A method, device and medium for analyzing electromagnetic response under broadband excitation signal

Abstract

This invention discloses a method, apparatus, and medium for analyzing the electromagnetic response under a wideband excitation signal, relating to the field of electromagnetics technology. The method involves performing Fourier decomposition on the wideband time-domain excitation signal to obtain its spectral signal; calculating the time-domain and frequency-domain simulation durations of the spectral signal at each frequency, and calculating the critical frequency based on these durations; extracting high-frequency signal components greater than or equal to the critical frequency from the spectral signal and calculating their time-domain electromagnetic response; extracting low-frequency signal components less than the critical frequency from the spectral signal and calculating their frequency-domain electromagnetic response at each frequency; and synthesizing the time-domain and frequency-domain electromagnetic responses to obtain the electromagnetic response of the wideband time-domain excitation signal. This method improves the computational efficiency of the wideband electromagnetic response.

Description

Technical Field

[0001] This invention relates to the field of electromagnetics, and in particular to a method, apparatus, and medium for analyzing electromagnetic response under broadband excitation signals. Background Technology

[0002] Currently, the high-altitude electromagnetic pulse (HEMP) generated by nuclear weapons explosions in the upper atmosphere poses a serious safety threat to basic energy infrastructure such as power plant electrical equipment due to its high field strength, wide spectral range, and long effective distance. Modeling and analyzing the electromagnetic response of power plant electrical equipment under HEMP is a crucial foundation for predicting the interference / damage effects of HEMP on equipment, optimizing electromagnetic compatibility design, and implementing effective HEMP protection measures.

[0003] In existing technologies, the most intuitive way to solve the HEMP response of key electrical equipment in power plants is through full-wave electromagnetic simulation. This involves accurately solving Maxwell's equations under HEMP excitation, calculating the precise field strength distribution inside the equipment, and further obtaining macroscopic response indicators such as induced voltage and current through post-processing. Although there are abundant algorithms and mature software in the field of electromagnetic field numerical calculation to accomplish this task, due to the unique transient waveform characteristics of HEMP and other similar ultra-wideband pulse excitations, existing full-wave electromagnetic simulation algorithms cannot directly calculate the broadband electromagnetic response in practical applications, resulting in low computational efficiency for calculating the broadband electromagnetic response in current technologies. Summary of the Invention

[0004] Therefore, it is necessary to provide a method, apparatus, and medium for analyzing electromagnetic response under broadband excitation signals to address the aforementioned technical problems. This method can improve the computational efficiency of broadband electromagnetic response.

[0005] The present invention adopts the following technical solution:

[0006] This invention provides a method for electromagnetic response analysis under broadband excitation signals, comprising:

[0007] Fourier decomposition is performed on the wideband time-domain excitation signal to be analyzed to obtain the spectrum signal of the wideband time-domain excitation signal;

[0008] Calculate the time-domain simulation duration and frequency-domain simulation duration of the spectral signal at each frequency, and calculate the critical frequency based on the time-domain simulation duration and frequency-domain simulation duration at each frequency;

[0009] Obtain the high-frequency signal components corresponding to the critical frequency from the spectrum signal, and calculate the time-domain electromagnetic response of the high-frequency signal components;

[0010] Obtain the low-frequency signal components below the critical frequency from the spectrum signal, and calculate the frequency domain electromagnetic response of each frequency in the low-frequency signal components.

[0011] The electromagnetic response of the broadband time-domain excitation signal is obtained by synthesizing the time-domain electromagnetic response and the frequency-domain electromagnetic response.

[0012] Preferably, calculating the time-domain simulation duration of the spectral signal at each frequency includes:

[0013] The maximum frequency of the spectrum signal is determined based on the number of truncated terms in the Fourier decomposition and the time length of the wideband time-domain excitation signal.

[0014] Calculate the required number of time iterations based on the maximum time step size that satisfies the time-domain computation stability condition of the wideband time-domain excitation signal and the time length of the wideband time-domain excitation signal.

