Time domain finite element fast algorithm for electromagnetic force coupling simulation of loudspeaker

Abstract

The invention provides a time domain finite element fast algorithm for electromagnetic force coupling simulation of a loudspeaker, which comprises the following steps of: performing three-dimensional modeling on a micro loudspeaker, setting parameter information of a solving region, and extracting a calculation model; performing discretization processing on the micro loudspeaker model by using a tetrahedral mesh; an electromagnetic force coupling discrete process is deduced, a hybrid finite element fast time domain solver is constructed, a discrete model and solving parameters of the miniature loudspeaker are imported into the solver, and the solver is initialized; and carrying out coil geometric analysis, calculating the current density in the coil, taking the current density as an excitation source of a magnetic field, calling a hybrid finite element fast time domain solver, calculating to obtain the displacement of the vibrating diaphragm, and finally obtaining the time domain vibration curve of the vibrating diaphragm. According to the time domain hybrid finite element fast algorithm, the tree-cotree technology and the Lanczos modal order reduction technology are introduced, the method can be used for analyzing the time domain electromagnetic force coupling simulation problem of the complex micro loudspeaker, and the method has the advantage of being high in solving efficiency under the condition that the solving precision is met.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi - physical field modeling and simulation of the coupling of electromagnetic fields and elastic waves, and particularly relates to a fast time - domain simulation algorithm for electromagnetic force coupling of a micro - speaker. Background Technique

[0002] Micro - speakers are playing an increasingly important role in electronic products, especially in products such as mobile devices, smart speakers, and headphones. At the same time, with the continuous development of Virtual Reality (VR) technology, the demand for immersive audio experiences is also increasing day by day, which further promotes the wide application of micro - speakers. In order to pursue higher - quality sound performance, higher requirements are put forward for the performance and characteristics of micro - speakers, including aspects such as frequency response, power consumption, and volume. The progress of material science, design technology, and manufacturing technology provides a broader development space for the research and development of micro - speakers.

[0003] With the proposal of various new structures, numerical simulation is usually used in engineering to guide the specific product design of micro - speakers. The basic method is to construct the model and parameter characteristics of the product, solve the partial differential equations of the coupling of electromagnetic fields and elastic waves by numerical methods, and finally calculate the performance parameters of the product. This method can reduce the number of physical prototype trials, thereby reducing the design cost and shortening the design cycle. The key step in the multi - physical field simulation design of micro - speakers is to accurately calculate the Lorentz force generated by the magnetic field and apply it to the elastic wave calculation, and finally obtain the vibration curve of the diaphragm.

[0004] The difficulties in the electromagnetic force coupling simulation of micro - speakers mainly lie in the magnetic field calculation, which is affected by two factors: 1. The working frequency of micro - speakers is generally between 20Hz and 20kHz. When directly using the time - domain finite - element method based on edge - based basis functions to discretely solve the magnetic vector potential Helmholtz equation, due to the ineffective constraint of the divergence of the magnetic vector potential at low frequencies, the "low - frequency breakdown" phenomenon will occur. By adopting the tree - cotree idea, the degrees of freedom of the tree edges can be approximated by the gradients of the nodal basis functions, the null space of the stiffness matrix can be analytically obtained, and the constraint equations can automatically satisfy the wave equation. Therefore, only the original wave equation needs to be solved to overcome the low - frequency breakdown problem. 2. For multi - physical field coupling simulation analysis, the finite - element method (FEM) is the most widely used method at present due to the flexibility of its mesh and high accuracy. However, as the complexity of the simulation model increases, the traditional time - domain finite - element solution method requires a large amount of solution time and memory. By adopting the Lanczos modal reduction technique, the matrix dimension to be solved by the time - domain finite - element method can be reduced to several hundred or even dozens. Therefore, during the time - domain iteration stage, the calculation efficiency can be greatly improved.

[0005] In summary, the present invention proposes a fast time-domain finite element algorithm for the electromagnetic force coupling simulation of speakers. By combining traditional time-domain finite elements with tree-cotree technology and Lanczos modal reduction technology, while taking into account the solution accuracy, the computational efficiency of the electromagnetic force coupling simulation is improved, thereby reducing the time for the design of micro-speaker products. Summary of the Invention

[0006] In order to solve the problems such as low-frequency collapse and time-consuming solution in the multi-physics field simulation design process of existing micro-speakers, the present invention provides a fast time-domain hybrid finite element algorithm for the electromagnetic force coupling of speakers to accurately and efficiently predict the magnetic field distribution in space and the vibration curve of the diaphragm, and improve the design efficiency of micro-speakers.

