CN116561494A

CN116561494A - Partial differential equation solving method and related equipment thereof

Info

Publication number: CN116561494A
Application number: CN202210111691.7A
Authority: CN
Inventors: 寇振中; 董思维; 李步扬
Original assignee: Huawei Technologies Co Ltd
Current assignee: Huawei Technologies Co Ltd
Priority date: 2022-01-29
Filing date: 2022-01-29
Publication date: 2023-08-08
Also published as: WO2023143110A1

Abstract

The partial differential equation solving method and the related equipment can reduce the cost of the calculation process and reduce the error of the calculation result when calculating the sound field of the three-dimensional space. The method comprises the following steps: when the sound field of the target three-dimensional space is required to be acquired, a partial differential equation is firstly acquired, the partial differential equation is used for describing the sound field of the target three-dimensional space to be solved, N grid points can be contained in the target three-dimensional space, and the length of the edge connected with the N grid points is smaller than a first threshold value. And then converting the partial differential equation to obtain a first finite element equation containing penalty parameters of N grid points, wherein the penalty parameters of the N grid points are penalty parameters applicable to the three-dimensional scene and are obtained based on a numerical method, namely, the penalty parameters of the i grid point are calculated based on the coordinates of the i grid point and preset sound wave incidence angles, and i=1, 2, … and N. And finally, solving the first finite element equation to obtain the sound field of the target three-dimensional space.

Description

Partial differential equation solving method and related equipment thereof

Technical Field

The application relates to the technical field of acoustic simulation, in particular to a partial differential equation solving method and related equipment thereof.

Background

The quality of sound in the automobile directly affects the quality of the automobile product, and is also an important index for evaluating the riding comfort of the automobile. Various manufacturers in China are invested in a great deal of energy and cost to solve the problem of sound quality in the automobile, and are subject to the reasons of long experimental test period, difficult determination of problem sources, high manufacturing cost of test equipment and the like, and simulation methods are often adopted to predict the sound field of the internal space of the automobile so as to determine the sound quality in the automobile.

In car acoustic simulations, the core problem is how to solve the partial differential equation describing the sound field of the interior space of the car to be solved quickly and accurately. The method can be solved by a finite element method at present, namely, a partial differential equation is expressed by a finite element equation, and then the finite element equation is solved to obtain the sound field of the inner space of the automobile. In order to make the resulting sound field sufficiently accurate, penalty parameters may be added to the finite element equation for constraining the accuracy of the resulting sound field.

However, the added penalty parameter is usually a parameter optimized based on a two-dimensional scene, so that the three-dimensional space inside the automobile needs to be converted into a two-dimensional plane, the plane is taken as an area to be solved, a finite element equation added with the penalty parameter is solved, a sound field on the plane is obtained, and then the sound field of the internal space of the automobile is estimated based on the sound field on the plane. Therefore, since the existing penalty parameters are limited to the two-dimensional scene, the sound field of the three-dimensional space needs to be estimated through the sound field of at least one plane in the space, and the calculation cost of the mode is high and the calculation error is large.

Disclosure of Invention

The embodiment of the application provides a partial differential equation solving method and related equipment thereof, which do not need repeated calculation and pre-estimation operation when calculating a sound field of a three-dimensional space, and are beneficial to reducing the calculation cost and the calculation error.

A first aspect of an embodiment of the present application provides a partial differential equation solving method, including:

when the sound field distribution of the target three-dimensional space needs to be solved, a partial differential equation can be acquired first, and the partial differential equation is used for describing the sound field of the target three-dimensional space to be solved. It should be noted that, the three-dimensional space of the target may be meshed so that the surface and the interior of the three-dimensional space of the target are spread over a plurality of grids, so that the three-dimensional space of the target may include N grid points, where the length of the edge connecting the N grid points is smaller than a preset first threshold value, and N is a positive integer greater than 1.

After the partial differential equation is obtained, the partial differential equation can be converted to obtain a first finite element equation, wherein the first finite element equation comprises penalty parameters of N grid points, and the penalty parameters of the N grid points are known parameters applicable to a three-dimensional scene. The penalty parameters of the N grid points are obtained based on a numerical method, that is, for the penalty parameters of the i grid point, the penalty parameters of the i grid point are calculated based on the coordinates of the i grid point and the preset sound wave incidence angles, i=1, 2, …, N.

After the first finite element equation is obtained, the first finite element equation can be solved, and the sound field of the target three-dimensional space is obtained.

