A method, device and storage medium for calculating a frequency domain response of an electromagnetic field

Abstract

The present application relates to the technical field of electromagnetic scattering, and particularly relates to a method and device for calculating frequency domain response of electromagnetic field, equipment and storage medium; a time domain basic system equation is recursively transformed according to a discrete time domain set and a backward Euler method to obtain a time domain transformation equation and an algebraic matrix equation; the algebraic matrix equation is back-substituted and solved according to a time domain stepping method and the time domain transformation equation; a time domain finite element solution is calculated based on a time domain finite element method to obtain a time domain base solution; the time domain base solution is calculated according to a preset linear superposition principle to obtain a frequency domain response; a continuous problem is discretized by the backward Euler method, and a fast back-substitution solution is obtained after one factor decomposition to reduce redundant calculation; the time domain base solution is phase-weighted and synthesized based on the linear superposition principle to quickly obtain an arbitrary frequency domain response, avoid repeated calculation for each frequency, improve efficiency, be suitable for wideband high-precision electromagnetic field analysis, and have significant application value.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electromagnetic scattering, and in particular to a method and device for calculating frequency domain response of electromagnetic field, equipment and storage medium. BACKGROUND

[0002] In the prior art, there are two main methods for calculating the frequency domain response of electromagnetic field. One is the frequency domain direct method, which needs to establish a system matrix and solve it independently for each frequency point. The matrix decomposition and solving process is repeated as the number of frequency points increases, and the calculation amount increases linearly. Especially in wideband analysis, the efficiency is very low, and the processing of frequency-varying materials requires repeated modeling, which takes a lot of time. The other is the time domain conversion method, which obtains the frequency response by Fourier transform of the time domain transient response. However, the time step is strictly limited by the CFL condition, and the calculation cost increases dramatically due to the extremely small step for fine structures. At the same time, the truncation of time domain signal can introduce errors, and it is difficult to guarantee the high frequency accuracy. Moreover, the Fourier transform has a large calculation amount for long time domain signals, and is easily disturbed by noise, making it difficult to balance the efficiency and accuracy of multi-frequency analysis. Therefore, the present application proposes a method for calculating the frequency domain response of electromagnetic field to solve the above technical problems. SUMMARY

[0003] In order to overcome the shortcomings of the prior art, the purpose of the present application is to provide a method for calculating the frequency domain response of electromagnetic field, device, equipment and storage medium.

[0004] A method for calculating the frequency domain response of electromagnetic field, comprising: obtaining electromagnetic properties, electric field intensity values and source current density; generating a time region according to a preset initial time and a preset termination time; constructing a time domain basic system equation according to the electromagnetic properties, the electric field intensity values, the source current density and the time region; decomposing the time region to obtain a discrete time domain set; performing recursive transformation on 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; performing back substitution solving operation on the algebraic matrix equation according to the time domain step 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 basis solution; and calculating the time domain basis solution according to a preset linear superposition principle to obtain a frequency domain response.

[0005] Further, the time-domain basic system equation is constructed according to the electromagnetic characteristic, the electric field intensity value, the source current density and the time region, including: generating a coefficient matrix according to the electromagnetic characteristic, the electric field intensity value and the source current density; obtaining a magnetic field potential value and a 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 a magnetic field eddy current region and a storage element coefficient, and constructing a constant matrix according to the magnetic field eddy current region and the storage element coefficient; obtaining a current excitation source and a 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] Further, the variable column matrix is generated according to the time region, the magnetic field potential value and the circuit current value, including: performing dimension analysis on the time region to obtain a time dimension; generating a magnetic field potential dimension according to the magnetic field potential value and the time dimension; correcting the magnetic field potential dimension according to a preset magnetic field potential dimension threshold to obtain a corrected potential dimension; generating a 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; generating a magnetic field current matrix according to the corrected current dimension; and generating the variable column matrix according to the magnetic field potential matrix and the magnetic field current matrix.

[0007] Further, the algebraic matrix equation is back-substituted and solved according to the time-domain step method and the time-domain transformation equation to obtain a time-domain finite element solution, including: type-converting the electromagnetic characteristic, the electric field intensity value and the source current density according to the time-domain transformation equation to obtain a current load vector; back-substituting and solving the algebraic matrix equation according to the time-domain step method and the current load vector to obtain an initial finite element solution; generating a boundary condition according to a preset initial time and a preset system state vector; and performing constraint processing on the initial finite element solution according to the boundary condition to obtain the time-domain finite element solution.

[0008] Further, the time-domain finite element solution is calculated for a full time-domain response based on the time-domain finite element method to obtain a time-domain base solution, including: constructing a magnetic field and circuit coupling model based on the time-domain finite element method;

[0009] An original sinusoidal voltage source is obtained, and a unit step function is constructed according to the magnetic field and circuit coupling model and the original sinusoidal voltage source; the time-domain finite element solution is calculated for a full time-domain response according to the unit step function to obtain the time-domain base solution.

[0010] Furthermore, the step of calculating the time-domain basis solution according to the preset linear superposition principle to obtain the frequency-domain response includes: decomposing the unit step function to obtain multiple step functions; calculating the difference between 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 the sinusoidal source excitation; and generating the frequency-domain response based on the sinusoidal source excitation.

