Frequency domain response calculation method and device of electromagnetic field, equipment and storage medium

Abstract

The invention relates to the technical field of electromagnetic scattering, in particular to a frequency domain response calculation method and device of an electromagnetic field, equipment and a storage medium. Performing recursive transformation on the time domain basic system equation according to the discrete time domain set and a backward Euler method to obtain a time domain transformation equation and an algebraic matrix equation; carrying out back substitution solving operation on the algebraic matrix equation according to a time domain stepping method and a time domain transformation equation; performing full-time-domain response calculation on the time-domain finite element solution based on a time-domain finite element method to obtain a time-domain base solution; calculating the time domain base solution according to a preset linear superposition principle to obtain a frequency domain response; a continuous problem is dispersed through a backward Euler method, rapid back substitution solution is carried out after factorization for one time, and redundant calculation is reduced; based on a linear superposition principle, phase weighting is carried out to synthesize a time domain base solution, frequency domain response of any frequency is rapidly obtained, frequency-by-frequency repeated calculation is avoided, efficiency is improved, and the method is suitable for broadband high-precision electromagnetic field analysis and has remarkable application value.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic scattering technology, and in particular to a method, device, equipment and storage medium for calculating the frequency domain response of an electromagnetic field. Background Art

[0002] In the prior art, there are two main methods for calculating the frequency domain response of electromagnetic fields. One is the direct frequency domain method, which requires the establishment and solution of a system matrix for each frequency point independently. The matrix decomposition and solution process are repeated as the number of frequency points increases, and the amount of calculation increases linearly. In particular, the efficiency is extremely low in broadband analysis, and the processing of frequency-varying materials requires repeated modeling, which is time-consuming. The other is the time domain conversion method, which obtains the frequency response through Fourier transform of the time domain transient response. However, the time step is strictly limited by the CFL condition, and the fine structure requires an extremely small step, which leads to a surge in computational costs. At the same time, time domain signal truncation is prone to introduce errors, and high-frequency accuracy is difficult to guarantee. In addition, Fourier transform has a large computational load for long time domain signals and is easily interfered by noise, making it difficult to balance the efficiency and accuracy of multi-frequency analysis. To this end, the present invention proposes a method for calculating the frequency domain response of electromagnetic fields to solve the above technical problems. Summary of the Invention

[0003] In order to overcome the deficiencies of the prior art, the present invention aims to provide a method, apparatus, device and storage medium for calculating the frequency domain response of an electromagnetic field.

[0004] A method for calculating the frequency domain response of an electromagnetic field comprises: obtaining electromagnetic characteristics, electric field strength values ​​and source current density; generating a time region according to a preset initial moment and a preset end moment; constructing a time domain basic system equation according to the electromagnetic characteristics, electric field strength values, source current density and the time region; decomposing the time region to obtain a discrete time domain set; recursively transforming the time domain basic system equation according to the discrete time domain set and the backward Euler method to obtain a time domain transformation equation and an algebraic matrix equation; back-substituting and solving the algebraic matrix equation according to the time domain stepping method and the time domain transformation equation to obtain a time domain finite element solution; performing full time domain response calculation on the time domain finite element solution based on the time domain finite element method to obtain a time domain base solution; and calculating the time domain base solution according to a preset linear superposition principle to obtain a frequency domain response.

[0005] Furthermore, the time domain basic system equation is constructed according to the electromagnetic characteristics, electric field strength values, source current density and time region, including: generating a coefficient matrix according to the electromagnetic characteristics, electric field strength values ​​and source current density; obtaining the magnetic field potential value and the circuit current value, and generating a variable column matrix according to the time region, the magnetic field potential value and the circuit current value; obtaining the magnetic field eddy current region and the energy storage element coefficient, and constructing a constant matrix according to the magnetic field eddy current region and the energy storage element coefficient; obtaining the current excitation source and the voltage excitation source, and generating a right-side column matrix according to the current excitation source and the voltage excitation source; and constructing the time domain basic system equation according to the coefficient matrix, the variable column matrix, the constant matrix and the right-side column matrix.

[0006] Furthermore, the method of generating a variable column matrix based on the time region, the magnetic field potential value and the circuit current value includes: performing dimensional analysis on the time region to obtain the time dimension; generating the magnetic field potential dimension based on the magnetic field potential value and the time dimension; correcting the magnetic field potential dimension based on a preset magnetic field potential dimension threshold to obtain a corrected potential dimension; generating a magnetic field potential matrix based on the corrected potential dimension; generating a circuit current dimension based on the circuit current value and the time dimension; correcting the circuit current dimension based on a preset circuit current dimension threshold to obtain a corrected current dimension; generating a magnetic field current matrix based on the corrected current dimension; and generating a variable column matrix based on the magnetic field potential matrix and the magnetic field current matrix.

[0007] Furthermore, the back-substitution solving operation of the algebraic matrix equation according to the time-domain stepping method and the time-domain transformation equation to obtain the time-domain finite element solution includes: performing type conversion on the electromagnetic characteristics, electric field intensity values ​​and source current density according to the time-domain transformation equation to obtain the current load vector; performing back-substitution solving operation on the algebraic matrix equation according to the time-domain stepping method and the current load vector to obtain the initial finite element solution; generating boundary conditions according to a preset initial moment and a preset system state vector; and constraining the initial finite element solution according to the boundary conditions to obtain the time-domain finite element solution.