[0007] The present invention includes the following steps:

[0008] S1. Perform three-dimensional modeling on the micro-speaker, set the parameter information of the solution region, and extract the corresponding calculation model;

[0009] S2. Discretize the micro-speaker calculation model using tetrahedral meshes to obtain a micro-speaker discrete model;

[0010] S3. Deduce the electromagnetic force coupling discretization process, construct a fast time-domain solver for hybrid finite elements, and import the micro-speaker discrete model and model physical parameters into the fast time-domain solver for hybrid finite elements. The model physical parameters include boundary conditions, initial values, and material properties, and initialize the solver;

[0011] S4. Perform time-domain iterative calculations. First, perform coil geometry analysis, calculate the current direction in the speaker coil, use it as the current source in the magnetic field calculation, call the fast time-domain solver for hybrid finite elements to perform electromagnetic force coupling simulation, calculate the diaphragm displacement at each time step of the time-domain iteration, and finally obtain the time-domain vibration curve of the diaphragm of the micro-speaker model.

[0012] In S1, the constructed geometric model should include the input and output boundaries of the coil and the loaded voltage pulse excitation parameters. The parameter information of the solution region includes: the structural parameters of the geometric structure and the material properties;

[0013] In S2, input the calculation model generated in S1 for discretization to obtain a discrete model, which includes the following information: the coordinates of the nodes; the node numbers that make up the tetrahedral meshes; the material numbers corresponding to the tetrahedral meshes; the element numbers of the tetrahedral meshes and their corresponding region numbers; the face numbers that make up the tetrahedral meshes;

[0014] Preferably, the commercial software COMSOL Multiphysics is used for geometric modeling and tetrahedral meshing of the micro-speaker, and the tetrahedral mesh information is exported as a discrete model.

[0015] In S3, during the solver initialization process, the physical parameters of the model and the discretized mesh are input. The physical parameters of the model include boundary conditions, initial values, and material properties. The weak form of the electromagnetic force coupling differential equation is constructed using the finite element method and the mixed finite element method to establish the coupling relationship between the electric field, magnetic field, and stress field.

[0016] Preferably, the solution parameter information should include: coil geometric analysis, the solution regions corresponding to the magnetic field and elastic waves respectively; the single-step size and total number of steps for time-domain simulation; the region corresponding to the coil; the excitation voltage pulse parameters applied to the coil; and the material parameters of the solution regions of the electric field, magnetic field, and stress field respectively.

[0017] Preferably, the electromagnetic force coupling differential equation includes a coil geometric analysis equation, a magnetic field equation, and an elastic wave equation:

[0018]

[0019] Among them, σ is the electrical conductivity of the material, ε is the permittivity of the material, μ is the magnetic permeability of the material, J e is the externally applied current density, B r is the residual magnetic flux density of the permanent magnetic material, A is the magnetic vector potential, B is the magnetic flux density, ρ is the density of the material, u is the geometric deformation of the model, τ is the stress tensor, f is the elastic wave excitation term, which is mainly the Lorentz force contribution term of the magnetic field f = J × B, to achieve the coupling of the magnetic field and elastic waves.

[0020] Preferably, the second-order basis function is used to discretize the electromagnetic force coupling differential equation. For the magnetic field problem, due to considering the problem of low-frequency breakdown, the idea of tree-cotree is used to divide the mesh edges into tree edges and cotree edges, and the magnetic vector potential is expanded by the edge basis function and the gradient of the node basis function defined on the cotree edges as:

[0021]

[0022] Among them, N c is the number of cotree edges, N n is the number of tree edges and also the number of free nodes. represents the edge basis function defined on the cotree edges, and φ j represents the node basis function defined on the free nodes.

[0023] In S4, the process of the fast algorithm for time-domain finite element of electromagnetic force coupling simulation is as follows:

[0024] S41. Set the single-step size d of the time-domain iteration t and the total number of steps nstep, the central frequency F of the Lanczos modal reduction req , the number of iterations N of the modal reduction max Lanczo

[0025] S42. According to the parameters set in S41, perform Lanczos modal reduction on the magnetic field matrix to generate the projection matrix V for restoring the reduced result. Among them, the parameter F req is the central frequency of the coil excitation pulse, and the number of iterations N max Lanczo represents the size of the reduced matrix

[0026] S43. Perform coil geometry analysis. By solving the Poisson equation for the coil region, obtain the magnitude and direction J of the current density at each integration point inside the coil e .