[0011] Furthermore, the decomposition of the unit step function to obtain multiple step functions includes:

[0012] Multiple time steps are calculated based on the discrete time domain set; the electromagnetic field change rate is obtained by performing characteristic analysis on the magnetic field eddy current region; the multiple time steps are smoothed based on the electromagnetic field change rate to obtain multiple smooth time steps; the unit step function is decomposed based on the multiple smooth time steps to obtain multiple step functions.

[0013] 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 based on a preset initial time and a preset termination time; and an equation construction module for constructing a basic time-domain system equation based on the electromagnetic characteristics, electric field strength values, source current density, and time region.

[0014] The time-domain decomposition module decomposes the time domain to obtain a discrete-time domain set; the recursive module performs a recursive transformation on the fundamental time-domain system equations based on the discrete-time domain set and the backward Euler method to obtain the time-domain transformation equations and algebraic matrix equations; the solution module performs a back-substitution operation on the algebraic matrix equations based on the time-domain step method and the time-domain transformation equations to obtain the time-domain finite element solution; the time-domain basis solution module calculates the full-time-domain response of the time-domain finite element solution based on the time-domain finite element method to obtain the time-domain basis solution; and the frequency-domain response module calculates the time-domain basis solution according to the preset linear superposition principle to obtain the frequency-domain response.

[0015] Furthermore, the present invention provides a frequency domain response calculation device for an electromagnetic field, the frequency domain response calculation device for an electromagnetic field comprising: a memory and at least one processor, the memory storing instructions; at least one processor calling the instructions in the memory to cause the computer device to execute the various steps of the frequency domain response calculation method for an electromagnetic field as described above.

[0016] Furthermore, the present invention provides a computer-readable storage medium storing instructions that, when executed by a processor, implement the various steps of the frequency domain response calculation method for an electromagnetic field as described above.

[0017] In the technical solution of this invention, by constructing the basic time-domain system equations and employing the backward Euler method recursive transformation, the continuous problem is discretized into algebraic matrix equations. Only one factorization of the coefficient matrix is ​​required, and subsequent time steps are solved quickly through back substitution operations, significantly reducing redundant calculations. The calculation of the time-domain basic solution captures the full frequency domain information of the system, providing core data support for frequency domain analysis. Based on the principle of linear superposition, phase-weighted synthesis of the time-domain basic solution can quickly obtain the frequency domain response of any frequency, avoiding repetitive calculations of frequency-by-frequency solutions in the frequency domain and improving computational efficiency. It is particularly suitable for wideband, high-precision electromagnetic field analysis scenarios and has significant application value in microwave device design, electromagnetic compatibility assessment, radar scattering calculation, and other fields. Attached Figure Description

[0018] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0019] Figure 1 A first flowchart of a method for calculating the frequency domain response of an electromagnetic field provided in an embodiment of the present invention;

[0020] Figure 2 A second flowchart of a method for calculating the frequency domain response of an electromagnetic field provided in an embodiment of the present invention;

[0021] Figure 3 A third flowchart of a method for calculating the frequency domain response of an electromagnetic field provided in an embodiment of the present invention;

[0022] Figure 4 A fourth flowchart of a method for calculating the frequency domain response of an electromagnetic field provided in an embodiment of the present invention;

[0023] Figure 5 A fifth flowchart of a method for calculating the frequency domain response of an electromagnetic field provided in an embodiment of the present invention;

[0024] Figure 6 A sixth flowchart of a method for calculating the frequency domain response of an electromagnetic field provided in an embodiment of the present invention;

[0025] Figure 7 A seventh flowchart of a method for calculating the frequency domain response of an electromagnetic field provided in an embodiment of the present invention;

[0026] Figure 8 A schematic diagram of the structure of a frequency domain response calculation device for an electromagnetic field provided in an embodiment of the present invention;

[0027] Figure 9 This is a schematic diagram of the structure of a frequency domain response calculation device for an electromagnetic field, provided as an embodiment of the present invention. Detailed Implementation

[0028] The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0029] For ease of understanding, the specific process of the embodiments of the present invention is described below. Please refer to [link / reference]. Figure 1 One embodiment of the frequency domain response calculation method for an electromagnetic field in this invention includes:

[0030] 101. Obtain electromagnetic properties, electric field strength values, and source current density;

[0031] In this embodiment, the electromagnetic properties, including dielectric constant ε, magnetic permeability μ, and electrical conductivity σ, are derived from a materials database.

[0032] 102. Generate a time range based on a preset initial time and a preset end time;

[0033] 103. Based on the electromagnetic properties, electric field strength, source current density, and time region, the basic time-domain system equations are constructed.

[0034] In this embodiment, the fundamental time-domain system equations describe the evolution of the electromagnetic field-circuit coupled system in the time domain. These equations are constructed based on electromagnetic properties (such as permittivity ε, permeability μ, conductivity σ, etc.), electric field strength, source current density, and the time region. By reasonably discretizing and matrixing these parameters, coefficient matrices, variable column matrices, constant matrices, and right-hand column matrices are generated, thus constructing the fundamental time-domain system equations. During the equation construction process, reasonable discretization and matrixing lay the groundwork for subsequent backward Euler recursion and algebraic matrix equation solving, transforming the continuous problem into a discrete form suitable for numerical computation in advance, reducing subsequent redundant calculations, and improving computational efficiency.

[0035] 104. Decompose the time region to obtain a set of discrete time domains;

[0036] 105. Based on the discrete-time domain set and the backward Euler method, perform a recursive transformation on the basic system equations in the time domain to obtain the time-domain transformation equations and algebraic matrix equations.