[0008] Furthermore, the performing of full time domain response calculation on the time domain finite element solution based on the time domain finite element method to obtain a time domain basic solution includes: constructing a magnetic field and circuit coupling model based on the time domain finite element method; The original sinusoidal voltage source is obtained, and a unit step function is constructed based on the magnetic field and circuit coupling model and the original sinusoidal voltage source. The full time domain response of the time domain finite element solution is calculated based on the unit step function to obtain the time domain basic solution.

[0009] Furthermore, the time domain basis solution is calculated according to a preset linear superposition principle to obtain a frequency domain response, including: decomposing a unit step function to obtain multiple step functions; performing difference calculations on adjacent functions of the multiple step functions to obtain multiple square wave functions; constructing a sinusoidal source function based on the multiple square wave functions and the multiple step functions; calculating the time domain basis solution according to the linear superposition principle and the sinusoidal source function to obtain a sinusoidal source excitation; and generating a frequency domain response based on the sinusoidal source excitation.

[0010] Furthermore, the unit step function is decomposed to obtain multiple step functions, including: Multiple time steps are obtained based on discrete time domain set calculations; characteristic analysis is performed on the magnetic field eddy current region to obtain the electromagnetic field change rate; the multiple time steps are smoothed based on the electromagnetic field change rate to obtain multiple smoothed time steps; and the unit step function is decomposed based on the multiple smoothed time steps to obtain multiple step functions.

[0011] Furthermore, a frequency domain response calculation device for an electromagnetic field includes: a data acquisition module for acquiring electromagnetic characteristics, electric field strength values, and source current density; a time region generation module for generating a time region according to a preset initial time and a preset end time; and an equation construction module for constructing a time domain basic system equation according to the electromagnetic characteristics, electric field strength values, source current density, and time region. The time domain decomposition module is used to decompose the time domain to obtain a discrete time domain set; the recursive module is used to perform recursive transformation on the time domain basic system equation according to the discrete time domain set and the backward Euler method to obtain the time domain transformation equation and the algebraic matrix equation; the solution operation module is used to perform back substitution solution operation on the algebraic matrix equation according to the time domain stepping method and the time domain transformation equation to obtain the time domain finite element solution; the time domain basis solution module is used to perform full time domain response calculation on the time domain finite element solution based on the time domain finite element method to obtain the time domain basis solution; the frequency domain response module is used to calculate the time domain basis solution according to the preset linear superposition principle to obtain the frequency domain response.

[0012] Furthermore, the present invention provides a device for calculating the frequency domain response of an electromagnetic field, the device comprising: a memory and at least one processor, the memory storing instructions; at least one processor calling the instructions in the memory so that the computer device executes each step of any one of the above-mentioned methods for calculating the frequency domain response of an electromagnetic field.

[0013] Furthermore, the present invention provides a computer-readable storage medium having instructions stored thereon, and when the instructions are executed by a processor, the various steps of any of the above-mentioned methods for calculating the frequency domain response of an electromagnetic field are implemented.

[0014] In the technical solution of the present invention, by constructing the basic system equation in the time domain and adopting the backward Euler method recursive transformation, the continuous problem is discretized into an algebraic matrix equation. The coefficient matrix only needs to be factorized once, and the subsequent time steps are quickly solved by back substitution operations, which significantly reduces redundant calculations. The calculation of the time domain basis solution captures the full frequency domain information of the system and provides core data support for frequency domain analysis. Based on the principle of linear superposition, the time domain basis solution is phase-weighted and synthesized to quickly obtain the frequency domain response of any frequency, avoiding repeated calculations of frequency-by-frequency solutions in the frequency domain and improving computing efficiency. It is particularly suitable for wide-band, high-precision electromagnetic field analysis scenarios, and has significant application value in microwave device design, electromagnetic compatibility assessment, radar scattering calculation and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments with reference to the accompanying drawings, in which: Figure 1 A first flow chart of a method for calculating the frequency domain response of an electromagnetic field provided by an embodiment of the present invention; Figure 2 A second flow chart of a method for calculating the frequency domain response of an electromagnetic field provided by an embodiment of the present invention; Figure 3 A third flow chart of a method for calculating the frequency domain response of an electromagnetic field provided by an embodiment of the present invention; Figure 4 A fourth flow chart of a method for calculating the frequency domain response of an electromagnetic field provided by an embodiment of the present invention; Figure 5 A fifth flow chart of a method for calculating the frequency domain response of an electromagnetic field provided by an embodiment of the present invention; Figure 6 A sixth flow chart of a method for calculating the frequency domain response of an electromagnetic field provided by an embodiment of the present invention; Figure 7 A seventh flow chart of a method for calculating the frequency domain response of an electromagnetic field provided by an embodiment of the present invention; Figure 8 A schematic structural diagram of a device for calculating the frequency domain response of an electromagnetic field provided by an embodiment of the present invention; Figure 9 A schematic structural diagram of a device for calculating the frequency domain response of an electromagnetic field provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0016] The terms "first," "second," "third," "fourth," and so on (if any) in the description and claims of the present invention and in the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a particular order or precedence. It should be understood that the terms used in this manner are interchangeable where appropriate, so that the embodiments described herein can be implemented in an order other than that shown or described herein. In addition, the terms "including" or "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus that includes a series of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, product, or apparatus.

