of formation, un+1Is represented by the electric field strength En+1And the intensity of the magnetic field
Figure FDA0003002298870000028
The (n + 1) th time step;
and carrying out simulation calculation by using a unified formula of the system matrix, and recording each time step of the three-dimensional time domain electromagnetic field quantity in the simulation calculation process.
6. The system matrix combination-based CN-FDTD simulation method according to claim 5, characterized in that it further comprises:
importing the 3D geometric model after subdivision into a simulation calculation process of a CN-FDTD method based on system matrix combination;
and performing time domain electromagnetic scattering calculation on the subdivided 3D geometric model by utilizing the simulation calculation process.
7. The CN-FDTD simulation method based on system matrix combination according to claim 6, wherein the performing time domain electromagnetic scattering calculation on the subdivided 3D geometric model by using the simulation calculation process comprises:
vector u in the system matrixnSeparation into electric field intensity EnAnd the intensity of the magnetic field
Figure FDA0003002298870000031
Determining a vector v from the system matrixnWherein v isn＝(R6×6+P+Q+PQ)un；
For vector vnPerforming expansion processing, and combining the system matrix to obtain a tri-diagonal matrix phi1＝I3×3-CEHACHEB；
And performing time domain electromagnetic scattering calculation on the subdivided 3D geometric model by using the three-diagonal matrix.
8. A CN-FDTD simulation device based on system matrix combination is characterized by comprising:
the device comprises a first establishing unit, a second establishing unit and a third establishing unit, wherein the first establishing unit is used for respectively establishing an electromagnetic parameter distribution model and a 3D geometric model for a material to be simulated;
an attribute assigning unit, configured to assign corresponding electromagnetic material attributes to the 3D geometric model based on the electromagnetic parameter distribution model;
a condition setting unit for setting corresponding initial conditions and boundary conditions based on the 3D geometric model;
the subdivision unit is used for dividing the 3D geometric model by utilizing a uniform grid in combination with the initial condition and the boundary condition;
the distribution acquisition unit is used for acquiring the distribution condition of the three-dimensional time domain electromagnetic field quantity by utilizing the oblique incidence of the plane electromagnetic wave to the subdivided 3D geometric model;
and the simulation realization unit is used for recording each time step of the three-dimensional time domain electromagnetic field quantity in the simulation calculation process through the simulation calculation process of a CN-FDTD method based on system matrix combination, and acquiring the three-dimensional frequency domain electromagnetic field quantity by adopting discrete Fourier transform to realize the three-dimensional full-wave electromagnetic simulation process.
9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the CN-FDTD simulation method based on system matrix combination according to any one of claims 1 to 7 when executing the computer program.
10. A computer-readable storage medium, characterized in that the computer-readable storage medium has stored thereon a computer program which, when being executed by a processor, implements the system matrix bonding based CN-FDTD simulation method according to any one of claims 1 to 7.
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