[0027] S44. Before the start of the time-domain iteration, solve the magnetic field distribution in space by the permanent magnet at the initial moment as the initial value of the magnetic field time-domain iteration

[0028] S45. During the time-domain iteration, within one time step, the magnetic field obtains the current excitation applied to the coil through the result of the coil geometry analysis, assembles the corresponding right-hand side term b, calculates the magnetic field matrix equation to obtain the magnetic flux density B and the magnetic vector potential A, and further through the following formula

[0029] F = J × B

[0030]

[0031]

[0032] where F represents the Lorentz force, J represents the current density, B represents the magnetic flux density, and the current density J includes the induced current density J i and the external current density J e , J i can be obtained from the partial derivative of the conductivity σ and the magnetic vector potential A with respect to time t

[0033] S46. Take the Lorentz force calculated by the magnetic field as the body load excitation in the elastic wave, and finally solve the elastic wave matrix equation to obtain the displacement u at this moment, and repeat this process at the next moment

[0034] As can be seen from the implementation steps of the present invention described above, compared with the prior art, the beneficial effects of the present invention are

[0035] The fast time-domain hybrid finite element algorithm for electromagnetic force coupling proposed by the present invention discretizes the magnetic field using the tree-cotree concept and the gradients of edge-based functions and node-based functions. While solving the wave equation, it normalizes the divergence of the magnetic vector potential A, effectively avoiding the low-frequency breakdown problem caused by the low operating frequency of micro-speakers. By performing Lanczos modal reduction on the magnetic field matrix equation, the computational complexity of the magnetic field time-domain iteration part can be reduced, improving the simulation efficiency while ensuring the solution accuracy. In summary, the present invention improves the design efficiency of micro-speakers by shortening the computational time of time-domain iteration and is easy to implement.

[0036] Figure 1 It is a flowchart of a fast time-domain hybrid finite element algorithm for electromagnetic force coupling simulation of micro-speakers proposed by the present invention. Description of the Drawings

[0037] The drawings are included to provide a further understanding of the embodiments and are incorporated into and constitute a part of this specification. The drawings illustrate the embodiments and, together with the description, are used to explain the principles of the present invention. Other embodiments and many of the expected advantages of the embodiments will be readily recognized, as they become better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale with each other. The same reference numerals refer to corresponding similar components.

[0038] Figure 1 It is a flowchart of a fast time-domain hybrid finite element algorithm for electromagnetic force coupling simulation of micro-speakers proposed by the present invention;

[0039] Figure 2 The geometric model of a specific example of the micro-speaker described in the present invention;

[0040] Figure 3 It is the discretized model of a specific example of the micro-speaker described in the present invention;

[0041] Figure 4 It is a flowchart of the fast time-domain electromagnetic force coupling algorithm proposed by the present invention.

[0042] Figure 5 It is a comparison of the results (magnetic flux density, Lorentz force, diaphragm vibration curve) obtained by the fast time-domain hybrid finite element algorithm proposed by the present invention and COMSOL Multiphysics. Detailed Embodiments

[0043] The present invention proposes a fast time-domain hybrid finite element algorithm for electromagnetic force coupling simulation of a micro-speaker, in which a tetrahedron is used to construct the discrete domain of the micro-speaker, the magnitude and direction of the current loaded on the coil are calculated through coil geometry analysis, and through time-domain iteration of the magnetic field and elastic waves, where the magnetic field calculation is accelerated by introducing tree-cotree and Lanczos modal reduction while ensuring the solution accuracy, and finally the vibration curve of the diaphragm is obtained to guide the design and optimization of micro-speaker products.

[0044] The features of each aspect of the invention will be described in detail below with reference to examples:

[0045] S1. Perform three-dimensional modeling on the micro-speaker, set the parameter information of the solution region, and extract the corresponding calculation model;

[0046] Figure 2 Fig. shows a specific example of the geometric model of the micro-speaker described in the present invention. In actual calculation, due to its symmetry, only 1 / 4 of the structure needs to be selected for simulation and surrounded by an air box. The speaker part mainly consists of a coil, a coil bobbin, a diaphragm, a magnet, a metal baffle, a dust cap, a paper cone, and a surround. The set parameter information includes: the geometric dimensions and material properties of the micro-speaker; the boundaries and pulse parameters of the voltage excitation loaded on the coil; the boundary conditions of the speaker and air.