[0017] For ease of understanding, the specific process of the embodiment of the present invention is described below. Figure 1 , an embodiment of a method for calculating the frequency domain response of an electromagnetic field in an embodiment of the present invention includes: 101. Obtain electromagnetic characteristics, electric field strength values ​​and source current density; In this embodiment, the electromagnetic properties include dielectric constant ε, magnetic permeability μ, electrical conductivity σ, etc., which are obtained from the material database; 102. Generate a time zone according to a preset initial time and a preset end time; 103. The basic system equation in the time domain is constructed based on the electromagnetic characteristics, electric field strength value, source current density and time region; In this embodiment, the time domain basic system equation is an equation that describes the evolution law of the electromagnetic field-circuit coupling system in the time domain. It is constructed based on electromagnetic properties (such as dielectric constant ε, magnetic permeability μ, conductivity σ, etc.), electric field intensity value, source current density and time region. By reasonably discretizing and matrixing these parameters, a coefficient matrix, a variable column matrix, a constant matrix and a right-side column matrix are generated, and then the time domain basic system equation is constructed; in the process of equation construction, reasonable discretization and matrixing are used to pave the way for subsequent backward Euler method recursion and algebraic matrix equation solution, and the continuous problem is converted into a discrete form suitable for numerical calculation in advance, thereby reducing subsequent redundant calculations and improving calculation efficiency; 104. Decompose the time region to obtain a discrete time domain set; 105. According to the discrete time domain set and the backward Euler method, the basic system equations in the time domain are recursively transformed to obtain the time domain transformation equation and the algebraic matrix equation; In this embodiment, the time domain basic system equation is the original time domain description of the electromagnetic field-circuit coupling system, which integrates various characteristic parameters and excitation source information of the system; and the time domain transformation equation is an equation obtained by recursive transformation based on the discrete time domain set and the backward Euler method on the basis of the time domain basic system equation; the time domain transformation equation is used to transform the continuous time domain problem into a discrete form so that it can be solved by numerical calculation methods later. For example, the time domain transformation equation (such as formula (1)) obtained after discretization by the backward Euler method introduces the time step , will be the moment and , and prepare for the subsequent back-substitution solution operation; The expression of the time domain transformation equation is: (1) Where, and Separate moments and Solution; time step ;Discrete-time domain sets can be discretized using the backward Euler method; The expression of the algebraic matrix equation is: (2); In the formula, the matrix It is a constant matrix of appropriate dimensions related to the eddy current area in the magnetic field and the energy storage elements such as inductance and capacitance in the circuit, matching the dimension of the system variable column matrix {x}; the coefficient matrix In a linear system, it is usually a constant (electromagnetic properties, electric field strength and source current density) and does not change with time; the right column matrix Corresponding to excitation sources such as voltage source and current source; it can also be understood as an excitation vector that changes with time. When ; 106. Perform back substitution on the algebraic matrix equation according to the time-domain stepping method and the time-domain transformation equation to obtain the time-domain finite element solution; In this embodiment, the algebraic matrix equation is solved by back-substitution through the time domain stepping method to obtain the time domain finite element solution of the kth step under unit step excitation: Equation (2) is solved by the time-stepping method in the time domain. According to Equation (1), the following algebraic matrix equation needs to be solved at each time step. In the initial time step, the coefficient matrix is ​​factored only once. In subsequent time steps, since only the solution of each step needs to be solved by back substitution, after the time-domain finite element solution is obtained by solving Equation (2), no finite element calculation is required in subsequent steps, thus significantly saving computation time. 107. Based on the time-domain finite element method, the full time-domain response calculation is performed on the time-domain finite element solution to obtain the time-domain basic solution; In this embodiment, the time domain basic solution is calculated to capture the full frequency domain information of the system and provide basic data for subsequent frequency domain analysis; 108. Calculate the time domain basis solution according to the preset linear superposition principle to obtain the frequency domain response; In this embodiment, the time domain basis solution stored in step 107 is subjected to phase weighting and addition and subtraction operations by the linear superposition principle to quickly synthesize the frequency domain response of any frequency, thereby avoiding repeated calculations of frequency-by-frequency solutions. In this embodiment, by constructing the basic system equation in the time domain and adopting the backward Euler method recursive transformation, the continuous problem is discretized into an algebraic matrix equation. The coefficient matrix only needs to be factorized once, and the subsequent time steps are quickly solved through back substitution operations, which significantly reduces redundant calculations. The calculation of the time domain basis solution captures the full frequency domain information of the system and provides core data support for frequency domain analysis. Based on the principle of linear superposition, the time domain basis solution is phase-weighted and synthesized to quickly obtain the frequency domain response of any frequency, avoiding repeated calculations of frequency-by-frequency solutions in the frequency domain and improving computing efficiency. It is especially suitable for wide-band, high-precision electromagnetic field analysis scenarios and has significant application value in microwave device design, electromagnetic compatibility assessment, radar scattering calculation and other fields.