[0015] Obtain the simulation time required to perform a preset number of iterations on the time length of the broadband time-domain excitation signal using the time-domain discontinuous Galerkin algorithm;

[0016] The time-domain simulation duration at each frequency is determined based on the maximum frequency, the required number of iterations, and the simulation time.

[0017] Preferably, the calculation method for the time-domain simulation duration at each frequency is as follows:

[0018]

[0019] N = [T / Δt] + 1;

[0020] Among them, t i Let f be the time-domain simulation duration for the i-th frequency. max f is the maximum frequency of the spectral signal. i Let represent the i-th frequency, Δt be the maximum time step of the wideband time-domain excitation signal to satisfy the time-domain computation stability condition, T be the time length of the wideband time-domain excitation signal, N be the required number of time iteration steps, n be the number of truncation terms, and t0 be the simulation time.

[0021] Preferably, calculating the frequency domain simulation duration of the spectral signal at each frequency includes:

[0022] Determine the intermediate frequency of the spectrum signal based on its maximum frequency.

[0023] Electromagnetic simulation of the spectrum signal at the intermediate frequency was performed using a boundary element-finite element solver to obtain the frequency domain calculation time.

[0024] The frequency domain calculation duration is defined as the frequency domain simulation duration of the spectral signal at each frequency.

[0025] Preferably, the critical frequency is calculated based on the time-domain simulation duration and frequency-domain simulation duration at each frequency, including:

[0026] A frequency optimization function is constructed with the objective of minimizing its value. Based on the time-domain and frequency-domain simulation durations at each frequency, the frequency optimization function is solved to obtain the critical frequency. The frequency optimization function is:

[0027]

[0028] Where n is the number of truncation terms in the Fourier decomposition, t f0 f is the duration of the frequency domain simulation. i For the i-th frequency, f max t is the maximum frequency of the spectral signal. i Let be the time-domain simulation duration at the i-th frequency.

[0029] Preferably, calculating the time-domain electromagnetic response of the high-frequency signal components includes:

[0030] The time-domain electromagnetic response of high-frequency signal components is calculated using a time-domain discontinuous Galerkin solver.

[0031] Preferably, calculating the frequency domain electromagnetic response at each frequency of the low-frequency signal component includes:

[0032] By sweeping frequencies, the boundary element-finite element solver is invoked to calculate the frequency domain electromagnetic response at each frequency in sequence.

[0033] Preferably, the electromagnetic response in the time domain and the electromagnetic response in the frequency domain are synthesized to obtain the electromagnetic response of the broadband time-domain excitation signal, including:

[0034] Perform an inverse Fourier transform on the frequency domain electromagnetic response to obtain the transformed frequency domain electromagnetic response;

[0035] The transformed frequency-domain electromagnetic response and time-domain electromagnetic response are superimposed to obtain the electromagnetic response of the broadband time-domain excitation signal.

[0036] This invention provides an electromagnetic response analysis device under a wideband excitation signal, comprising:

[0037] The decomposition module is used to perform Fourier decomposition on the wideband time-domain excitation signal to be analyzed, so as to obtain the spectrum signal of the wideband time-domain excitation signal.

[0038] The first calculation module is used to calculate the time-domain simulation duration and frequency-domain simulation duration of the spectrum signal at each frequency, and to calculate the critical frequency based on the time-domain simulation duration and frequency-domain simulation duration at each frequency.

[0039] The second calculation module is used to obtain the high-frequency signal components corresponding to the critical frequency from the spectrum signal and calculate the time-domain electromagnetic response of the high-frequency signal components.

[0040] The third calculation module is used to obtain the low-frequency signal components below the critical frequency from the spectrum signal and calculate the frequency domain electromagnetic response of each frequency in the low-frequency signal components.