[0047] In a preferred example,

[0048] The coil needs to set the input and output boundaries of the voltage excitation, and apply the transient voltage signal V(t) = V0·sin(2πf0t) on the coil. The input signal frequency and magnitude are f0 = 500 Hz and V0 = 1 V respectively. For the boundary conditions, in the elastic wave part, the surfaces where the diaphragm and the surround are connected to the electrode plate are set as fixed constraint boundaries; in the magnetic field part, the outer surface of the entire model (including air) is set as magnetically insulated.

[0049] S2. Discretize the calculation model of the micro-speaker using tetrahedral meshes to obtain a discrete model of the micro-speaker; Figure 3 Fig. shows the tetrahedral mesh discrete model of the preferred example. In a specific implementation, the COMSOL Multiphysics software is used to perform mesh generation on the geometric model of the micro-speaker, and the mesh information is exported for subsequent time-domain hybrid finite element analysis in electromagnetic force coupling simulation.

[0050] S3. Deduce the electromagnetic force coupling discretization process, construct a fast time-domain solver for hybrid finite elements, and import the discrete model of the micro-speaker and the model physical parameters into the fast time-domain solver for hybrid finite elements. The model physical parameters include boundary conditions, initial values, and material properties, and initialize the solver;

[0051] During the coil geometry analysis, it is necessary to solve the current continuity equation for the geometric region where the coil is located:

[0052]

[0053] where σ is the conductivity of the material, ε is the permittivity of the material, and the electric potential inside the coil is obtained. After obtaining the distribution, the magnitude and direction of the current density in the coil are further obtained, which is the external current density term for magnetic field calculation. During the time-domain iteration process, for the voice coil excitation at each moment, an electromagnetic force-coupled time-domain hybrid finite element solver is used to calculate the geometric deformation of the model.

[0054] Specifically, the deformation calculation of the micro speaker involves the coupling between the magnetic field and elastic waves, and it is necessary to construct an electromagnetic force-coupled time-domain hybrid finite element solver based on the following equations.

[0055] The control equation of the magnetic field is:

[0056]

[0057] where σ is the conductivity of the material, ε is the permittivity of the material, μ is the permeability of the material, J e is the applied current density, B r is the remanent magnetic flux density of the permanent magnetic material, A is the magnetic vector potential which is the dependent variable of the equation, and the magnetic flux density B can be obtained through after solving the matrix.

[0058] The control equation of the elastic wave is:

[0059]

[0060] where ρ is the density of the material, u is the geometric deformation of the model, τ is the stress tensor, and f is the elastic wave excitation term.

[0061] There is the following relationship between the electric field strength E and the electric potential :

[0062]

[0063] There is the following relationship between the strain tensor and the displacement:

[0064]

[0065] When considering the electromagnetic force coupling, the connection between the two physical fields is:

[0066] F = J × B

[0067] Using second-order Lagrange basis functions, the Galerkin method is adopted to discretize the electromagnetic force coupling control equation, where the coil geometric analysis and the weak solution form of the elastic wave equation are as follows:

[0068]

[0069]

[0070] For the magnetic field control equation, since the frequency of the applied excitation source is low, an exact solution cannot be obtained by directly solving the wave equation. Therefore, based on tree-cotree, the grid is divided into edges and free nodes, and the magnetic vector potential A is discretized by using the gradients of edge basis functions and node basis functions:

[0071]

[0072] The weak solution form of the magnetic field equation can be obtained by using the Galerkin method:

[0073]

[0074] where φ i is the edge basis function corresponding to the i-th edge, φ j is the node basis function of the j-th free node, N c is the number of edges after the grid tree-cotree division, N n is the number of free nodes; v is the volume where the magnetic field integration domain is located. The element integrals of the finite element are all calculated in the physical space, while the basis functions and their gradients and curls are defined on the reference element. Through the covariant mapping, the integral on the reference element can be transformed to the physical element:

[0075]

[0076] φ and φ are the basis functions in the physical domain, and are the basis functions in the reference domain. Where J is the Jacobian matrix.

[0077] Based on the above weak form, the original differential equation is transformed into a matrix equation system form. The above equation system can be calculated by a matrix solver to perform the electromagnetic force coupling time-domain analysis and obtain the vibration curve on the diaphragm.

[0078] Based on the above derivation process, a hybrid finite element fast time-domain solver is developed. The solver has two parts of the process: In the initialization process, the discretized model and simulation parameters are input, and through model setting, element assembly, and matrix assembly, the equation system in the time domain is obtained.

