CN111460593B - Method and system for determining electromagnetic component of spatial domain - Google Patents
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Abstract
The invention relates to a method and a system for determining electromagnetic components in a spatial domain. The method comprises the following steps: deducing an electromagnetic numerical value stability condition by adopting a octyl time domain finite difference method; determining an expansion factor according to the electromagnetic numerical value stability condition; determining the value range of the expansion factor; defining a low-pass filter according to the value range; and filtering the spatial electromagnetic field component according to the low-pass filter to obtain the filtered spatial electromagnetic field component. The invention can improve the computational simulation efficiency of determining the electromagnetic component by the octyl time domain finite difference method.
Description
Technical Field
The invention relates to the field of determination of spatial domain electromagnetic components, in particular to a method and a system for determining spatial domain electromagnetic components.
Background
The rapid development of nanotechnology has led to the increasingly shrinking structure sizes of modern integrated circuits and nanometer components, and the research and processing technology of novel materials has entered into the nanometer era, and it is very tedious and difficult to perform various performance tests by means of experiments, so that the research of accurate and efficient numerical calculation methods is an important subject of modern nanometer device modeling and optimization. Computational electromagnetism is an emerging leading-edge interdisciplinary subject in recent years, and is a combination of an electromagnetic field theory and a numerical method based on a computer, and plays an important role in the fields of modeling, simulation, optimization, design and the like of modern electronic equipment. Electromagnetism is essentially a simulation subject, models and simulates according to the current cognitive range and actual requirements, then predicts and discovers new scientific phenomena, widens the research range of multiple subject fields and leads new research directions. At present, computational electromagnetism has become an important subject indispensable for relevant research and development in the subject fields of medicine, optics, communication, integrated circuits, materials and the like. The calculation methods of electromagnetic problems are mainly divided into two categories: the analytic method is generally to establish a mathematical physical equation describing the electromagnetic problem and then solve the problem by adopting a conventional mathematical method. The analytic method can obtain an accurate calculation result and can be used as a standard solution to check the correctness of the approximation method and the numerical method. However, if the analysis object includes a complicated structure and boundary conditions, it is difficult to obtain a specific analytical expression. Compared with an analytical method, the numerical method has higher flexibility and can process models with complex geometric shapes and material characteristics. In addition, the numerical method also provides conditions for the development and design of software and hardware. The frequency domain numerical method has a dominant position in the field of computational electromagnetism, however, with the increasing complexity and the increasing range of the problems, the time domain method has been gradually found to have some excellent characteristics in calculating and analyzing some electromagnetic problems. For example, for a structure containing a plurality of material compositions and a plurality of fine holes, slits, cavities and the like, simulation based on a frequency domain method is often clumsy, and the computational efficiency needs to be improved. Due to the rapid development of computer technology, time-domain algorithms have been widely researched and developed. The time domain algorithm improves the analysis capability of people on transient electromagnetic calculation with the broadband characteristic, so that the occurrence process of some electromagnetic phenomena can be observed more visually and vividly, and the understanding of the electromagnetic problems is deepened. In recent years, the sinc algorithm based on the Hamiltonian system is widely researched and applied in the field of time domain electromagnetic calculation. By keeping the octane structure of the whole numerical system, the octane time domain finite difference (SFDTD) algorithm shows some excellent performances which are not possessed by a non-octane method when solving the electromagnetic problem, such as the characteristics of late stability, accuracy, lower numerical dispersion error and the like. However, the explicit SFDTD method is conditionally stable, and the time step is limited by the size of the mesh, which is an electromagnetic structure and characteristic material that needs to be finely meshed for simulation, and the accuracy advantage of the SFDTD cannot compensate the disadvantage of the SFDTD on the computational efficiency.
Disclosure of Invention
The invention aims to provide a method and a system for determining a spatial domain electromagnetic component, which can improve the computational simulation efficiency of determining the electromagnetic component by a octyl time domain finite difference method.
In order to achieve the purpose, the invention provides the following scheme:
a method of spatial domain electromagnetic component determination, comprising:
deducing an electromagnetic numerical value stability condition by adopting a octyl time domain finite difference method;
determining an expansion factor according to the electromagnetic numerical value stability condition;
determining the value range of the expansion factor;
defining a low-pass filter according to the value range;
and filtering the spatial electromagnetic field component according to the low-pass filter to obtain the filtered spatial electromagnetic field component.