[0041] The synthesis module is used to synthesize the time-domain electromagnetic response and the frequency-domain electromagnetic response to obtain the electromagnetic response of the broadband time-domain excitation signal.

[0042] The present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described electromagnetic response analysis method under a wideband excitation signal.

[0043] The present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-described electromagnetic response analysis method under a wideband excitation signal.

[0044] The above-mentioned at least one technical solution adopted in this invention can achieve the following beneficial effects:

[0045] In this invention, the critical frequency is calculated by using the time-domain simulation duration and frequency-domain simulation duration of the wideband time-domain excitation signal at each frequency. Then, using the critical frequency, the low-frequency and high-frequency signal components of the wideband time-domain excitation signal are found. Thus, the low-frequency signal component of the wideband time-domain excitation signal is simulated in the frequency domain, and the high-frequency signal component is sampled and simulated in the frequency domain. The complete electromagnetic response is then synthesized. This method combines the advantages of time-domain and frequency-domain algorithms, enabling the wideband time-domain excitation signal to achieve optimal computational efficiency, thereby improving the computational efficiency of the electromagnetic response of the wideband time-domain excitation signal. Attached Figure Description

[0046] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0047] Figure 1 This is a schematic flowchart of an electromagnetic response analysis method under a wideband excitation signal provided by the present invention;

[0048] Figure 2 A schematic diagram of another electromagnetic response analysis method under a wideband excitation signal provided by the present invention;

[0049] Figure 3A schematic diagram of an electromagnetic response analysis device under a wideband excitation signal provided by the present invention;

[0050] Figure 4 This is a schematic diagram of a computer device for implementing an electromagnetic response analysis method under a wideband excitation signal, as provided by the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0052] The spectral range of typical ultra-wideband excitations such as HEMP spans from 10kHz to 100MHz. This wide spectrum makes the computational burden of mainstream frequency domain simulation methods unbearable (requiring a huge number of frequency sweep operations to cover the HEMP spectrum range); in addition, for applications involving nonlinear components (such as transformer cores), the assumption that the physical field distribution of the excitation source and any location in space follows a sinusoidal law in the time domain no longer holds, requiring special equivalent modeling methods. Therefore, time domain methods are a more widely applicable choice.

[0053] While time-domain methods theoretically applicable to any wideband excitation exist, they also face efficiency bottlenecks in practical applications. To simulate infinitely large open-domain problems on computers with limited memory, time-domain electromagnetic simulations require truncating the computational domain with virtual boundary surfaces or layers, and using techniques such as absorbing boundary conditions and perfectly matched layers to ensure that the electromagnetic field energy within the computational domain is absorbed without reflection. To guarantee computational accuracy, the truncated boundary is typically required to be at least half a wavelength away from the object of study. For low-frequency signals of several hundred kHz, half a wavelength exceeds 300 meters, and the computational domain is at least 600 meters long in each coordinate axis direction, resulting in massive mesh partitioning that is unacceptable in practical calculations. Frequency-domain computation can use boundary element discretization closely adjacent to the object of study as open-domain boundary conditions for low-frequency signals, but this method requires inverting high-dimensional matrices in the time domain and cannot be directly applied.

[0054] To address the aforementioned bottlenecks, this invention proposes an electromagnetic response analysis method for ultra-wideband electromagnetic excitations such as HEMP signals. The method employs a frequency-domain simulation algorithm for the low-frequency components of the excitation signal and a time-domain simulation algorithm for the high-frequency components, then synthesizes the results to obtain the complete wideband electromagnetic response. This method combines the advantages of both frequency-domain and time-domain algorithms, achieving optimal computational efficiency for ultra-wideband excitations.

[0055] The device that implements the present invention can be a server set up on a business platform, or a device such as a desktop computer or laptop computer that can implement the present invention.