[0037] In this embodiment, the fundamental time-domain system equation is the original time-domain description of the electromagnetic field-circuit coupled system, which integrates various characteristic parameters and excitation source information of the system; while the time-domain transformation equation is the equation obtained by recursively transforming the fundamental time-domain system equation according to the discrete time-domain set and the backward Euler method; 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. For example, the time-domain transformation equation obtained by discretization by the backward Euler method (as shown in formula (1)) introduces the time step. , will be the moment and The solutions are linked together to prepare for subsequent back-substitution calculations;

[0038] The expression for the time-domain transformation equation is:

[0039] (1)

[0040] In the formula, and They are time points and Solution; time step Discrete-time domain sets can be discretized using the backward Euler method.

[0041] The expression for the algebraic matrix equation is:

[0042] (2);

[0043] In the formula, the matrix It is an appropriate dimension constant matrix related to the eddy current region in the magnetic field and energy storage elements such as inductors and capacitors in the circuit, matching the dimension of the system variable column matrix {x}; coefficient matrix In linear systems, these are typically constants (electromagnetic properties, electric field strength, and source current density), and do not change with time; the right-hand column matrix... This corresponds to excitation sources such as voltage and current sources; it can also be understood as an excitation vector that changes with time. When, it is represented as ;

[0044] 106. The algebraic matrix equation is solved by back substitution using the time-domain step method and the time-domain transformation equation to obtain the time-domain finite element solution.

[0045] In this embodiment, the algebraic matrix equation is solved by back substitution using the time-domain step method to obtain the time-domain finite element solution for the k-th step under unit step excitation. Equation (2) is solved by the time step 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 the solution of each step only needs to be solved by back substitution, after obtaining the time domain finite element solution by solving equation (2), there is no need to perform finite element calculation in subsequent steps, thus significantly saving computation time.

[0046] 107. Calculate the full-time response of the time-domain finite element solution based on the time-domain finite element method to obtain the time-domain fundamental solution;

[0047] In this embodiment, the time-domain basis solution is calculated to capture the full frequency domain information of the system, providing basic data for subsequent frequency domain analysis;

[0048] 108. Calculate the time-domain fundamental solution according to the preset linear superposition principle to obtain the frequency-domain response;

[0049] In this embodiment, the time-domain basic solution stored in step 107 is subjected to phase weighting and addition / subtraction operations by the principle of linear superposition, so as to quickly synthesize the frequency domain response of arbitrary frequency and avoid repeated calculations of frequency-by-frequency solution.

[0050] In this embodiment, by constructing the fundamental time-domain system equations and employing the backward Euler method recursive transformation, the continuous problem is discretized into algebraic matrix equations. Only one factorization of the coefficient matrix is ​​required, and subsequent time steps are solved quickly through back substitution, significantly reducing redundant calculations. The calculation of the fundamental time-domain solution captures the full frequency domain information of the system, providing core data support for frequency domain analysis. Based on the principle of linear superposition, phase-weighted synthesis of the fundamental time-domain solution can quickly obtain the frequency domain response at any frequency, avoiding repetitive calculations of frequency-by-frequency solutions in the frequency domain and improving computational efficiency. It is particularly suitable for wideband, high-precision electromagnetic field analysis scenarios and has significant application value in microwave device design, electromagnetic compatibility assessment, radar scattering calculation, and other fields.

[0051] Please see Figure 2 In a second embodiment of the frequency domain response calculation method for an electromagnetic field according to the present invention, step 103 includes:

[0052] 201. Generate a coefficient matrix based on electromagnetic properties, electric field strength, and source current density;

[0053] 202. Obtain the magnetic field potential value and the circuit current value, and generate a variable column matrix based on the time region, the magnetic field potential value, and the circuit current value;

[0054] 203. Obtain the magnetic field eddy current region and energy storage element coefficients, and construct a constant matrix based on the magnetic field eddy current region and energy storage element coefficients;

[0055] In this embodiment, a constant matrix describing the inherent characteristics of the system is generated based on the magnetic field eddy current region (distribution of the conductive medium) and the coefficients of the energy storage elements (such as inductors and capacitors), reflecting the coupling relationship between the electromagnetic field and the circuit.

[0056] 204. Obtain the current excitation source and the voltage excitation source, and generate the right column matrix based on the current excitation source and the voltage excitation source;

[0057] 205. The fundamental system equations in the time domain are constructed based on the coefficient matrix, variable column matrix, constant matrix, and right-hand column matrix.

[0058] In this embodiment, due to the presence of eddy currents in the electromagnetic field, the fundamental system equations in the time domain can be expressed as the following initial value problem in the time domain:

[0059] (3)

[0060] In the formula, It is a variable column matrix containing magnetic field potential and current in the circuit. This variable is... to The interval (the interval is large enough) (When the solution is considered to have reached a steady state); the fundamental system equations in the time domain describe the time-domain evolution of the electromagnetic field-circuit coupled system.