[0018] See also Figure 2 In a second embodiment of a method for calculating a frequency domain response of an electromagnetic field according to an embodiment of the present invention, step 103 includes: 201. Generate a coefficient matrix based on electromagnetic characteristics, electric field strength values ​​and source current density; 202. Obtain the magnetic field potential value and the circuit current value, and generate a variable column matrix according to the time zone, the magnetic field potential value and the circuit current value; 203. Obtain the magnetic field eddy current area and the energy storage element coefficient, and construct a constant matrix based on the magnetic field eddy current area and the energy storage element coefficient; In this embodiment, a constant matrix describing the inherent characteristics of the system is generated based on the eddy current area of ​​the magnetic field (distribution of the conductive medium) and the coefficients of the energy storage elements (such as inductance and capacitance), reflecting the coupling relationship between the electromagnetic field and the circuit; 204. Obtain a current excitation source and a voltage excitation source, and generate a right column matrix according to the current excitation source and the voltage excitation source; 205. The basic system equation in the time domain is constructed according to the coefficient matrix, variable column matrix, constant matrix and right column matrix; In this embodiment, due to the existence of eddy currents in the electromagnetic field, the basic system equation in the time domain can be expressed as the following time domain initial value problem: (3) Where, is a variable column matrix containing the magnetic field potential and the current in the circuit. to interval (the interval is large enough, The solution is considered to have reached a steady state when ); the time domain basic system equation describes the time domain evolution law of the electromagnetic field-circuit coupling system; In this embodiment, by decomposing the electromagnetic characteristics, field quantity parameters and excitation sources into a coefficient matrix, a variable column matrix, a constant matrix and a right-hand column matrix, a standard form of the time domain basic system equation is constructed, and the modular matrix design supports the natural coupling of the electromagnetic field and the circuit; the pre-calculation characteristics of the coefficient matrix and the constant matrix, combined with the sparse storage technology, significantly reduce memory usage and improve computing efficiency; the modeling of eddy current areas and energy storage elements improves the computational accuracy of scenarios such as transient analysis of power equipment and electromagnetic compatibility simulation; compared with the existing technology, this solution achieves orders of magnitude improvement in computing efficiency, memory optimization and multi-field compatibility, and is particularly suitable for the efficient solution of large-scale electromagnetic-circuit coupling systems.

[0019] See also Figure 3 In a third embodiment of a method for calculating a frequency domain response of an electromagnetic field according to an embodiment of the present invention, step 202 includes: 301. Perform dimensional analysis on the time region to obtain the time dimension; In this embodiment, dimensional analysis is performed on the time domain to discretize continuous time into quantized time dimensions (such as time steps and the number of time nodes), providing a benchmark scale for subsequent time evolution analysis of field quantities and circuit parameters. 302. Generate a magnetic field potential dimension according to the magnetic field potential value and the time dimension; In this embodiment, the magnetic field potential value reflects the magnetic field energy distribution and the magnetic field potential dimension (including the characteristics of the potential amplitude and phase changing with time); 303. Correcting the magnetic field potential dimension according to a preset magnetic field potential dimension threshold to obtain a corrected potential dimension; In this embodiment, the magnetic field potential dimension is corrected based on a preset threshold (such as the upper limit of potential fluctuation, the physical rationality boundary), and abnormal values ​​(such as local overshoot caused by eddy current effect) are eliminated to obtain a corrected potential dimension; 304. Generate a magnetic field potential matrix according to the corrected potential dimension; In this embodiment, the modified potential dimension is converted into a structured magnetic field potential matrix to achieve recording of the distribution characteristics of the magnetic field potential in the entire time domain; 305. Generate a circuit current dimension according to the circuit current value and the time dimension; In this embodiment, the circuit current value is used to reflect the dynamic characteristics of the circuit. The circuit current dimension includes the change pattern of the current amplitude and frequency over time; 306. Correct the circuit current dimension according to a preset circuit current dimension threshold to obtain a corrected current dimension; In this embodiment, the circuit current dimension is corrected based on a preset threshold (such as a current safety limit, a circuit component rated parameter), and invalid fluctuations (such as non-physical peaks caused by transient impacts) are filtered to obtain a corrected current dimension; 307. Generate a magnetic field current matrix according to the corrected current dimension; In this embodiment, the corrected current dimension is converted into a circuit current matrix to record the changing characteristics of the circuit current in the entire time domain; 308. Generate a variable column matrix based on the magnetic field potential matrix and the magnetic field current matrix; In this embodiment, the magnetic field potential matrix and the circuit current matrix are aligned according to the time dimension and integrated into a variable column matrix, which uniformly contains the key variable information of the magnetic field and the circuit; In this embodiment, a dimensional analysis is performed on the time domain, and the continuous time is discretized into quantitative dimensions such as time steps and number of nodes, providing a benchmark for the time evolution of field quantities and circuit parameters; the time dimension is combined to generate the magnetic field potential dimension and the circuit current dimension, which respectively reflect the magnetic field energy distribution and the circuit dynamic characteristics, and then corrected by a preset threshold to eliminate outliers, converted into a structured matrix, and finally integrated into a column matrix containing key variables of the magnetic field and circuit; this scheme improves modeling accuracy through threshold correction, reduces data conversion time through matrix integration, realizes natural coupling of field-circuit variables, and provides high-quality input for subsequent solution of time-domain system equations. It is suitable for complex coupling analysis such as high-frequency eddy current scenarios, and has significant engineering practicality.