[0056] The technical solutions provided by the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0057] Figure 1 This is a schematic flowchart of an electromagnetic response analysis method under a wideband excitation signal according to the present invention, which specifically includes the following steps:

[0058] S101, Perform Fourier decomposition on the wideband time-domain excitation signal to be analyzed to obtain the spectrum signal of the wideband time-domain excitation signal.

[0059] The transient waveform expression of the wideband time-domain excitation is G(t), which is expanded into a Fourier series as shown in formula (1), i.e., the spectrum signal.

[0060] G(t)≈g(t)=a0+a1 cos(ωt)+b1 sin(ωt)+Ka n cos(nωt)+b n sin(nωt) (1)

[0061] Wherein, the fundamental angular frequency ω = 1 / 2πT, T is the time length of the broadband time-domain excitation signal, and n is the number of truncation terms. The selection of the number of truncation terms n can satisfy:

[0062]

[0063] The L2 norm of any wideband time-domain excitation signal waveform x(t) can be calculated by the following formula:

[0064]

[0065] S102, calculate the time-domain simulation duration and frequency-domain simulation duration of the spectrum signal at each frequency, and calculate the critical frequency based on the time-domain simulation duration and frequency-domain simulation duration at each frequency.

[0066] Optionally, the time-domain simulation duration of the spectral signal at each frequency is calculated, including: determining the maximum frequency of the spectral signal based on the number of truncated terms in the Fourier decomposition and the duration of the wideband time-domain excitation signal; calculating the required number of time iteration steps based on the maximum time step size of the wideband time-domain excitation signal satisfying the time-domain computation stability condition and the duration of the wideband time-domain excitation signal; obtaining the simulation time required to iterate the duration of the wideband time-domain excitation signal a preset number of times using the time-domain discontinuous Galerkin algorithm; and determining the time-domain simulation duration at each frequency based on the maximum frequency, the required number of time iteration steps, and the simulation time.

[0067] Specifically, the characteristic scale of the problem at a certain frequency f is defined as follows:

[0068]

[0069] Where Δl1 is the minimum operating wavelength, Δl2 is the minimum penetration depth of the system when the object under study is conductive, and v C Let be the speed of light, and μ and σ be the magnetic permeability and electrical conductivity, respectively.

[0070] Assuming the frequency of the spectral signal is the maximum frequency, i.e., taking... According to the research object (equipment) being at least d = v from the boundary surface (launch point). c / 2f max The computational domain is selected based on the principle of [missing information], and the geometric meshing of the model is completed, requiring the mesh feature size to not exceed Δl / 10. The maximum time step Δt satisfying the time-domain computational stability condition and the time length T of the broadband time-domain excitation signal are calculated, and the required number of time iterations N = [T / Δt] + 1 is calculated. The Discontinuous Galerkin Time-Domain (DGTD) algorithm is called for 10 time iterations, with a simulation time of t0. Then, for the spectral signal with frequencies not lower than f... i The time estimate of the electromagnetic response of all frequency components (1≤i≤n) obtained by time-domain simulation is:

[0071]

[0072] Therefore, the time-domain simulation duration of the spectral signal at each frequency can be calculated according to formula (5), t i Let be the time-domain simulation duration for the i-th frequency.

[0073] It should be noted that the Discontinuous Galerkin Time-Domain (DGTD) algorithm is an improvement on the classical time-domain finite element method. Its essential advantage is that it does not require inverting high-dimensional matrices in each time iteration as in the time-domain finite element method, allowing purely explicit time-domain iterations. It is efficient and consumes little memory. Therefore, this invention selects the DGTD algorithm as the solver for time-domain electromagnetic simulation.

[0074] Optionally, the frequency domain simulation duration of the spectrum signal at each frequency is calculated, including: determining the intermediate frequency of the spectrum signal based on the maximum frequency of the spectrum signal; performing electromagnetic simulation on the spectrum signal at the intermediate frequency using a boundary element-finite element solver to obtain the frequency domain calculation duration; and determining the frequency domain calculation duration as the frequency domain simulation duration of the spectrum signal at each frequency.