[0079] S4. Perform time-domain iterative calculations. First, perform coil geometry analysis to calculate the current direction in the speaker coil, which serves as the current source in magnetic field calculations. Then, call the hybrid finite element fast time-domain solver to conduct electromagnetic force coupling simulations, calculate the diaphragm displacement at each time step of the time-domain iteration, and finally obtain the time-domain vibration curve of the diaphragm of the micro-speaker model. The process is as follows Figure 4 as shown.

[0080] S41. Set the single-step size d t and the total number of steps nstep of the time-domain iteration, and the central frequency F req of Lanczos modal reduction, and the number of iterations N max of Lanczo.

[0081] For the preferred case, the time-domain iteration parameters are set as: d t = 4e -5 s, nstep = 300. The parameters of modal reduction are set as: F req Select the frequency F req consistent with the excitation pulse, N max Lanczo = 20.

[0082] S42. According to the parameters set in S41, perform Lanczos modal reduction on the magnetic field matrix to generate the projection matrix V for restoring the reduced result. Among them, the parameter F req is the central frequency of the coil excitation pulse, and the number of iterations N max Lanczo represents the size of the reduced matrix.

[0083] S43. Perform coil geometry analysis. By solving the Poisson equation for the coil region, obtain the magnitude and direction J e of the current density at each integration point in the coil.

[0084] Before the start of the time-domain iteration, solve the magnetic field distribution in space by the permanent magnet at the initial moment as the initial value of the magnetic field in the time-domain iteration process.

[0085] During the time-domain iteration process, within one time step, the magnetic field obtains the current excitation loaded on the coil through the result of the coil geometry analysis, assembles the corresponding right-hand side term b, calculates the magnetic field matrix equation to obtain the magnetic flux density B and the magnetic vector potential A through the following formula:

[0086] F = J × B

[0087]

[0088] Among them, the Lorentz force F is calculated from the current density J and the magnetic flux density B. The current density J includes the induced current density J iWith the external current density J e , J i can be obtained through the partial derivative of the conductivity σ and the magnetic vector potential A with respect to time t.

[0089] S46. Take the Lorentz force calculated by the magnetic field as the body load excitation in the elastic wave, and finally solve the elastic wave matrix equation to obtain the displacement u at this moment. Repeat this process at the next moment.

[0090] For the preferred case, the adopted modal reduction strategy is to select as few iteration times as possible. While ensuring the accuracy, the solution time is reduced to the greatest extent. In other embodiments, other iteration times can be selected, and no further research is done here.

[0091] Use the fast time-domain hybrid finite element algorithm for electromagnetic force coupling simulation of micro-speakers proposed by the present invention and the commercial software COMSOL Multiphysics to calculate the preferred model respectively. Under the condition of using the same model, compared with COMSOL, it can be seen from Table 1 that the calculation time of the electromagnetic force simulation of the entire micro-speaker is greatly reduced. Figure 5 It is a comparison of the point results obtained by the fast time-domain hybrid finite element algorithm proposed by the present invention and COMSOL Multiphysics, which are respectively: (a) the magnetic flux density By in the y direction, (b) the Lorentz force Fz in the z direction, (c) the vibration curve Uz of the diaphragm in the z direction, ensuring that the proposed method meets the solution accuracy. It can be seen that the fast time-domain hybrid finite element algorithm for electromagnetic force coupling simulation of micro-speakers proposed by the present invention has significant advantages in the optimal design of micro-speakers.

[0092] Table 1 Comparison of the efficiency of the method proposed by the present invention and COMSOL Multiphysics

[0093] Degrees of Freedom (DoF) CPU Time Speedup COMSOL Multiphysics 492177 402s 1 MFEM-fast 475020 61.7s 6.5

Claims

1. A fast time-domain finite element algorithm for electromagnetic force coupling simulation of a loudspeaker, characterized in that The method includes the following steps: S1. Perform three-dimensional modeling on the micro speaker, set the parameter information of the solution region, and extract the corresponding micro speaker calculation model; S2. Discretize the micro speaker calculation model using tetrahedral meshes to obtain a micro speaker discrete model; S3. Deduce the discrete process of electromagnetic force coupling, construct a hybrid finite element fast time-domain solver, and import the micro speaker discrete model and model physical parameters into the hybrid finite element fast time-domain solver. The model physical parameters include boundary conditions, initial values, and material properties, and initialize the hybrid finite element fast time-domain solver; S4. Perform time-domain iterative calculations. First, conduct coil geometry analysis to calculate the current direction in the speaker coil, which serves as the current source in magnetic field calculations. Call the hybrid finite element fast time-domain solver for electromagnetic force coupling simulation, calculate the diaphragm displacement at each time step of the time-domain iteration, and finally obtain the diaphragm time-domain vibration curve of the micro speaker calculation model.