Optionally, the determining an expansion factor according to the electromagnetic numerical stability condition specifically includes:
expanding the stability condition of the electromagnetic numerical value through high-frequency filtering processing to obtain an expanded time step;
acquiring a time step before expansion;
and determining the expansion multiple of the time step length according to the expanded time step length and the time step length before expansion, wherein the expansion multiple is an expansion factor.
Optionally, the determining the value range of the expansion factor specifically includes:
analyzing numerical dispersion errors of the sine-time domain finite difference method in different numerical wave number ranges;
and determining the value range of the expansion factors in different wave number ranges according to the numerical dispersion error.
Optionally, the filtering the spatial electromagnetic field component according to the low-pass filter to obtain the filtered spatial electromagnetic field component specifically includes:
performing space frequency domain transformation on the space electromagnetic field component to obtain a space frequency domain electromagnetic component;
obtaining a space frequency domain electromagnetic component according to the low-pass filter and the space frequency domain electromagnetic component;
and carrying out inverse space frequency domain transformation on the space frequency domain electromagnetic component to obtain the filtered space frequency domain electromagnetic component.
A spatial domain electromagnetic component determination system, comprising:
the stability condition determining module is used for deducing an electromagnetic numerical value stability condition by adopting a octyl time domain finite difference method;
the expansion factor determining module is used for determining an expansion factor according to the electromagnetic value stability condition;
a value range determining module, configured to determine a value range of the expansion factor;
a low-pass filter definition module used for defining a low-pass filter according to the value range;
and the filtering processing module is used for carrying out filtering processing on the spatial electromagnetic field component according to the low-pass filter to obtain the filtered spatial electromagnetic field component.
Optionally, the expansion factor determining module specifically includes:
the extended time step determining unit is used for extending the electromagnetic value stability condition through high-frequency filtering processing to obtain an extended time step;
a pre-expansion time step determining unit, configured to obtain a pre-expansion time step;
and the expansion factor determining unit is used for determining the expansion multiple of the time step length according to the time step length after the expansion and the time step length before the expansion, wherein the expansion multiple is an expansion factor.
Optionally, the value range determining module specifically includes:
the dispersion error determining unit is used for analyzing numerical dispersion errors of the sine-time domain finite difference method in different numerical wave number ranges;
and the value range determining unit is used for determining the value ranges of the expansion factors in different wave number ranges according to the numerical dispersion error.
Optionally, the filtering processing module specifically includes:
the spatial frequency domain transformation unit is used for carrying out spatial frequency domain transformation on the spatial electromagnetic field component to obtain a spatial frequency domain electromagnetic component;
the filtering unit is used for obtaining a space frequency domain electromagnetic component according to the low-pass filter and the space frequency domain electromagnetic component;
and the inverse spatial frequency domain transformation unit is used for performing inverse spatial frequency domain transformation on the spatial frequency domain electromagnetic component to obtain the filtered spatial frequency domain electromagnetic component.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
1. the invention can realize the expansion of the stability condition of the SFDTD method only by adopting spatial filtering processing, does not need complex formula derivation compared with the implicit high-order FDTD algorithm, and greatly simplifies the application difficulty of the high-order implicit unconditional stability algorithm.
2. The invention is suitable for analyzing electromagnetic materials and structures with fine structures or needing high grid resolution, so that the stability condition of the invention is higher, and the calculation advantage is further expanded.
3. The invention has higher calculation efficiency and simultaneously ensures the calculation precision.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a method for determining a spatial domain electromagnetic component according to the present invention;
FIG. 2 is
By theta +>
Variations inThe amplitude distribution map of (a);
in FIG. 3, for values of θ = π/12 and φ = π/12, ω Δ/c follows
A graph of the variation;
FIG. 4 is a spatial frequency domain information distribution plot of spatial electromagnetic field components under one-dimensional to three-dimensional conditions;
FIG. 5 is a diagram of a pattern distribution of a two-dimensional metal cavity calculated using an SFDTD method and an SF-SFDTD method with different time step lengths;
FIG. 6 is a schematic diagram of a three-dimensional metal cavity calculated by an SFDTD method and an SF-SFDTD method with different time step lengths;
FIG. 7 is the non-correlation coefficients of the first eight resonant frequency points calculated by the SFDTD method and the SF-SFDTD method;
FIG. 8 is a schematic diagram of a simulation of a dielectric waveguide model;
FIG. 9 is a comparison graph of the reflection coefficient results calculated using the RCWA method, the SFDTD method, and the SF-SFDTD method with different time steps;
fig. 10 is a block diagram of a spatial domain electromagnetic component determination system of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for determining a spatial domain electromagnetic component, which can improve the computational simulation efficiency of determining the electromagnetic component by a octyl time domain finite difference method.