[0061] In this embodiment, by decomposing electromagnetic properties, field parameters, and excitation sources into coefficient matrices, variable column matrices, constant matrices, and right-hand column matrices, a standard form of the time-domain fundamental system equations is constructed. The modular matrix design supports the natural coupling of electromagnetic fields and circuits. The pre-computation characteristics of the coefficient and constant matrices, combined with sparse storage technology, significantly reduce memory usage and improve computational efficiency. Modeling of eddy current regions and energy storage elements improves the computational accuracy in scenarios such as transient analysis of power equipment and electromagnetic compatibility simulation. Compared with existing technologies, this scheme achieves orders of magnitude improvements in computational efficiency, memory optimization, and multi-field compatibility, making it particularly suitable for the efficient solution of large-scale electromagnetic-circuit coupled systems.

[0062] Please see Figure 3 In a third embodiment of the frequency domain response calculation method for an electromagnetic field according to the present invention, step 202 includes:

[0063] 301. Perform dimensional analysis on the time region to obtain the time dimension;

[0064] In this embodiment, a dimensional analysis is performed on the time region, discretizing continuous time into quantized time dimensions (such as time step size and number of time nodes), providing a benchmark scale for subsequent analysis of the time evolution of field quantities and circuit parameters.

[0065] 302. Generate the magnetic field potential dimension based on the magnetic field potential value and the time dimension;

[0066] In this embodiment, the magnetic field potential value reflects the distribution of magnetic field energy and the dimension of magnetic field potential (including the characteristics of the change of potential amplitude and phase over time).

[0067] 303. Correct the magnetic field potential dimension according to the preset magnetic field potential dimension threshold to obtain the corrected potential dimension;

[0068] In this embodiment, the magnetic field potential dimension is corrected based on a preset threshold (such as the upper limit of potential fluctuation and the physical rationality boundary), and outliers (such as local overshoot caused by eddy current effect) are eliminated to obtain the corrected potential dimension.

[0069] 304. Generate the magnetic field potential matrix based on the corrected potential dimension;

[0070] In this embodiment, the modified potential dimension is transformed into a structured magnetic field potential matrix to record the distribution characteristics of the magnetic field potential in the entire time domain.

[0071] 305. Generate the circuit current dimension based on the circuit current value and the time dimension;

[0072] In this embodiment, the circuit current value is used to reflect the dynamic characteristics of the circuit, and the circuit current dimension includes the variation of current amplitude and frequency over time.

[0073] 306. Correct the circuit current dimension according to the preset circuit current dimension threshold to obtain the corrected current dimension;

[0074] In this embodiment, the circuit current dimension is corrected based on a preset threshold (such as current safety limit, rated parameters of circuit components) to filter out invalid fluctuations (such as non-physical peaks caused by transient impacts) and obtain the corrected current dimension.

[0075] 307. Generate the magnetic field-current matrix based on the corrected current dimension;

[0076] In this embodiment, the corrected current dimension is transformed into a circuit current matrix to record the variation characteristics of the circuit current in the entire time domain.

[0077] 308. Generate a variable column matrix based on the magnetic field potential matrix and the magnetic field current matrix;

[0078] In this embodiment, the magnetic field potential matrix and the circuit current matrix are aligned along the time dimension and integrated into a variable column matrix, which uniformly contains key variable information of the magnetic field and the circuit.

[0079] In this embodiment, a dimensional analysis is performed on the time region, discretizing continuous time into quantitative dimensions such as time step and number of nodes, providing a benchmark for the temporal evolution of field quantities and circuit parameters. The time dimension is combined to generate magnetic field potential and circuit current dimensions, reflecting the magnetic field energy distribution and circuit dynamic characteristics, respectively. Outliers are then removed through preset threshold correction, transforming the data into a structured matrix, and finally integrated into a column matrix containing key magnetic field and circuit variables. This scheme improves modeling accuracy through threshold correction, reduces data conversion time through matrix integration, and achieves natural coupling of field-circuit variables, providing high-quality input for subsequent time-domain system equation solving. It is suitable for complex coupling analyses such as high-frequency eddy current scenarios, demonstrating significant engineering practicality.

[0080] Please see Figure 4 The fourth embodiment of the frequency domain response calculation method for an electromagnetic field in this invention, 106, includes:

[0081] 401. Based on the time-domain transformation equation, perform type conversion on the electromagnetic properties, electric field strength value and source current density to obtain the current load vector;

[0082] In this embodiment, the load vector serves as the input term of the equation, integrating all excitation and field quantity information of the current time step to ensure compatibility with the format of the algebraic matrix equation. The field quantity information is obtained by converting electromagnetic properties and electric field strength values. The core features of the field quantity information include dielectric constant ε, permeability μ, conductivity σ, electric field strength amplitude E, and electric field direction vector.

[0083] 402. The algebraic matrix equations are solved by back substitution using the time-domain step method and the current load vector to obtain the initial finite element solution;

[0084] In this embodiment, the current load vector integrates relevant information such as electromagnetic characteristic parameters, electric field strength, and source current density at the current moment. It is transformed according to the rules of the time-domain transformation equation to obtain a vector form compatible with the algebraic matrix equation format, used for subsequent back-substitution calculations to ensure the accuracy and consistency of the equation solution; {P}: the right-hand column matrix (generated by the current excitation source and voltage excitation source, representing the system's "external excitation input"), where "current load vector" corresponds to the "right-hand column matrix at the current time step". (The subscript k indicates the kth time step), which is the external excitation parameter that drives the change of system state at this time step; the core of the operation based on the time-domain stepping method is to use the time-domain finite element solution of the previous time step to derive the solution of the current time step, and combine it with the current load vector to perform back substitution to solve the algebraic matrix equation to obtain the initial finite element solution, thus avoiding redundant calculations of repeated matrix decomposition in frequency-by-frequency solution.