From the above method, it can be seen that: when the sound field distribution of the target three-dimensional space needs to be solved, a partial differential equation can be obtained, wherein the partial differential equation is used for describing the sound field of the target three-dimensional space to be solved, and the target three-dimensional space is meshed, so that the target three-dimensional space comprises N grid points, and N is a positive integer greater than 1. The partial differential equation may then be converted to a first finite element equation including penalty parameters for the N grid points. Finally, the first finite element equation can be solved to obtain the sound field of the target three-dimensional space. In the foregoing process, since the sizes of all the grids in the target three-dimensional space are sufficiently small, that is, the lengths of the edges where the N grid points are connected are limited to be smaller than the preset first threshold (the first threshold is sufficiently small), under this condition, the penalty parameters of the N grid points may be obtained based on a numerical method, that is, the penalty parameters of the i grid point may be calculated by using the coordinates of the i grid point and the preset sound wave incident angle, i=1, 2, …, N, so as to obtain the penalty parameters of the N grid points. Because the penalty parameters of the N grid points are penalty parameters applicable to the three-dimensional scene, the first finite element equation added with the penalty parameters of the N grid points is solved, the sound field of the target three-dimensional space can be directly obtained, repeated calculation and pre-estimation operations are not needed, the calculation cost is reduced, and the calculation error is reduced.

In one possible implementation, converting the partial differential equation to obtain the first finite element equation includes: converting the partial differential equation to obtain a second finite element equation, wherein the second finite element equation comprises a penalty adding parameter to be solved; calculating based on the coordinates of the ith grid point and a preset sound wave incidence angle to obtain a predicted sound wave of the ith grid point; substituting the predicted sound wave of the ith grid point into a second finite element equation to obtain a penalty parameter of the ith grid point, wherein the penalty parameter of the ith grid point comprises a plurality of same subparameters, and the subparameters are in one-to-one correspondence with a plurality of edges connected with the ith network point; and in the second finite element equation, replacing the penalty parameters to be solved with the penalty parameters of the N grid points to obtain a first finite element equation. In the foregoing implementation, for the ith grid point (any one of the N grid points) among the N grid points, the penalty parameter of the ith grid point may be obtained by: the partial differential equation may be converted based on an internal penalty finite element method to obtain a second finite element equation (which may also be understood as the original finite element equation), where the second finite element equation contains the penalty parameters to be solved. Then, calculation can be performed based on the coordinates of the ith grid point and a preset sound wave incident angle, so as to obtain a predicted sound wave of the ith grid point. The predicted sound wave of the ith grid point can then be substituted into the second finite element equation to obtain the penalty parameter of the ith grid point, which is typically a vector comprising a plurality of identical subparameters in one-to-one correspondence with the plurality of edges to which the ith grid point is connected. Likewise, for the remaining grid points, the same operations as performed for the ith grid point may be performed, so that the penalty parameters for the N grid points may be obtained. Finally, the penalty parameters to be solved may be replaced with the penalty parameters of the N grid points in the second finite element equation, resulting in the first finite element equation (i.e., the finite element equation for which the penalty parameters are known). Therefore, based on a numerical method, the penalty adding parameters suitable for the three-dimensional scene can be accurately obtained and applied to the subsequent finite element equation solving, so that the calculating cost of the solving process can be reduced, and the calculating error of a final result can be reduced.

In one possible implementation, solving the first finite element equation to obtain the sound field of the target three-dimensional space includes: solving a first finite element equation on the boundary condition of the partial differential equation to obtain a sound field of a target three-dimensional space; the boundary condition is a first difference value equal to a second difference value, the first difference value is a difference between a first DtN boundary condition of the partial differential equation and the partial differential equation, the second difference value is a difference between a second DtN boundary condition of the partial differential equation and the partial differential equation, the value range of the boundary condition is a superposition area between the target three-dimensional space and the rest three-dimensional space, the value range of the first DtN boundary condition is the target three-dimensional space, and the value range of the second DtN boundary condition is the rest three-dimensional space. In the implementation manner, the novel DtN boundary condition is provided as the boundary condition of the partial differential equation, is suitable for three-dimensional spaces of various shapes, can be adapted to a finite element equation added with penalty parameters when solving the problem of high wave numbers, and is beneficial to improving the calculation precision and performance.