In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, the present invention is described in detail with reference to the accompanying drawings and the detailed description thereof.
In order to efficiently and accurately research the statistical change rule of the electromagnetic scattering property of the random material with a fine structure and uncertain electromagnetic parameters, the invention combines a spatial filtering method with the traditional SFDTD method and solves the problems of cavity resonance and waveguide transmission by using a spatial filtering sine time domain finite difference method (SF-SFDTD) with expandable stability conditions. According to the invention, a result very close to the traditional SFDTD can be obtained through less time domain iterative solution, and the simulation accuracy is also ensured while the calculation efficiency of the original method is greatly improved.
FIG. 1 is a flow chart of a method for determining electromagnetic components in the spatial domain according to the present invention. As shown in fig. 1, a method for determining an electromagnetic component in a spatial domain includes:
step 101: and deducing the stability condition of the electromagnetic numerical value by adopting a octyl time domain finite difference method.
A numerical stability condition formula is deduced according to a discrete equation of a traditional sine time domain finite difference (SFDTD) method, and then high-frequency components influencing the numerical stability of the SFDTD method are subjected to spatial filtering treatment, namely, a condition that only low-frequency components in space are reserved is substituted into the traditional stability condition formula to obtain a new stability condition formula. The new stability condition formula shows that the stability condition of the SFDTD method can be further expanded through high-frequency filtering treatment, namely the value range of the time step can be further expanded, the expansion multiple is defined as an expansion factor CE, and the CE value depends on the ratio of the grid size to the minimum working wavelength.
The trace of the stability matrix S of the sine time domain finite algorithm is:
the satisfied stability condition is that | tr (S) | is less than or equal to 2.
Wherein,
is obtained by | tr (S) | is less than or equal to 2
Make->
The following can be obtained:
-4≤g 1 (-x)+g 2 (-x)+g 3 (-x)+g 4 (-x)≤0 (2)
(g l coefficient (c): g = [ 1.00.0833333333333333330.002638563229860.000026634757910 =])
The range of the function independent variable obtained by the solution is
Wherein:
order to
And Δ x = Δ y = Δ z = Δ, available:
in setting the Q function
Stability of the kushin algorithm:
assuming that the wave number in each direction is limited to a maximum wave number (k) max ) Within the range, i.e.:
substituting the formula (8) into the formula (5) to obtain
Order to
N represents the number of grids in which a minimum wavelength is split, in general N.gtoreq.10, and therefore ≥ R>
The following can be obtained:
step 102: determining an expansion factor according to the electromagnetic numerical value stability condition, specifically comprising:
and expanding the stability condition of the electromagnetic numerical value through high-frequency filtering treatment to obtain the expanded time step length.
And acquiring the time step before expansion.
And determining the expansion multiple of the time step length according to the expanded time step length and the time step length before expansion, wherein the expansion multiple is an expansion factor.
FIG. 2 is
By theta +>
As can be seen from fig. 2, the function Q is equal to θ =0.304 pi,
an extreme value is obtained. (Q can take any value from 0 to pi/10. The value of Q only changes the value of the extreme value of the Q function, does not change the position of the extreme point of Q, but only needs to know the position of the maximum value, because when the SFDTD method is applied to simulate different models, Q is a changed value), theta =0.304 pi, \\ is used for changing the value of the maximum value>
And k max Substituting =2q into equation (9) to obtain: />
From the formula (6):
CE denotes the fold of expansion of the stability of the conventional SFDTD method, i.e. the expansion factor.
Step 103: determining the value range of the expansion factor, specifically including:
and analyzing the numerical dispersion error of the sine time domain finite difference method in different numerical wave number ranges.
And determining the value range of the expansion factors in different wave number ranges according to the numerical dispersion error.