[0020] See also Figure 4 In a fourth embodiment of a method for calculating a frequency domain response of an electromagnetic field according to an embodiment of the present invention, step 106 includes: 401. Perform type conversion on electromagnetic characteristics, electric field intensity values ​​and source current density according to the time domain transformation equation to obtain the current load vector; In this embodiment, the load vector is used as the input of the equation, integrating all excitation and field information of the current time step to ensure compatibility with the format of the algebraic matrix equation. The field information is obtained by converting electromagnetic properties and electric field strength values. The core features of the field information include the dielectric constant ε, magnetic permeability μ, electrical conductivity σ, the electric field strength amplitude E, and the electric field direction vector. 402. Perform back substitution on the algebraic matrix equation based on the time-domain stepping method and the current load vector to obtain an initial finite element solution; In this embodiment, the current load vector integrates the electromagnetic characteristic parameters, electric field strength value and source current density information at the current moment, and is converted according to the rules of the time domain transformation equation to obtain a vector form compatible with the algebraic matrix equation format for subsequent back substitution solution operations to ensure the accuracy and consistency of the equation solution; {P}: right column matrix (generated by the current excitation source and voltage excitation source, which is the "external excitation input" of the system), and the "current load vector" corresponds to the "right column matrix of the current time step "(subscript k represents the kth time step) is the external excitation parameter that drives the state change of the system at this time step. The core operation of the time-domain stepping method is to use the time-domain finite element solution of the previous time step to derive the recursive logic of the current time step solution. Combined with the current load vector, the algebraic matrix equation is back-substituted to solve and obtain the initial finite element solution, avoiding the redundant calculation of repeated matrix decomposition in the frequency-by-frequency solution. 403. Generate boundary conditions according to a preset initial moment and a preset system state vector; In this embodiment, the boundary conditions include electromagnetic field boundary constraints (ensuring that the electromagnetic field at the boundary matches the initial state), current and magnetic field association constraints (ensuring the consistency of the circuit current and the boundary magnetic field), and time initial constraints (avoiding sudden changes or contradictions in the solution at the time starting point). 404. Constraining the initial finite element solution according to the boundary conditions to obtain a time-domain finite element solution; In this embodiment, the time-domain finite element solution bridges the gap between the mathematical solution and the physical reality, avoiding numerical oscillations or solution distortion caused by missing boundary conditions; In this embodiment, the electromagnetic characteristics, field quantities and source parameters (the source parameters are the source current density (such as the current density amplitude, distribution vector, time-domain variation of the amplitude of the current excitation source, and the equivalent voltage excitation corresponding to the current excitation)) are converted into the current load vector through the time-domain transformation equation, and the current time step excitation and field quantity information are integrated to ensure compatibility with the algebraic matrix equation format and avoid time-consuming data format conversion; based on the recursive logic of the time-domain stepping method, the algebraic matrix equation is back-substituted and solved in combination with the load vector, and the initial matrix decomposition results are reused, eliminating the repeated decomposition steps of frequency-by-frequency solution and improving computational efficiency; at the same time, multiple boundary constraints are generated through the initial moment and the system state vector, and the initial solution is corrected to match physical reality, avoiding numerical oscillation and solution distortion, and ensuring the physical rationality of the solution. This scheme takes into account both efficiency and accuracy, is suitable for time-domain analysis of complex electromagnetic fields, lays a high-quality data foundation for wide-band response calculations, and has significant engineering practical value.

[0021] See also Figure 5 In a fifth embodiment of a method for calculating a frequency domain response of an electromagnetic field according to an embodiment of the present invention, step 107 includes: 501. The magnetic field and circuit coupling model is constructed based on the time domain finite element method; In this embodiment, the model incorporates both Maxwell's equations for electromagnetic fields (describing magnetic field energy distribution, eddy current effects, etc.) and Kirchhoff's laws for circuits (describing the conduction patterns of current and voltage), achieving dynamic coupling between the two. This overcomes the limitations of independent analysis of magnetic fields and circuits, characterizing the coupling mechanism whereby changes in the magnetic field generate induced currents, and changes in current react on the magnetic field. This provides a physically consistent model foundation for subsequent excitation response calculations. 502. Obtain an original sinusoidal voltage source, and construct a unit step function based on the magnetic field and circuit coupling model and the original sinusoidal voltage source; In this embodiment, the specific form of the unit step function is: the mathematical expression of the unit step function is: ,in is the step moment (the value is consistent with the initial moment of the basic system equation in the time domain ), the function value "1" corresponds to the excitation of unit amplitude; The relationship between the unit step function and the original sinusoidal voltage source: The original sinusoidal voltage source expression is , ( is the amplitude, is the angular frequency); The unit step function is a universal excitation in the full frequency domain. Its spectrum covers all frequencies. A "time domain basis solution" containing full frequency domain information can be obtained through a single time domain calculation. The original sinusoidal voltage source is a single-frequency target excitation, and its response can be synthesized from the time-domain basis solution using the linear superposition principle (decomposing the sine wave into a weighted sum of square waves, which are obtained by taking the difference of step functions). Ultimately, a single calculation covers multiple frequency responses, overcoming the efficiency bottleneck of the traditional frequency-domain method of frequency-by-frequency solution. 503. Perform full time domain response calculation on the time domain finite element solution according to the unit step function to obtain the time domain basis solution; In this embodiment, the core of the “full time domain response calculation” is to convert “time-step-by-time (time domain basic solution)" is integrated according to the time dimension to form a "complete response sequence of the system to unit step excitation in the entire time domain", that is, "time domain basic solution: The form of the time domain basic solution is a "time-response" sequence: with time step k as the horizontal axis (corresponding to the actual time t=k×Δt), The key components (such as the magnetic field potential amplitude and circuit current amplitude) in the (time domain basic solution) are the vertical axis, forming a continuous time domain response curve; In this embodiment, the frequency spectrum of the unit step function covers the entire frequency domain. By solving the full time domain response under a single excitation, rather than independently modeling each frequency point, only one time domain solution is required to obtain the potential response of all frequency points. In this embodiment, by constructing a magnetic field and circuit coupling model and using unit step function excitation, efficient acquisition of full-frequency domain response is achieved, and the original sinusoidal voltage source is converted into a unit step function. Its full spectrum characteristics make its excitation response contain potential information of all frequency points; based on this function, the time domain finite element solution is calculated in the full time domain, and the time domain basic solution is obtained in one solution, replacing independent modeling and solution for each frequency, reducing redundant calculations, and improving the efficiency of broadband analysis. It is suitable for broadband design of strongly coupled systems such as transformers and wireless charging, and has significant application value.