2. The fast time-domain finite element algorithm for the electromagnetic force coupling simulation of a loudspeaker according to claim 1, characterized in that The micro speaker calculation model proposed in step S1 includes the following information: geometric parameters and material properties of the micro speaker; input-output boundaries and pulse parameters of the excitation voltage applied to the coil; Boundary conditions of the speaker region and the air region.

3. The fast time-domain finite element algorithm for electromagnetic force coupling simulation of a speaker according to claim 1, characterized in that The discretization process in step S2 refers to modeling the micro speaker through COMSOL Multiphysics and performing tetrahedral mesh division.

4. The fast time-domain finite element algorithm for electromagnetic force coupling simulation of a speaker according to claim 3, characterized in that The discretization process generates the following information: coordinates of the nodes; node numbers constituting the tetrahedral meshes; material numbers corresponding to the tetrahedral meshes; node numbers constituting the surface meshes; boundary condition numbers corresponding to the surface meshes.

5. The fast time-domain finite element algorithm for speaker electromagnetic force coupling simulation according to claim 1, characterized in that For the initialization of the hybrid finite element fast time-domain solver proposed in step S3, the imported solution parameters include the following information: solution regions corresponding to coil geometry analysis, magnetic field, and elastic wave respectively; single-step size and total number of steps of the time-domain simulation; boundary condition parameters and material parameters of the solution regions of the electric field, magnetic field, and stress field respectively.

6. The fast time-domain finite element algorithm for electromagnetic force coupling simulation of a speaker according to claim 5, wherein The initialization process of the hybrid finite element fast time-domain solver is to use finite element and hybrid finite element to construct the weak form of the electromagnetic force coupling differential equation, which includes coil geometry analysis, magnetic field, and elastic wave. After discretization, a magnetic field matrix equation in the form of Kx = b is obtained.

7. The fast time-domain finite element algorithm for electromagnetic force coupling simulation of a speaker according to claim 1, characterized in that The time-domain iterative calculation proposed in step S4 includes the following initial parameters: the single-step length d of the time-domain iteration t and the total number of steps nstep, the central frequency F of the Lanczos modal reduction req , the number of iterations N of the modal reduction max Lanczo.

8. The fast time-domain finite element algorithm for electromagnetic force coupling simulation of a speaker according to claim 1, characterized in that When calculating the diaphragm displacement at each time step of the time-domain iteration proposed in step S4, the following process is adopted: Before calculating the diaphragm displacement at each time step of the time-domain iteration, conduct coil geometry analysis to obtain the current direction in the coil, which is used to calculate the right-hand side term in the magnetic field matrix equation; During the process of calculating the diaphragm displacement at each time step of the time-domain iteration, within one time step, the magnetic field obtains the current excitation applied to the coil through the result of coil geometry analysis, assembles the corresponding right-hand side term b, calculates the magnetic field matrix equation to obtain the magnetic flux density B and magnetic vector potential A, further processes to obtain the Lorentz force F on the coil, which serves as the body load excitation in the elastic wave, and finally solves the elastic wave matrix equation to obtain the displacement u at this moment. Repeat this process at the next moment.

9. The fast time-domain finite element algorithm for electromagnetic force coupling simulation of a speaker according to claim 8, wherein The calculation formula for the Lorentz force F is: F = J × B Among them, the Lorentz force F is calculated from the current density J and the magnetic flux density B, and the current density J includes the induced current density J i and the external current density J e , J i can be obtained from the partial derivative of the conductivity σ and the magnetic vector potential A with respect to time t.

10. The fast time-domain finite element algorithm for electromagnetic force coupling simulation of a speaker according to claim 6, characterized in that, For the magnetic field matrix equation Kx = b obtained by initializing the hybrid finite element fast time domain solver, the matrix is reduced in order by the Lanczos modal reduction technique, and the dimension size of the reduced matrix is the initial parameter N max Lanczo, and at the same time generate the projection matrix V for the change of the matrix before and after the order reduction: K′ = V·K b′ = V·b x = V T ·x' The reduced-order magnetic field matrix equation is: K'x' = b'. The calculated x' is the result after reduction, and its size dimension is equal to N max Lanczo, by multiplying by the transpose V of the projection matrix V T , the correct solution x of the original equation Kx = b is obtained, which is the value of the physical quantity to be sought.

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