[0075] Specifically, take f=f max / 2=n / 4πT, and the electromagnetic simulation at this frequency is calculated using frequency domain finite element method and boundary element method algorithms. The calculation time is t. f0 This can be used as an approximate estimate of the frequency domain simulation calculation time for each frequency component, i.e., t f0 This serves as the frequency domain simulation duration for the spectral signal at each frequency.

[0076] Based on the time-domain and frequency-domain simulation durations at each frequency, the critical frequency is calculated as follows: First, a frequency optimization function is constructed, with the goal of minimizing the frequency optimization function value. The frequency optimization function is then solved based on the time-domain and frequency-domain simulation durations at each frequency to obtain the critical frequency. The frequency optimization function is:

[0077]

[0078] Where n is the number of truncation terms in the Fourier decomposition, t f0 f is the duration of the frequency domain simulation. i For the i-th frequency, f max t is the maximum frequency of the spectral signal. i Let be the time-domain simulation duration at the i-th frequency.

[0079] The independent variable of the above optimization problem is the critical frequency number i. Since the number is a positive integer between 0 and n, formula (6) defines an integer optimization problem. In practice, the typical value of n can be within 1000. The number i and the corresponding optimal critical frequency f can be easily obtained by exhaustive search. i .

[0080] In this invention, the critical frequency f i The definition is: in formula (1), the frequency is not lower than f i The components are calculated using the time domain to determine their response, while frequencies below f0 are used. i The electromagnetic response of the component is obtained through multiple frequency domain simulations. The optimal critical frequency minimizes the total computation time, thus satisfying the optimization problem.

[0081] S103: Obtain the high-frequency signal component corresponding to the critical frequency from the spectrum signal, and calculate the time-domain electromagnetic response of the high-frequency signal component.

[0082] According to the research object being at least d = v from the boundary surface c / 2f i The computational domain was selected and meshed according to the principle that the feature size of the mesh element should not exceed Δl / 10, with the critical frequency f as the reference value. i For example, the high-frequency signal component is defined as:

[0083] R(t)=G(t)-[a0+a1cos(ωt)+b1sin(ωt)+Kai-1 cos((i-1)ωt)+b i-1 sin((i-1)ωt)](7)

[0084] The time-domain electromagnetic response of the high-frequency signal component can be calculated using the time-domain discontinuous Galerkin solver. The high-frequency signal component refers to the high-frequency portion of the broadband time-domain excitation signal.

[0085] S104: Obtain the low-frequency signal components below the critical frequency from the spectrum signal, and calculate the frequency domain electromagnetic response of each frequency in the low-frequency signal components.

[0086] By sweeping frequencies, the boundary element-finite element solver is invoked to calculate the frequency domain electromagnetic response at each frequency sequentially. For example, with the critical frequency f... i For example, for frequencies lower than f i The low-frequency signal components are used to sequentially calculate the frequency domain electromagnetic response at each frequency point using a frequency sweep method. The boundary element-finite element solver is then invoked to sequentially calculate frequencies f0, f1, L, f... i-1 The frequency domain electromagnetic response is calculated (the DC component is considered as a special case of f0 = 0), and the calculation results for each group are stored. Among them, the low-frequency signal component is the low-frequency part of the broadband time-domain excitation signal.

[0087] S105 synthesizes the time-domain electromagnetic response and the frequency-domain electromagnetic response to obtain the electromagnetic response of the broadband time-domain excitation signal.

[0088] In one embodiment, the electromagnetic response of the time-domain electromagnetic response and the electromagnetic response of the frequency-domain electromagnetic response are synthesized to obtain the electromagnetic response of the broadband time-domain excitation signal, including: performing an inverse Fourier transform on the frequency-domain electromagnetic response to obtain the transformed frequency-domain electromagnetic response; and superimposing the transformed frequency-domain electromagnetic response and the time-domain electromagnetic response to obtain the electromagnetic response of the broadband time-domain excitation signal.