[0022] See also Figure 6 In a sixth embodiment of a method for calculating a frequency domain response of an electromagnetic field according to an embodiment of the present invention, step 108 includes: 601. Decomposing the unit step function to obtain multiple step functions; 602. Performing adjacent function difference calculation on the plurality of step functions to obtain a plurality of square wave functions; In this embodiment, the expression of the step function is: ( is the subscript for the time step count, is the time step), indicating that "at time Then maintain the unit amplitude excitation"; Square wave function Equal to two adjacent step functions and The difference is: (4) Where, the time step is Used as the pulse width of the square wave function; the square wave is a basic signal with clear frequency domain characteristics, providing a building block for synthesizing arbitrary waveforms; the square wave function is the difference between two adjacent step functions, and its physical meaning is "in the time interval The square wave function is the differential form of the step function. The sine wave can be formed by superimposing multiple square waves with different weights, providing the basis for subsequent frequency domain response calculations. 603. Constructing a sine source function according to multiple square wave functions and multiple step functions; In this embodiment, the expression of the sine source function is: (5) Where K is the maximum value of the count subscript, is the angular frequency system; 604. Calculate the time domain basis solution according to the linear superposition principle and the sinusoidal source function to obtain the sinusoidal source excitation; Specific calculation steps for sinusoidal source excitation: Step 1: Find the response of the square wave function The time domain basis solution is a step function The response of ), according to the linear superposition principle, the square wave function The response is: (i.e., the difference between adjacent step responses), is a square wave response; Step 2: Find the response of the sine source function Sine source function ,in For the The amplitude weights of the square waves are given, so the sinusoidal source excitation (the response of the sinusoidal source) is: (i.e., square wave responses are weighted and summed, is the sinusoidal source response; In this embodiment, since the solution of the step function has been obtained by the time-domain finite element method, according to the linear superposition principle, the solution of the sinusoidal source excitation can be quickly obtained by adding and subtracting the step function solution; avoiding directly solving the system response under sinusoidal excitation, and reusing the existing basic solution to reduce the amount of calculation; 605. Generate a frequency domain response based on the sinusoidal source excitation; In this embodiment, based on the principle of linear system superposition, the time domain basis solution is used to quickly synthesize the frequency domain response of any frequency through simple addition and subtraction operations, replacing the inefficient mode of traditional frequency-by-frequency matrix solution. There is no need to perform matrix inversion or iterative solution for each frequency point, breaking through the efficiency bottleneck of frequency-by-frequency calculation in traditional frequency domain methods. In this embodiment, the unit step function is decomposed into multiple step functions, and a square wave function is obtained by taking adjacent differences. The clear frequency domain characteristics of the square wave are used as a waveform synthesis unit to construct a sinusoidal source function. Based on the principle of linear superposition, the existing time domain basis solution is reused, and the sinusoidal source excitation is quickly obtained through addition and subtraction operations of the step function solution, avoiding redundant calculations of direct solution. When the frequency domain response is finally generated, there is no need to perform matrix inversion or iteration frequency by frequency. This solution significantly reduces the overall computational complexity, and the sinusoidal waveform approximation error is controllable. It is suitable for wide-band electromagnetic field analysis and has outstanding engineering value in scenarios such as radar and filter design, taking into account both efficiency and accuracy.

[0023] See also Figure 7 In a seventh embodiment of a method for calculating a frequency domain response of an electromagnetic field according to an embodiment of the present invention, step 601 includes: 701. Calculating a plurality of time steps based on a discrete time domain set; In this embodiment, the continuous time domain is converted into a discrete step sequence to provide an initial benchmark for subsequent adaptive adjustment; 702. Perform characteristic analysis on the eddy current region of the magnetic field to obtain the electromagnetic field change rate; 703. Smoothing the multiple time steps according to the electromagnetic field change rate to obtain multiple smoothed time steps; In this embodiment, dynamic matching of the time step and the physical field change is achieved, redundant steps in the flat area are reduced, and accuracy and efficiency are balanced; 704. Decompose the unit step function according to multiple smoothing time steps to obtain multiple step functions; In this embodiment, the unit step function is decomposed so that the decomposed step function is distributed as needed in terms of time resolution, making the step function interval smaller (capturing high-frequency details) and the smooth area interval larger (reducing redundancy), providing a more accurate time grid for subsequent square wave synthesis and sine source function construction; In this embodiment, the continuous time domain is converted into a discrete step sequence, and then the time step is smoothed based on the electromagnetic field change rate obtained by the analysis of the magnetic field eddy current area characteristics. The step size in the narrow area is reduced to capture high-frequency details, and the step size in the flat area is enlarged to reduce redundancy. The unit step function is decomposed based on the smooth step size, and the step function interval is allocated on demand, providing a more accurate time grid for subsequent square wave synthesis and sinusoidal source construction, adapting to complex eddy current scenarios, and laying a high-quality foundation for frequency domain response calculation, with significant engineering practical value.