In one possible implementation manner, after solving the first finite element equation to obtain the sound field of the target three-dimensional space, the method further includes: calculating based on the sound field of the target three-dimensional space to obtain an error between the sound field of the target three-dimensional space and the real sound field of the target three-dimensional space; and if the error is greater than or equal to a preset second threshold value, adjusting the size of the target three-dimensional space to obtain a new boundary condition of the partial differential equation, wherein the value range of the new boundary condition is the superposition area between the adjusted target three-dimensional space and the adjusted rest three-dimensional space. And solving the first finite element equation on the new boundary condition to obtain a new sound field of the target three-dimensional space. In the foregoing implementation manner, after the sound field of the target three-dimensional space is obtained, the sound field of the target three-dimensional space may be calculated by using a preset error indicator, so as to obtain an error between the sound field of the target three-dimensional space and the real sound field of the target three-dimensional space. Then, whether the error is greater than or equal to a preset second threshold value can be judged, if the error is greater than or equal to the preset second threshold value, the obtained sound field of the target three-dimensional space can be considered to be unqualified, the size of the target three-dimensional space needs to be readjusted, and correspondingly, the sizes of other adjacent spaces of the target three-dimensional space are also adjusted, so that the new DtN boundary condition needs to update the value range, and the updated new DtN boundary condition has the value range: and a superposition area between the adjusted target three-dimensional space and the adjusted rest three-dimensional space. Then, the first finite element equation can be solved again on the updated novel DtN boundary condition to obtain a new sound field of the target three-dimensional space. Finally, the steps can be repeatedly executed based on the new sound field of the target three-dimensional space until the error is smaller than a second threshold value, and the final sound field of the target three-dimensional space can be obtained.

In one possible implementation, before obtaining the partial differential equation, the method further includes: acquiring a three-dimensional model of a target object; the three-dimensional model internal space is divided into a target three-dimensional space and the rest three-dimensional space based on characteristic information of the target object, wherein the characteristic information comprises a plurality of materials of the target object and/or a plurality of functions of the target object. In the foregoing implementation, when an acoustic simulation experiment needs to be performed on the inside of the target object, a three-dimensional model of the target object may be constructed first. Then, the characteristic information of the target object may be further acquired, where the characteristic information of the target object may include information such as a plurality of materials of the target object and/or a plurality of functions of the target object. Then, the internal space of the three-dimensional model of the target object may be divided into a plurality of three-dimensional spaces based on the feature information of the target object, where the plurality of three-dimensional spaces include the target three-dimensional space to be solved currently and the remaining three-dimensional spaces, and it should be noted that the plurality of three-dimensional spaces just constitute the internal space of the three-dimensional model of the target object, i.e., for any one three-dimensional space, at least one three-dimensional space is connected around the internal space.

A second aspect of embodiments of the present application provides a partial differential equation solving apparatus, including: the first acquisition module is used for acquiring a partial differential equation, wherein the partial differential equation is used for describing a sound field of a target three-dimensional space to be solved, the target three-dimensional space comprises N grid points, the length of a side connected with the N grid points is smaller than a preset first threshold value, and N is more than 1; the conversion module is used for converting the partial differential equation to obtain a first finite element equation, wherein the first finite element equation comprises penalty parameters of N grid points, the penalty parameters of the ith grid point are obtained based on coordinates of the ith grid point and preset sound wave incidence angles, and i=1, 2, … and N; and the first solving module is used for solving the first finite element equation to obtain the sound field of the target three-dimensional space.

From the above device, it can be seen that: when the sound field distribution of the target three-dimensional space needs to be solved, a partial differential equation can be obtained, wherein the partial differential equation is used for describing the sound field of the target three-dimensional space to be solved, and the target three-dimensional space is meshed, so that the target three-dimensional space comprises N grid points, and N is a positive integer greater than 1. The partial differential equation may then be converted to a first finite element equation including penalty parameters for the N grid points. Finally, the first finite element equation can be solved to obtain the sound field of the target three-dimensional space. In the foregoing process, since the sizes of all the grids in the target three-dimensional space are sufficiently small, that is, the lengths of the edges where the N grid points are connected are limited to be smaller than the preset first threshold (the first threshold is sufficiently small), under this condition, the penalty parameters of the N grid points may be obtained based on a numerical method, that is, the penalty parameters of the i grid point may be calculated by using the coordinates of the i grid point and the preset sound wave incident angle, i=1, 2, …, N, so as to obtain the penalty parameters of the N grid points. Because the penalty parameters of the N grid points are penalty parameters applicable to the three-dimensional scene, the first finite element equation added with the penalty parameters of the N grid points is solved, the sound field of the target three-dimensional space can be directly obtained, repeated calculation and pre-estimation operations are not needed, the calculation cost is reduced, and the calculation error is reduced.

In one possible implementation, the conversion module is configured to: converting the partial differential equation to obtain a second finite element equation, wherein the second finite element equation comprises a penalty adding parameter to be solved; calculating based on the coordinates of the ith grid point and a preset sound wave incidence angle to obtain a predicted sound wave of the ith grid point; substituting the predicted sound wave of the ith grid point into a second finite element equation to obtain a penalty parameter of the ith grid point, wherein the penalty parameter of the ith grid point comprises a plurality of same subparameters, and the subparameters are in one-to-one correspondence with a plurality of edges connected with the ith network point; and in the second finite element equation, replacing the penalty parameters to be solved with the penalty parameters of the N grid points to obtain a first finite element equation.