[0089] Specifically, the frequency domain electromagnetic response obtained at each frequency point in S104 is extracted by inverse Fourier transform to obtain its corresponding time domain waveform. Then, based on the principle of linear superposition, it is synthesized with the time domain electromagnetic response (high frequency part) obtained in S103 to obtain the complete electromagnetic response under broadband excitation signal.

[0090] For example, when studying the electric field intensity at a certain spatial point, assuming the high-frequency time-domain response calculated in S103 is H(t), the frequency responses obtained in S104 are l0(f), l1(f), ..., l i-1 (f) Then the actual electric field intensity time-domain waveform (electromagnetic response of the broadband time-domain excitation signal) is:

[0091]

[0092] Among them, the operator This represents the inverse Fourier transform, and l k The inverse transformation of (f) is L k (t)(0≤k≤i-1).

[0093] In one exemplary embodiment, the present invention also provides a method for electromagnetic response analysis under broadband excitation signals, such as... Figure 2 As shown, this embodiment includes the following steps:

[0094] S201 performs Fourier decomposition on the wideband time-domain excitation signal to obtain the spectrum signal of the wideband time-domain excitation signal.

[0095] S202 estimates the computational complexity of lower frequency domain and time domain simulations of wideband time-domain excitation signals through methods such as trial calculations at typical frequency points.

[0096] S203, calculate the optimal critical frequency by solving the integer optimization problem defined by formula (6).

[0097] S204: For the portion of the spectrum not lower than the optimal critical frequency, the time-domain discontinuous Galerkin solver is called to obtain the corresponding time-domain electromagnetic response in one step; for the portion of the spectrum lower than the optimal critical frequency, the boundary element-finite element solver is called by frequency sweeping to calculate and store the frequency-domain electromagnetic response corresponding to each frequency point in sequence.

[0098] S205: The frequency domain electromagnetic response at each frequency point in the low-frequency part is inverse Fourier transformed to obtain the corresponding time domain waveform. Then, based on the principle of linear superposition, it is synthesized with the time domain electromagnetic response in the high-frequency part to obtain the complete electromagnetic response under wideband excitation such as HEMP.

[0099] This invention targets ultra-wideband electromagnetic excitations such as HEMP. It performs frequency-domain simulation on the low-frequency components of the wideband excitation and uses a time-domain simulation algorithm for the high-frequency components, then synthesizes the complete wideband electromagnetic response. This method fully combines the advantages of frequency-domain and time-domain algorithms, achieving optimal computational efficiency for ultra-wideband excitations, and has the following advantages:

[0100] First, the most efficient solution methods are tailored for each band of the broadband excitation spectrum: For low-frequency components, a finite element-boundary element hybrid solver is selected (the boundary element discrete domain closely following the research object is used as the open domain boundary condition of the finite element algorithm), avoiding the bottleneck of setting up a huge computational region when applying open domain boundary conditions in low-frequency simulation; For high-frequency components, a time-domain discontinuous Galerkin (DGTD) solver is selected, which eliminates the huge burden of frequency sweep calculation in frequency domain simulation and also overcomes the problem that the classical time-domain finite element method requires inverting a large-scale matrix in each time iteration.

[0101] Second, the optimal critical frequency for frequency domain and time domain simulation calculations is determined through a standard process of trial calculations at typical frequency points and then solving the optimization model, avoiding the burden and efficiency bottleneck of relying on manual experience to select this parameter.

[0102] When applying the electromagnetic response analysis method under wideband excitation signals provided by this invention, it is not necessary to consider... Figure 1 The steps shown are executed in sequence. The specific execution order of each step can be determined as needed, and this invention does not impose any restrictions on it.