[0024] The above describes a method for calculating the frequency domain response of an electromagnetic field in an embodiment of the present invention. The following describes a device for calculating the frequency domain response of an electromagnetic field in an embodiment of the present invention. Figure 8 In one embodiment of the present invention, a device for calculating the frequency domain response of an electromagnetic field includes: Data acquisition module 1, used to obtain electromagnetic characteristics, electric field strength values ​​and source current density; A time zone generating module 2 is configured to generate a time zone according to a preset initial time and a preset end time; Equation construction module 3, used for constructing a time domain basic system equation according to electromagnetic characteristics, electric field intensity value, source current density and time region; The time domain decomposition module 4 is used to decompose the time domain to obtain a discrete time domain set; A recursive module 5 is used to perform recursive transformation on the time domain basic system equation according to the discrete time domain set and the backward Euler method to obtain the time domain transformation equation and the algebraic matrix equation; A solution operation module 6 is used to perform back substitution solution operation on the algebraic matrix equation according to the time domain stepping method and the time domain transformation equation to obtain a time domain finite element solution; A time domain basic solution module 7 is used to perform full time domain response calculation on the time domain finite element solution based on the time domain finite element method to obtain a time domain basic solution; The frequency domain response module 8 is used to calculate the time domain basis solution according to a preset linear superposition principle to obtain the frequency domain response; In this embodiment, by constructing the basic system equation in the time domain and adopting the backward Euler method recursive transformation, the continuous problem is discretized into an algebraic matrix equation. The coefficient matrix only needs to be factorized once, and the subsequent time steps are quickly solved through back substitution operations, which significantly reduces redundant calculations. The calculation of the time domain basis solution captures the full frequency domain information of the system and provides core data support for frequency domain analysis. Based on the principle of linear superposition, the time domain basis solution is phase-weighted and synthesized to quickly obtain the frequency domain response of any frequency, avoiding repeated calculations of frequency-by-frequency solutions in the frequency domain and improving computing efficiency. It is especially suitable for wide-band, high-precision electromagnetic field analysis scenarios and has significant application value in microwave device design, electromagnetic compatibility assessment, radar scattering calculation and other fields.

[0025] Figure 9 This is a schematic diagram of the structure of a device for calculating the frequency domain response of an electromagnetic field, provided in an embodiment of the present invention. Device 900 for calculating the frequency domain response of an electromagnetic field may vary significantly depending on configuration or performance. It may include one or more processors (central processing units, CPUs) 910 (e.g., one or more processors), memory 920, and one or more storage media 930 (e.g., one or more mass storage devices) storing application programs 933 or data 932. Memory 920 and storage medium 930 may be either transient or persistent storage. The program stored in storage medium 930 may include one or more modules (not shown), each of which may include a series of instructions for calculating the frequency domain response of an electromagnetic field in device 900. Furthermore, processor 910 may be configured to communicate with storage medium 930, executing the series of instructions stored in storage medium 930 on device 900 to implement the steps of the method for calculating the frequency domain response of an electromagnetic field, as provided in the aforementioned method embodiments.

[0026] An electromagnetic field frequency domain response calculation device 900 may also include one or more power supplies 940, one or more wired or wireless network interfaces 950, one or more input and output interfaces 960, and / or one or more operating systems 931, such as Windows Server, Mac OS X, Unix, Linux, FreeBSD, etc. It will be understood by those skilled in the art that Figure 9 The structure of the device for calculating the frequency domain response of an electromagnetic field shown does not limit the device for calculating the frequency domain response of an electromagnetic field, and the device may include more or fewer components than shown in the figure, or combine certain components, or arrange components differently.

[0027] The present invention also provides a computer-readable storage medium, which may be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium. The computer-readable storage medium stores instructions that, when executed on a computer, cause the computer to execute the steps of a method for calculating the frequency domain response of an electromagnetic field.

[0028] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described systems, devices, and units can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0029] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program code, such as a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0030] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for calculating the frequency domain response of an electromagnetic field, characterized in that: include: Obtain electromagnetic properties, electric field strength values, and source current density; Generate a time zone according to a preset initial time and a preset end time; The basic system equation in time domain is constructed based on electromagnetic characteristics, electric field intensity value, source current density and time region; Decompose the time region to obtain a set of discrete time domains; According to the discrete time domain set and the backward Euler method, the basic system equations in the time domain are recursively transformed to obtain the time domain transformation equations and algebraic matrix equations; The algebraic matrix equation is back-substituted and solved according to the time-domain stepping method and the time-domain transformation equation to obtain the time-domain finite element solution; Perform full time domain response calculation on the time domain finite element solution based on the time domain finite element method to obtain the time domain basic solution; The time domain basis solution is calculated according to the preset linear superposition principle to obtain the frequency domain response.