The stability of the SFDTD method cannot be expanded without limit, that is, the value of the CE cannot be infinite, because a larger time step affects the numerical calculation accuracy of the SFDTD method, the reasonable value range of the CE needs to be determined according to the numerical calculation accuracy. As can be seen from the equations (13) and (14), the value range of CE is limited by k max The influence of the value of delta, when the SFDTD method needs to be deduced about k max The numerical dispersion curve of Delta is compared with the analytic solution, and k is analyzed max Influence of the value range of delta on the numerical dispersion error of the SFDTD method (numerical dispersion error: difference between the dispersion curve of the numerical method and the dispersion curve of the analytical solution), and finding the maximum k meeting the calculation precision max Value of Δ, k max Substituting the delta value into the formula (13) to obtain the maximum value range of the CE meeting the calculation precision.
The dispersion equation for the SFDTD method can be described as:
wherein the form of Q (θ, φ) is given in equation (10) above, let
From equation (7) it is known that: in the three-dimensional SFDTD method, delta t is less than or equal to 0.7431 delta/c 0 Therefore, R is less than or equal to 0.7431. (15) substituting equation (14) yields the following equation:
in FIG. 3, ω Δ/c follows θ = π/12 and φ = π/12
A graph of the variation (similar results can be obtained when theta and phi are equal to other values). As can be seen from FIG. 3, when R.ltoreq.0.7431 (R1, R2, R3) and ≦ H>
In time, the SFDTD method has almost the same dispersion property as the analytical solution, and the remaining portion deviates greatly from the analytical solution. This means that the SFDTD method will have a high computational accuracy when the grid size in the computation region is smaller than one tenth of the minimum operating wavelength. For R > 0.7431 (R4) and->
The numerical dispersion property of the SFDTD method is still better, but it follows->
The dispersion property is worse and worse, and in addition, the high frequency spectrum components will become unstable, which finally leads to the divergence of numerical results, and the spatial filtering indicates that the unstable high frequency components can ensure the stability of the numerical results through the filtering processing. It can be found from the curve corresponding to R5 even in->
Within the range, the SFDTD method also has poor dispersion properties, and the accuracy of the numerical result can only be guaranteed within a smaller spectral range.
Based on the above analysis, it can be concluded that the numerical dispersion property of the SF-SFDTD method will not be a factor affecting the correctness of the numerical result if the spatial sampling rate is reasonable.
Step 104: and defining a low-pass filter according to the value range.
In order to visually describe the spatial frequency domain information of the spatial electromagnetic field component when the SFDTD method is used to iterate the electromagnetic component, fig. 4 is a distribution diagram of the spatial frequency domain information of the spatial electromagnetic field component from one dimension to three dimensions. The results in FIG. 4 reflect: when the time step satisfies the stability condition, the frequency domain information is mainly concentrated at the low frequency, and the value of the high frequency component is almost zero, so the influence on the numerical result is extremely small. However, when the time step does not satisfy the stability condition, the high frequency component value thereof is large and increases rapidly, eventually causing the calculation result to diverge. From the above spatial frequency spectrum information of the electromagnetic component, it can be known that by filtering the spatial high frequency component, the stability condition of the SFDTD method will be expanded and a more stable result will be obtained.
The definition of the filter is as follows: according to the value of the spreading factor CE, k max Can be obtained by the equations (11) and (13) according to k max The value of (3), the three-dimensional low-pass filter is defined as follows
As can be seen from the definition formula of the filter, spectral components above the filter radius need to be completely filtered out, since even a small fraction of high frequency components cause the numerical result to diverge in the time-domain iteration.
Step 105: filtering the spatial electromagnetic field component according to the low-pass filter to obtain a filtered spatial electromagnetic field component, which specifically comprises:
and carrying out space frequency domain transformation on the space electromagnetic field component to obtain a space frequency domain electromagnetic component.
And obtaining the electromagnetic component of the spatial frequency domain according to the low-pass filter and the electromagnetic component of the spatial frequency domain.
And carrying out inverse spatial frequency domain transformation on the spatial frequency domain electromagnetic component to obtain a filtered spatial frequency domain electromagnetic component.