[0103] The above describes one or more embodiments of the electromagnetic response analysis method under wideband excitation signals provided by the present invention. Based on the same idea, the present invention also provides a corresponding electromagnetic response analysis device under wideband excitation signals, such as... Figure 3 As shown.

[0104] Figure 3 This is a schematic diagram of an electromagnetic response analysis device under a wideband excitation signal provided by the present invention. The device 300 includes:

[0105] The decomposition module 301 is used to perform Fourier decomposition on the wideband time-domain excitation signal to be analyzed, so as to obtain the spectrum signal of the wideband time-domain excitation signal.

[0106] The first calculation module 302 is used to calculate the time-domain simulation duration and frequency-domain simulation duration of the spectrum signal at each frequency, and to calculate the critical frequency based on the time-domain simulation duration and frequency-domain simulation duration at each frequency.

[0107] The second calculation module 303 is used to obtain the high-frequency signal component corresponding to the critical frequency from the spectrum signal and calculate the time-domain electromagnetic response of the high-frequency signal component.

[0108] The third calculation module 304 is used to obtain the low-frequency signal components corresponding to frequencies below the critical frequency from the spectrum signal, and to calculate the frequency domain electromagnetic response of each frequency in the low-frequency signal components.

[0109] The synthesis module 305 is used to synthesize the time-domain electromagnetic response and the frequency-domain electromagnetic response to obtain the electromagnetic response of the broadband time-domain excitation signal.

[0110] Specific limitations regarding the electromagnetic response analysis device under broadband excitation signals can be found in the limitations of the electromagnetic response analysis method under broadband excitation signals described above, and will not be repeated here. Each module in the aforementioned electromagnetic response analysis device under broadband excitation signals can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the corresponding operations of each module.

[0111] The present invention also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 A method for analyzing electromagnetic response under wideband excitation signals is provided.

[0112] The present invention also provides Figure 4 The schematic diagram of the computer device shown is as follows: Figure 4 As shown, at the hardware level, this computer device includes a processor, internal bus, network interface, memory, and non-volatile memory, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then executes it to achieve the above. Figure 1 A method for analyzing electromagnetic response under wideband excitation signals is provided.

[0113] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0114] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this invention.

Claims

1. A method for analyzing electromagnetic response under broadband excitation signals, characterized in that, include: The wideband time-domain excitation signal to be analyzed is subjected to Fourier decomposition to obtain the spectrum signal of the wideband time-domain excitation signal; Calculate the time-domain simulation duration and frequency-domain simulation duration of the spectrum signal at each frequency, and calculate the critical frequency based on the time-domain simulation duration and frequency-domain simulation duration at each frequency; Obtain the high-frequency signal component corresponding to the critical frequency from the spectrum signal, and calculate the time-domain electromagnetic response of the high-frequency signal component; Obtain the low-frequency signal components corresponding to frequencies below the critical frequency from the spectrum signal, and calculate the frequency domain electromagnetic response of each frequency in the low-frequency signal components; The electromagnetic response of the broadband time-domain excitation signal is obtained by synthesizing the time-domain electromagnetic response and the frequency-domain electromagnetic response. The step of calculating the critical frequency based on the time-domain simulation duration and frequency-domain simulation duration at each frequency includes: constructing a frequency optimization function with the objective of minimizing the frequency optimization function value; solving the frequency optimization function based on the time-domain simulation duration and frequency-domain simulation duration at each frequency to obtain the critical frequency; the frequency optimization function is: ； in, The number of truncated terms in the Fourier decomposition. For frequency domain simulation duration, For the first i One frequency, The maximum frequency of the spectrum signal. For the first i Time-domain simulation duration at each frequency.