[0085] 403. Generate boundary conditions based on the preset initial time and the preset system state vector;

[0086] 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 correlation constraints (ensuring the consistency between the circuit current and the boundary magnetic field), and time initial constraints (avoiding abrupt changes or contradictions in the solution at the time starting point).

[0087] 404. Constrain the initial finite element solution according to the boundary conditions to obtain the time-domain finite element solution;

[0088] In this embodiment, the time-domain finite element solution bridges the gap between mathematical solutions and physical reality, avoiding numerical oscillations or solution distortion caused by missing boundary conditions.

[0089] In this embodiment, electromagnetic characteristics, field quantities, and source parameters (source parameters being source current densities such as current density amplitude, distribution vector, time-domain variation of current excitation source amplitude, and equivalent voltage excitation corresponding to current excitation) are transformed into the current load vector through a time-domain transformation equation. This integrates the excitation and field quantity information of the current time step, ensuring compatibility with the algebraic matrix equation format and avoiding time-consuming data format conversion. Based on the recursive logic of the time-domain stepping method, the algebraic matrix equation is solved back-substituted using the load vector, reusing the initial matrix decomposition results and eliminating the repetitive decomposition steps of frequency-by-frequency solution, thus improving computational efficiency. Simultaneously, multiple boundary constraints are generated by the initial time and system state vector to correct the initial solution to match physical reality, avoiding numerical oscillations and solution distortion, and ensuring the physical rationality of the solution. This scheme balances efficiency and accuracy, is suitable for time-domain analysis of complex electromagnetic fields, lays a high-quality data foundation for broadband response calculation, and has significant engineering practical value.

[0090] Please see Figure 5 In the fifth embodiment of the frequency domain response calculation method for an electromagnetic field in this invention, step 107 includes:

[0091] 501. A magnetic field-circuit coupling model was constructed based on the time-domain finite element method;

[0092] In this embodiment, the model simultaneously incorporates Maxwell's equations for electromagnetic fields (describing magnetic field energy distribution, eddy current effects, etc.) and Kirchhoff's laws for circuits (describing the conduction laws 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 of "magnetic field changes generating induced current, and current changes reacting to the magnetic field," providing a physically consistent model basis for subsequent excitation response calculations.

[0093] 502. Obtain the original sinusoidal voltage source, and construct the unit step function based on the magnetic field-circuit coupling model and the original sinusoidal voltage source;

[0094] In this embodiment, the unit step function has the following specific form: The mathematical expression of the unit step function is: ,in The step time (its value is consistent with the initial time of the fundamental system equations in the time domain). The function value "1" corresponds to an excitation of unit amplitude;

[0095] The relationship between the unit step function and the original sinusoidal voltage source: The expression for the original sinusoidal voltage source is as follows: , ( For amplitude, (where angular frequency is the angular frequency).

[0096] The unit step function is a universal excitation in the entire frequency domain, and its spectrum covers all frequencies. A "time-domain basic solution" containing information in the entire frequency domain can be obtained through a single time-domain calculation.

[0097] The original sinusoidal voltage source is a single-frequency target excitation, and its response can be synthesized from the time-domain basis solution through the principle of linear superposition (decomposing the sine wave into a weighted sum of square waves, which are obtained by subtracting the step function). This ultimately achieves a single calculation covering multiple frequency responses, solving the efficiency bottleneck of the traditional frequency-domain method of solving frequency by frequency.

[0098] 503. Calculate the full-time response of the time-domain finite element solution based on the unit step function to obtain the time-domain fundamental solution;

[0099] In this embodiment, the core of "full-time domain response calculation" is: to calculate "time-step-by-time response". The "(Time-domain fundamental solution)" is integrated along the time dimension to form a "complete response sequence of the system to a unit step excitation across the entire time domain," namely, "Time-domain fundamental solution: The time-domain fundamental solution takes the form of a "time-response" sequence: with time step k as the horizontal axis (corresponding to the actual time t = k × Δt), and..." The key components (such as the magnitude of the magnetic field potential and the magnitude of the circuit current) in the (time-domain basic solution) form a continuous time-domain response curve with the vertical axis as the vertical axis.

[0100] In this embodiment, the spectrum of the unit step function covers the full frequency domain information. By solving the full time domain response under a single excitation, rather than modeling each frequency point independently, the potential response of all frequency points can be obtained with only one time domain solution.

[0101] In this embodiment, by constructing a magnetic field-circuit coupling model and using a unit step function for excitation, the full-frequency response is efficiently obtained. The original sinusoidal voltage source is transformed into a unit step function, whose full-spectrum characteristics enable its excitation response to contain potential information at all frequency points. Based on this function, the time-domain finite element solution is calculated in the full time domain, and the time-domain fundamental solution is obtained in one solution, replacing frequency-by-frequency independent modeling and solving, reducing redundant calculations, improving broadband analysis efficiency, and making it suitable for broadband design of strongly coupled systems such as transformers and wireless charging, with significant application value.