2. The method for calculating the frequency domain response of an electromagnetic field according to claim 1, wherein: The time domain basic system equation is constructed based on the electromagnetic characteristics, electric field strength value, source current density and time region, including: generating a coefficient matrix based on electromagnetic characteristics, electric field strength values, and source current density; Obtaining magnetic field potential values ​​and circuit current values, and generating a variable column matrix according to the time region, magnetic field potential values, and circuit current values; Obtaining the magnetic field eddy current area and the energy storage element coefficient, and constructing a constant matrix according to the magnetic field eddy current area and the energy storage element coefficient; Obtain a current excitation source and a voltage excitation source, and generate a right column matrix according to the current excitation source and the voltage excitation source; The basic system equation in the time domain is constructed according to the coefficient matrix, variable column matrix, constant matrix and right-hand column matrix.

3. The method for calculating the frequency domain response of an electromagnetic field according to claim 2, wherein: The generating of the variable column matrix according to the time zone, the magnetic field potential value and the circuit current value includes: Perform dimensional analysis on the time region to obtain the time dimension; Generate magnetic field potential dimension according to magnetic field potential value and time dimension; Correcting the magnetic field potential dimension according to a preset magnetic field potential dimension threshold to obtain a corrected potential dimension; Generate magnetic field potential matrix according to the corrected potential dimension; generating a circuit current dimension according to the circuit current value and the time dimension; Correcting the circuit current dimension according to a preset circuit current dimension threshold to obtain a corrected current dimension; Generate a magnetic field current matrix based on the corrected current dimension; Generate a variable column matrix based on the magnetic field potential matrix and the magnetic field current matrix.

4. The method for calculating the frequency domain response of an electromagnetic field according to claim 1, wherein: The back-substitution operation of the algebraic matrix equation according to the time-domain stepping method and the time-domain transformation equation to obtain a time-domain finite element solution includes: According to the time domain transformation equation, the electromagnetic characteristics, electric field strength values ​​and source current density are converted to obtain the current load vector; Perform back-substitution on the algebraic matrix equations based on the time-domain stepping method and the current load vector to obtain the initial finite element solution; Generate boundary conditions based on a preset initial moment and a preset system state vector; The initial finite element solution is constrained according to the boundary conditions to obtain the time domain finite element solution.

5. The method for calculating the frequency domain response of an electromagnetic field according to claim 2, wherein: The full time-domain response calculation of the time-domain finite element solution based on the time-domain finite element method to obtain the time-domain basic solution includes: The magnetic field and circuit coupling model is constructed based on the time domain finite element method; Obtain an original sinusoidal voltage source, and construct a unit step function based on the magnetic field and circuit coupling model and the original sinusoidal voltage source; The full time domain response of the time domain finite element solution is calculated according to the unit step function to obtain the time domain basic solution.

6. The method for calculating the frequency domain response of an electromagnetic field according to claim 5, wherein: The time domain basis solution is calculated according to a preset linear superposition principle to obtain a frequency domain response, including: Decomposing the unit step function to obtain multiple step functions; Performing difference calculation on adjacent functions of multiple step functions to obtain multiple square wave functions; A sine source function is constructed based on multiple square wave functions and multiple step functions; The time domain basis solution is calculated according to the linear superposition principle and the sinusoidal source function to obtain the sinusoidal source excitation; Generates frequency domain responses based on sinusoidal source excitation.

7. The method for calculating the frequency domain response of an electromagnetic field according to claim 6, wherein: The unit step function is decomposed to obtain multiple step functions, including: Multiple time steps are calculated based on the discrete time domain set; Conduct characteristic analysis on the eddy current area of ​​the magnetic field to obtain the rate of change of the electromagnetic field; Smoothing multiple time steps according to the rate of change of the electromagnetic field to obtain multiple smoothed time steps; The unit step function is decomposed according to a number of smoothing time steps to obtain multiple step functions.

8. A device for calculating the frequency domain response of an electromagnetic field, characterized in that: include: A data acquisition module is used to obtain electromagnetic characteristics, electric field strength values ​​and source current density; A time zone generation module, configured to generate a time zone according to a preset initial time and a preset end time; Equation construction module, used to construct the basic system equation in the time domain according to electromagnetic characteristics, electric field strength value, source current density and time region; The time domain decomposition module is used to decompose the time domain to obtain a discrete time domain set; A recursive module is used to perform recursive transformation on the time domain basic system equations according to the discrete time domain set and the backward Euler method to obtain the time domain transformation equations and the algebraic matrix equations; A solution operation module is used to perform back substitution solution operation on the algebraic matrix equation according to the time domain stepping method and the time domain transformation equation to obtain a time domain finite element solution; The time domain basic solution module is used to perform full time domain response calculation on the time domain finite element solution based on the time domain finite element method to obtain the time domain basic solution; The frequency domain response module is used to calculate the time domain basis solution according to the preset linear superposition principle to obtain the frequency domain response.

9. A device for calculating the frequency domain response of an electromagnetic field, characterized in that: The device for calculating the frequency domain response of an electromagnetic field comprises: a memory and at least one processor, wherein the memory stores instructions; At least one of the processors calls the instructions in the memory to enable the device for calculating the frequency domain response of an electromagnetic field to perform each step of the method for calculating the frequency domain response of an electromagnetic field according to any one of claims 1 to 7.

10. A computer-readable storage medium having instructions stored thereon, characterized in that: When the instructions are executed by a processor, the various steps of the method for calculating the frequency domain response of an electromagnetic field as claimed in any one of claims 1 to 7 are implemented.

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