2. The method according to claim 1, characterized in that, Calculate the time-domain simulation duration of the spectral signal at each frequency, including: The maximum frequency of the spectral signal is determined based on the number of truncated terms in the Fourier decomposition and the time length of the wideband time-domain excitation signal. The required number of time iteration steps is calculated based on the maximum time step size that satisfies the time-domain computation stability condition of the wideband time-domain excitation signal and the time length of the wideband time-domain excitation signal; The simulation time required to perform a preset number of iterations on the time length of the broadband time-domain excitation signal using the time-domain discontinuous Galerkin algorithm is obtained. The time-domain simulation duration at each frequency is determined based on the maximum frequency, the required number of iteration steps, and the simulation time.

3. The method according to claim 2, characterized in that, The calculation method for the time-domain simulation duration at each frequency is as follows: ； ； ； in, For the first i The time-domain simulation duration for each frequency, The maximum frequency of the spectrum signal. Indicates the first i One frequency, The maximum time step for a wideband time-domain excitation signal to satisfy the time-domain computational stability condition. T The duration of the wideband time-domain excitation signal. The number of iterations required. The number of truncated terms, This is the simulation time.

4. The method according to claim 1, characterized in that, Calculate the frequency domain simulation duration of the spectral signal at each frequency, including: Determine the intermediate frequency of the spectrum signal based on its maximum frequency; Electromagnetic simulation of the spectral signal at the intermediate frequency was performed using a boundary element-finite element solver to obtain the frequency domain calculation duration. The frequency domain calculation duration is determined as the frequency domain simulation duration of the spectral signal at each frequency.

5. The method according to claim 1, characterized in that, The calculation of the time-domain electromagnetic response of the high-frequency signal component includes: The time-domain electromagnetic response of the high-frequency signal component is calculated using a time-domain discontinuous Galerkin solver.

6. The method according to claim 1, characterized in that, The calculation of the frequency domain electromagnetic response at each frequency of the low-frequency signal component includes: By sweeping frequencies, the boundary element-finite element solver is invoked to calculate the frequency domain electromagnetic response at each frequency in sequence.

7. The method according to claim 1, characterized in that, The synthesis of the time-domain electromagnetic response and the frequency-domain electromagnetic response to obtain the electromagnetic response of the broadband time-domain excitation signal includes: Perform an inverse Fourier transform on the frequency domain electromagnetic response to obtain the transformed frequency domain electromagnetic response; The electromagnetic response of the broadband time-domain excitation signal is obtained by superimposing the transformed frequency-domain electromagnetic response and the time-domain electromagnetic response.

8. An electromagnetic response analysis device under a wideband excitation signal, characterized in that, include: The decomposition module is used to perform Fourier decomposition on the wideband time-domain excitation signal to be analyzed, so as to obtain the spectrum signal of the wideband time-domain excitation signal. The first calculation module is used to calculate the time-domain simulation duration and frequency-domain simulation duration of the spectral signal at each frequency, and to calculate the critical frequency based on the time-domain simulation duration and frequency-domain simulation duration at each frequency; wherein, calculating the critical frequency based on the time-domain simulation duration and frequency-domain simulation duration at each frequency includes: constructing a frequency optimization function with the objective of minimizing the frequency optimization function value, and solving the frequency optimization function based on the time-domain simulation duration and frequency-domain simulation duration at each frequency to obtain the critical frequency; the frequency optimization function is: ； in, The number of truncated terms in the Fourier decomposition. For frequency domain simulation duration, For the first i One frequency, The maximum frequency of the spectrum signal. For the first i Time-domain simulation duration at each frequency; The second calculation module is used to obtain the high-frequency signal component corresponding to the critical frequency from the spectrum signal, and to calculate the time-domain electromagnetic response of the high-frequency signal component. The third calculation module is used to obtain the low-frequency signal component corresponding to the critical frequency from the spectrum signal, and to calculate the frequency domain electromagnetic response of the low-frequency signal component at each frequency. The synthesis module is used to synthesize the time-domain electromagnetic response and the frequency-domain electromagnetic response to obtain the electromagnetic response of the broadband time-domain excitation signal.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program that, when executed by a processor, implements the method as described in any one of claims 1 to 7.

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