[0102] Please see Figure 6 In the sixth embodiment of the frequency domain response calculation method for an electromagnetic field in this invention, step 108 includes:

[0103] 601. Decompose the unit step function to obtain multiple step functions;

[0104] 602. Calculate the difference between adjacent functions of multiple step functions to obtain multiple square wave functions;

[0105] In this embodiment, the expression for the step function is: ( The index for the time step count. (where the time step is) indicates "at time..." "Then maintain the unit amplitude of the excitation";

[0106] Square wave function Equal to two adjacent step functions and The difference is:

[0107] (4)

[0108] In the formula, the time step is... The pulse width used as the square wave function; a square wave is a fundamental signal with well-defined frequency domain characteristics, providing a building block for synthesizing arbitrary waveforms; square wave function It is the difference between two adjacent step functions, and its physical meaning is "within the time interval..." "A rectangular wave with a unit amplitude at the inside and zero at the other times"; the square wave function is the difference form of the step function; a sine wave can be formed by superimposing multiple square waves with different weights, which provides a basis for subsequent frequency domain response calculation.

[0109] 603. Construct a sinusoidal source function based on multiple square wave functions and multiple step functions;

[0110] In this embodiment, the expression for the sinusoidal source function is:

[0111] (5)

[0112] In the formula, K is the maximum value of the counting subscript. For angular frequency;

[0113] 604. Calculate the time-domain basis solution based on the principle of linear superposition and the sinusoidal source function to obtain the sinusoidal source excitation;

[0114] Specific calculation steps for sinusoidal source excitation:

[0115] Step 1: Calculate the response of the square wave function

[0116] The time-domain basis solution is a "step function" The response (denoted as) According to the principle of linear superposition, the square wave function The response is: (i.e., the difference between adjacent step responses) It has a square wave response;

[0117] Step 2: Find the response of the sinusoidal source function.

[0118] Sine source function ,in For the first Given the amplitude weights of the square waves, the excitation from the sinusoidal source (the response of the sinusoidal source) is: (That is, the square wave response is summed according to weights,) The response is that of a sinusoidal source.

[0119] In this embodiment, since the solution of the step function has been obtained by the time-domain finite element method, according to the principle of linear superposition, the solution of the sinusoidal source excitation can be quickly obtained by adding and subtracting the solution of the step function; thus avoiding the direct solution of the system response under sinusoidal excitation, the existing basic solution is reused, reducing the amount of computation.

[0120] 605. Generate the frequency domain response based on the sinusoidal source excitation;

[0121] In this embodiment, based on the principle of superposition of linear systems, the frequency domain response of any frequency is quickly synthesized by simple addition and subtraction operations using the time-domain basis solution, replacing the inefficient mode of solving the matrix by frequency in the traditional method. It does not require matrix inversion or iterative solution for each frequency point, thus breaking through the efficiency bottleneck of calculation by frequency point in the traditional frequency domain method.

[0122] In this embodiment, the unit step function is decomposed into multiple step functions, and a square wave function is obtained by subtracting adjacent steps. The definite frequency domain characteristics of the square wave are used as waveform synthesis units to construct a sinusoidal source function. Based on the principle of linear superposition, the existing time-domain basis solution is reused. The sinusoidal source excitation is quickly obtained by adding and subtracting the step function solution, avoiding redundant calculations in direct solution. When generating the final frequency domain response, there is no need to perform matrix inversion or iteration frequency by frequency. This scheme significantly reduces the overall computational load, and the sinusoidal waveform approximation error is controllable. It is suitable for broadband electromagnetic field analysis and has outstanding engineering value in radar, filter design and other scenarios, balancing efficiency and accuracy.

[0123] Please see Figure 7 In the seventh embodiment of the frequency domain response calculation method for an electromagnetic field in this invention, step 601 includes:

[0124] 701. Calculate multiple time steps based on the discrete time domain set;

[0125] In this embodiment, the continuous time domain is transformed into an discrete long sequence to provide an initial benchmark for subsequent adaptive adjustment;

[0126] 702. Perform characteristic analysis on the magnetic field eddy current region to obtain the electromagnetic field change rate;

[0127] 703. Smooth multiple time steps based on the rate of change of the electromagnetic field to obtain multiple smooth time steps;

[0128] In this embodiment, the time step is dynamically matched with the changes in the physical field, reducing redundant step sizes in flat regions and balancing accuracy and efficiency.

[0129] 704. Decompose the unit step function according to multiple smooth time steps to obtain multiple step functions;

[0130] In this embodiment, the unit step function is decomposed so that the decomposed step functions are allocated as needed in terms of time resolution, making the step function interval smaller (capturing high-frequency details) and the smooth region interval larger (reducing redundancy), providing a more accurate time grid for subsequent square wave synthesis and sine source function construction.

[0131] In this embodiment, the continuous time domain is transformed into an discrete time step sequence. Then, the electromagnetic field change rate obtained by analyzing the characteristics of the magnetic field eddy current region is combined to smooth the time step. The time step is reduced in a smaller region to capture high-frequency details, while the time step is increased in a smoother region to reduce redundancy. Based on the smooth step decomposition, the unit step function is decomposed, and the step function interval is allocated as needed. This provides a more accurate time grid for subsequent square wave synthesis and sine source construction, adapting to complex eddy current scenarios and laying a high-quality foundation for frequency domain response calculation. It has significant engineering practical value.