And carrying out filtering processing on the spatial electromagnetic field components. Setting simulation space and electromagnetic parameters, and iteratively solving the electric field and the magnetic field in the Maxwell equation. And then, carrying out frequency domain transformation on the obtained electromagnetic field component of the spatial domain to obtain a frequency domain electromagnetic field component. And filtering the transformed frequency domain electromagnetic field component by using a low-pass filter, and finally performing inverse frequency domain transformation on the filtered frequency domain electromagnetic field component to finally obtain the filtered space electromagnetic field component. Specifically, the method comprises the following steps:
since the filter can only be applied to the spatial frequency domain, the spatial electromagnetic field component needs to be converted into the spatial frequency domain, and the detailed filtering process is as follows:
(1) Space frequency domain transformation is carried out on the space electromagnetic field component to obtain a space frequency domain electromagnetic component E n (k，nΔt)＝F(E n (r，nΔt))
(2) Filtering out high frequency component by multiplying filter function by above formula
(3) The space frequency domain electromagnetic component is subjected to inverse space frequency domain transformation to obtain a filtered space domain electromagnetic component
(4) The boundary conditions are reloaded.
The invention will now be further described and verified with reference to two numerical examples and the accompanying drawings of the specification. FIG. 5 is a diagram of a pattern distribution of a two-dimensional metal cavity calculated using an SFDTD method and an SF-SFDTD method with different time step lengths; FIG. 6 is a schematic diagram of a three-dimensional metal cavity calculated by an SFDTD method and an SF-SFDTD method with different time step lengths; FIG. 7 shows the autocorrelation coefficients of the first eight resonant frequency points calculated by the SFDTD method and the SF-SFDTD method, which are smaller. The calculation efficiency of the CPU is shown in table 1, and it can be seen that the present invention has higher calculation efficiency and also ensures higher calculation accuracy.
TABLE 1 computational efficiency of CPU
FIG. 8 is a schematic diagram of a simulation of a dielectric waveguide model; FIG. 9 is a comparison graph of reflection coefficient results calculated using the RCWA method, the SFDTD method, and the SF-SFDTD method with different time steps;
it can be seen from fig. 8 and 9 that the present invention has high calculation accuracy.
Because the grid size in the SFDTD method limits the value range of the time step, especially when the simulation model contains a fine structure, the higher grid resolution (grid resolution: the ratio of the minimum operating wavelength to the grid size) severely reduces the value range of the time step. The reduction of the value range of the time step causes the SFDTD method to need more iteration steps under the same physical simulation time, and increases the CPU running time. The method eliminates the dependence of the time step in the SFDTD method on the grid size in the calculation area, and particularly has weaker dependence on the fine grid size. Therefore, the SFDTD method can take larger time step, needs less iteration times under the same physical simulation time, reduces the running time of a CPU, and improves the calculation simulation efficiency of the SFDTD method.
The invention also provides a system for determining the electromagnetic component of the spatial domain. FIG. 10 is a block diagram of a spatial domain electromagnetic component determination system of the present invention. As shown in fig. 10, a spatial domain electromagnetic component determination system includes:
and a stability condition determining module 201, configured to derive an electromagnetic numerical stability condition by using a octyl time domain finite difference method.
And an expansion factor determining module 202, configured to determine an expansion factor according to the electromagnetic value stability condition.
A value range determining module 203, configured to determine a value range of the spreading factor.
A low-pass filter defining module 204, configured to define a low-pass filter according to the value range.
And the filtering processing module 205 is configured to perform filtering processing on the spatial electromagnetic field component according to the low-pass filter to obtain a filtered spatial electromagnetic field component.
The spreading factor determining module 202 specifically includes:
and the extended time step determining unit is used for extending the electromagnetic value stability condition through high-frequency filtering processing to obtain the extended time step.
And the pre-expansion time step determining unit is used for acquiring the pre-expansion time step.
And the expansion factor determining unit is used for determining the expansion multiple of the time step length according to the time step length after the expansion and the time step length before the expansion, wherein the expansion multiple is an expansion factor.
The value range determining module 203 specifically includes:
and the dispersion error determining unit is used for analyzing the numerical dispersion errors of the sine-time domain finite difference method in different numerical wave number ranges.
And the value range determining unit is used for determining the value ranges of the expansion factors in different wave number ranges according to the numerical dispersion error.