[0132] The above describes a method for calculating the frequency domain response of an electromagnetic field according to an embodiment of the present invention. The following describes a device for calculating the frequency domain response of an electromagnetic field according to an embodiment of the present invention. Please refer to [link / reference]. Figure 8 One embodiment of the frequency domain response calculation device for an electromagnetic field according to the present invention includes:

[0133] Data acquisition module 1 is used to acquire electromagnetic properties, electric field strength values, and source current density;

[0134] Time zone generation module 2 is used to generate a time zone based on a preset initial time and a preset end time;

[0135] Equation building module 3 is used to construct the basic time-domain system equations based on electromagnetic properties, electric field strength values, source current density, and time region.

[0136] Time region decomposition module 4 is used to decompose the time region to obtain a discrete time domain set;

[0137] Recursive module 5 is used to perform recursive transformations on the basic system equations in the time domain based on the discrete time domain set and the backward Euler method, so as to obtain the time domain transformation equations and algebraic matrix equations.

[0138] The solution module 6 is used to perform back-substitution solution operations on the algebraic matrix equations according to the time-domain step method and the time-domain transformation equations to obtain the time-domain finite element solution;

[0139] The time-domain basis solution module 7 is used to perform full-time response calculation on the time-domain finite element solution based on the time-domain finite element method to obtain the time-domain basis solution;

[0140] Frequency domain response module 8 is used to calculate the time domain basis solution according to the preset linear superposition principle to obtain the frequency domain response;

[0141] In this embodiment, by constructing the fundamental time-domain system equations and employing the backward Euler method recursive transformation, the continuous problem is discretized into algebraic matrix equations. Only one factorization of the coefficient matrix is ​​required, and subsequent time steps are solved quickly through back substitution, significantly reducing redundant calculations. The calculation of the fundamental time-domain solution captures the full frequency domain information of the system, providing core data support for frequency domain analysis. Based on the principle of linear superposition, phase-weighted synthesis of the fundamental time-domain solution can quickly obtain the frequency domain response at any frequency, avoiding repetitive calculations of frequency-by-frequency solutions in the frequency domain and improving computational efficiency. It is particularly suitable for wideband, high-precision electromagnetic field analysis scenarios and has significant application value in microwave device design, electromagnetic compatibility assessment, radar scattering calculation, and other fields.

[0142] Figure 9This is a schematic diagram of the structure of an electromagnetic field frequency domain response calculation device 900 provided in an embodiment of the present invention. This electromagnetic field frequency domain response calculation device 900 can vary considerably due to different configurations or performance. It may include one or more central processing units (CPUs) 910 (e.g., one or more processors) and a memory 920, and one or more storage media 930 (e.g., one or more mass storage devices) storing application programs 933 or data 932. The memory 920 and storage media 930 can be temporary or persistent storage. The program stored in the storage media 930 may include one or more modules (not shown in the diagram), each module may include a series of instruction operations on the electromagnetic field frequency domain response calculation device 900. Furthermore, the processor 910 may be configured to communicate with the storage media 930 and execute a series of instruction operations in the storage media 930 on the electromagnetic field frequency domain response calculation device 900 to implement the steps of the electromagnetic field frequency domain response calculation method provided in the above-described method embodiments.

[0143] An electromagnetic field frequency domain response computing device 900 may further include one or more power supplies 940, one or more wired or wireless network interfaces 950, one or more input / output interfaces 960, and / or one or more operating systems 931, such as Windows Server, MacOSX, Unix, Linux, FreeBSD, etc. Those skilled in the art will understand that... Figure 9 The illustrated structure of a frequency domain response calculation device for an electromagnetic field does not constitute a limitation on a frequency domain response calculation device for an electromagnetic field. It may include more or fewer components than illustrated, or combine certain components, or have different component arrangements.

[0144] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when executed on a computer, cause the computer to perform the steps of a method for calculating the frequency domain response of an electromagnetic field.

[0145] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system, device, or unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0146] 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, in essence, or the part 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 to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0147] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope 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; A time zone is generated based on a preset initial time and a preset end time; The fundamental time-domain system equations are constructed based on electromagnetic properties, electric field strength, source current density, and time region. The time region is decomposed to obtain a set of discrete time domains; The fundamental system equations in the time domain are recursively transformed using the discrete-time domain set and the backward Euler method to obtain the time-domain transformation equations and algebraic matrix equations. The algebraic matrix equations are solved by back substitution using the time-domain stepping method and the time-domain transformation equations to obtain the time-domain finite element solution. The time-domain response of the time-domain finite element solution is calculated based on the time-domain finite element method to obtain the time-domain basic solution; The time-domain fundamental solution is calculated based on the pre-defined principle of linear superposition to obtain the frequency-domain response; The fundamental time-domain system equations, constructed based on electromagnetic properties, electric field strength, source current density, and time region, include: Generate a coefficient matrix based on electromagnetic properties, electric field strength, and source current density; Obtain the magnetic field potential value and the circuit current value, and generate a variable column matrix based on the time region, magnetic field potential value, and circuit current value; Obtain the magnetic field eddy current region and energy storage element coefficients, and construct a constant matrix based on the magnetic field eddy current region and energy storage element coefficients; Obtain the current excitation source and voltage excitation source, and generate the right column matrix based on the current excitation source and voltage excitation source; The fundamental system equations in the time domain are constructed based on the coefficient matrix, variable column matrix, constant matrix, and right-hand column matrix. The calculation of the full-time response of the time-domain finite element solution based on the time-domain finite element method to obtain the time-domain fundamental solution includes: A magnetic field-circuit coupling model was constructed based on the time-domain finite element method. Obtain the original sinusoidal voltage source, and construct the unit step function based on the magnetic field-circuit coupling model and the original sinusoidal voltage source; The time-domain response of the finite element solution is calculated based on the unit step function to obtain the time-domain basic solution; The step of calculating the time-domain fundamental solution according to the preset linear superposition principle to obtain the frequency-domain response includes: The unit step function is decomposed to obtain multiple step functions; Multiple square wave functions are obtained by calculating the difference between adjacent functions of multiple step functions; A sinusoidal source function is constructed based on multiple square wave functions and multiple step functions; The time-domain basis solution is calculated based on the principle of linear superposition and the sinusoidal source function to obtain the sinusoidal source excitation; The frequency domain response is generated based on the excitation from the sinusoidal source.

2. The method for calculating the frequency domain response of an electromagnetic field as described in claim 1, characterized in that, The process of generating a variable column matrix based on the time region, magnetic field potential value, and circuit current value includes: Perform dimensional analysis on the time region to obtain the time dimension; The magnetic field potential dimension is generated based on the magnetic field potential value and the time dimension. The magnetic field potential dimension is corrected according to the preset magnetic field potential dimension threshold to obtain the corrected potential dimension. Generate the magnetic field potential matrix based on the corrected potential dimension; Generate the circuit current dimension based on the circuit current value and the time dimension; The circuit current dimension is corrected according to the preset circuit current dimension threshold to obtain the corrected current dimension. Generate the magnetic field and 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.

3. The method for calculating the frequency domain response of an electromagnetic field as described in claim 1, characterized in that, The back-substitution solution operation of the algebraic matrix equation based on the time-domain stepping method and the time-domain transformation equation to obtain the time-domain finite element solution includes: The electromagnetic properties, electric field strength values, and source current density are converted according to the time-domain transformation equation to obtain the current load vector; The algebraic matrix equations are solved by back substitution using the time-domain step method and the current load vector to obtain the initial finite element solution. Boundary conditions are generated based on the preset initial time and the preset system state vector; The initial finite element solution is constrained according to the boundary conditions to obtain the time-domain finite element solution.

4. The method for calculating the frequency domain response of an electromagnetic field as described in claim 1, characterized in that, The decomposition of the unit step function to obtain multiple step functions includes: Multiple time steps are calculated based on the discrete time domain set; Characteristic analysis of the magnetic field eddy current region is performed to obtain the rate of change of the electromagnetic field; Multiple time steps are smoothed based on the rate of change of the electromagnetic field to obtain multiple smoothed time steps. The unit step function is decomposed into multiple step functions by multiple smooth time steps.

5. A frequency domain response calculation device for an electromagnetic field, characterized in that, include: The data acquisition module is used to acquire electromagnetic properties, electric field strength values, and source current density. The time zone generation module is used to generate a time zone based on a preset initial time and a preset end time. The equation construction module is used to construct the fundamental time-domain system equations based on electromagnetic properties, electric field strength values, source current densities, and time regions. Specifically, it includes: Generate a coefficient matrix based on electromagnetic properties, electric field strength, and source current density; Obtain the magnetic field potential value and the circuit current value, and generate a variable column matrix based on the time region, magnetic field potential value, and circuit current value; Obtain the magnetic field eddy current region and energy storage element coefficients, and construct a constant matrix based on the magnetic field eddy current region and energy storage element coefficients; Obtain the current excitation source and voltage excitation source, and generate the right column matrix based on the current excitation source and voltage excitation source; The fundamental system equations in the time domain are constructed based on the coefficient matrix, variable column matrix, constant matrix, and right-hand column matrix. The time region decomposition module is used to decompose a time region to obtain a set of discrete time domains. The recursive module is used to perform recursive transformations on the basic system equations in the time domain based on the discrete time domain set and the backward Euler method, so as to obtain the time domain transformation equations and algebraic matrix equations. The solution module is used to perform back-substitution operations on algebraic matrix equations based on the time-domain step method and time-domain transformation equations to obtain time-domain finite element solutions. The time-domain basis solution module is used to perform full-time response calculations on the time-domain finite element solution based on the time-domain finite element method to obtain the time-domain basis solution. Specifically, it includes: A magnetic field-circuit coupling model was constructed based on the time-domain finite element method. Obtain the original sinusoidal voltage source, and construct the unit step function based on the magnetic field-circuit coupling model and the original sinusoidal voltage source; The time-domain response of the finite element solution is calculated based on the unit step function 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, specifically including: The unit step function is decomposed to obtain multiple step functions; Multiple square wave functions are obtained by calculating the difference between adjacent functions of multiple step functions; A sinusoidal source function is constructed based on multiple square wave functions and multiple step functions; The time-domain basis solution is calculated based on the principle of linear superposition and the sinusoidal source function to obtain the sinusoidal source excitation; The frequency domain response is generated based on the excitation from the sinusoidal source.

6. A frequency domain response calculation device for an electromagnetic field, characterized in that, The frequency domain response computing device for an electromagnetic field includes: a memory and at least one processor, wherein the memory stores instructions; At least one of the processors invokes the instructions in the memory to cause the electromagnetic field frequency domain response calculation device to perform the steps of the electromagnetic field frequency domain response calculation method as claimed in any one of claims 1-4.

7. A computer-readable storage medium storing instructions thereon, characterized in that, When the instructions are executed by the processor, they implement the various steps of the frequency domain response calculation method for an electromagnetic field as described in any one of claims 1-4.

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