The filtering processing module 205 specifically includes:
and the space frequency domain transformation unit is used for carrying out space frequency domain transformation on the space electromagnetic field component to obtain a space frequency domain electromagnetic component.
And the filtering unit is used for obtaining the electromagnetic component of the spatial frequency domain according to the low-pass filter and the electromagnetic component of the spatial frequency domain.
And the inverse space frequency domain transformation unit is used for performing inverse space frequency domain transformation on the space frequency domain electromagnetic component to obtain the filtered space frequency domain electromagnetic component.
The embodiments in the present description 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 description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (8)
1. A method for determining a spatial domain electromagnetic component, comprising:
deducing an electromagnetic numerical value stability condition by adopting a octyl time domain finite difference method;
determining an expansion factor according to the electromagnetic value stability condition;
determining the value range of the expansion factor;
defining a low-pass filter according to the value range;
and filtering the spatial electromagnetic field component according to the low-pass filter to obtain the filtered spatial electromagnetic field component.
2. The method for determining the electromagnetic component in the spatial domain according to claim 1, wherein the determining the spreading factor according to the electromagnetic numerical stability condition specifically includes:
expanding the stability condition of the electromagnetic value through high-frequency filtering processing to obtain an expanded time step;
acquiring a time step before expansion;
and determining the expansion multiple of the time step length according to the time step length after the expansion and the time step length before the expansion, wherein the expansion multiple is an expansion factor.
3. The method for determining the electromagnetic component in the spatial domain according to claim 1, wherein the determining the value range of the spreading factor specifically includes:
analyzing numerical dispersion errors of the sine-time domain finite difference method in different numerical wave number ranges;
and determining the value range of the expansion factor in different wave number ranges according to the numerical dispersion error.
4. The method for determining a spatial domain electromagnetic component according to claim 1, wherein the filtering the spatial electromagnetic field component according to the low-pass filter to obtain the filtered spatial domain electromagnetic component specifically includes:
performing space frequency domain transformation on the space electromagnetic field component to obtain a space frequency domain electromagnetic component;
obtaining a space frequency domain electromagnetic component according to the low-pass filter and the space frequency domain electromagnetic component;
and carrying out inverse space frequency domain transformation on the space frequency domain electromagnetic component to obtain the filtered space frequency domain electromagnetic component.
5. A spatial domain electromagnetic component determination system, comprising:
the stability condition determining module is used for deducing an electromagnetic numerical value stability condition by adopting a octyl time domain finite difference method;
the expansion factor determining module is used for determining an expansion factor according to the electromagnetic value stability condition;
a value range determining module, configured to determine a value range of the expansion factor;
a low-pass filter defining module for defining a low-pass filter according to the value range;
and the filtering processing module is used for carrying out filtering processing on the spatial electromagnetic field component according to the low-pass filter to obtain the filtered spatial electromagnetic field component.
6. The system for determining electromagnetic components in spatial domain according to claim 5, wherein the expansion factor determining module specifically comprises:
the extended time step determining unit is used for extending the electromagnetic value stability condition through high-frequency filtering processing to obtain an extended time step;
a pre-expansion time step determining unit, configured to obtain a pre-expansion time step;
and the expansion factor determining unit is used for determining the expansion multiple of the time step length according to the expanded time step length and the time step length before expansion, wherein the expansion multiple is an expansion factor.
7. The system for determining an electromagnetic component in a spatial domain according to claim 5, wherein the value range determining module specifically includes:
the dispersion error determining unit is used for analyzing numerical dispersion errors of the sine time domain finite difference method in different numerical wave number ranges;
and the value range determining unit is used for determining the value ranges of the expansion factors in different wave number ranges according to the numerical dispersion error.
8. The system for determining an electromagnetic component in a spatial domain according to claim 5, wherein the filtering module specifically includes:
the spatial frequency domain transformation unit is used for carrying out spatial frequency domain transformation on the spatial electromagnetic field component to obtain a spatial frequency domain electromagnetic component;
the filtering unit is used for obtaining a space frequency domain electromagnetic component according to the low-pass filter and the space frequency domain electromagnetic component;
and the inverse spatial frequency domain transformation unit is used for performing inverse spatial frequency domain transformation on the spatial frequency domain electromagnetic component to obtain the filtered spatial frequency domain electromagnetic component.
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