In one possible implementation manner, a first solving module is configured to solve a first finite element equation on a boundary condition of a partial differential equation to obtain a sound field of a target three-dimensional space; the boundary condition is a first difference value equal to a second difference value, the first difference value is a difference between a first DtN boundary condition of the partial differential equation and the partial differential equation, the second difference value is a difference between a second DtN boundary condition of the partial differential equation and the partial differential equation, the value range of the boundary condition is a superposition area between the target three-dimensional space and the rest three-dimensional space, the value range of the first DtN boundary condition is the target three-dimensional space, and the value range of the second DtN boundary condition is the rest three-dimensional space.

In one possible implementation, the apparatus further includes: the computing module is used for computing based on the sound field of the target three-dimensional space to obtain an error between the sound field of the target three-dimensional space and the real sound field of the target three-dimensional space; the adjusting module is used for adjusting the size of the target three-dimensional space if the error is greater than or equal to a preset second threshold value to obtain a new boundary condition of the partial differential equation, wherein the value range of the new boundary condition is the superposition area between the adjusted target three-dimensional space and the adjusted rest three-dimensional space. And the second solving module is used for solving the first finite element equation on the new boundary condition to obtain a new sound field of the target three-dimensional space.

In one possible implementation, the apparatus further includes: the second acquisition module is used for acquiring a three-dimensional model of the target object; the dividing module is used for dividing the internal space of the three-dimensional model into a target three-dimensional space and other three-dimensional spaces based on the characteristic information of the target object, wherein the characteristic information comprises a plurality of materials of the target object and/or a plurality of functions of the target object.

A third aspect of embodiments of the present application provides a partial differential equation solving apparatus, the apparatus including a memory and a processor; the memory stores code, the processor being configured to execute the code, the partial differential equation solving means performing the method as described in the first aspect or any one of the possible implementations of the first aspect when the code is executed.

A fourth aspect of embodiments of the present application provides a computer storage medium storing one or more instructions that, when executed by one or more computers, cause the one or more computers to implement the method as described in the first aspect or any one of the possible implementations of the first aspect.

A fifth aspect of embodiments of the present application provides a computer program product storing instructions that, when executed by a computer, cause the computer to carry out the method according to the first aspect or any one of the possible implementations of the first aspect.

In the embodiment of the present application, when the sound field distribution of the target three-dimensional space needs to be solved, a partial differential equation may be obtained, where the partial differential equation is used to describe the sound field of the target three-dimensional space to be solved, and the target three-dimensional space completes grid division, so that the target three-dimensional space includes N grid points, where N is a positive integer greater than 1. The partial differential equation may then be converted to a first finite element equation including penalty parameters for the N grid points. Finally, the first finite element equation can be solved to obtain the sound field of the target three-dimensional space. In the foregoing process, since the sizes of all the grids in the target three-dimensional space are sufficiently small, that is, the lengths of the edges where the N grid points are connected are limited to be smaller than the preset first threshold (the first threshold is sufficiently small), under this condition, the penalty parameters of the N grid points may be obtained based on a numerical method, that is, the penalty parameters of the i grid point may be calculated by using the coordinates of the i grid point and the preset sound wave incident angle, i=1, 2, …, N, so as to obtain the penalty parameters of the N grid points. Because the penalty parameters of the N grid points are penalty parameters applicable to the three-dimensional scene, the first finite element equation added with the penalty parameters of the N grid points is solved, the sound field of the target three-dimensional space can be directly obtained, repeated calculation and pre-estimation operations are not needed, the calculation cost is reduced, and the calculation error is reduced.

Drawings

FIG. 1 is a schematic diagram of an algorithm framework provided in an embodiment of the present application;

FIG. 2 is a schematic flow chart of a partial differential equation solving method according to an embodiment of the present application;

FIG. 3a is a schematic diagram of a mesh provided in an embodiment of the present application;

FIG. 3b is another schematic diagram of a mesh provided in an embodiment of the present application;

FIG. 4 is a schematic diagram of simulation experiment results provided in the embodiment of the present application;

FIG. 5 is another schematic diagram of simulation experiment results provided in the embodiment of the present application;

FIG. 6 is another schematic diagram of simulation experiment results provided in an embodiment of the present application;

FIG. 7 is another schematic diagram of simulation experiment results provided in the embodiment of the present application;

FIG. 8 is a schematic diagram of a partial differential equation solving apparatus according to an embodiment of the present disclosure;

fig. 9 is another schematic structural diagram of a partial differential equation solving apparatus according to an embodiment of the present application.

Detailed Description

The terms first, second and the like in the description and in the claims of the present application and in the above-described figures, are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances and are merely illustrative of the manner in which the embodiments of the application described herein have been described for objects of the same nature. Furthermore, the terms "comprises," "comprising," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of elements is not necessarily limited to those elements, but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.

The quality of sound in the automobile directly affects the quality of the automobile product, and is also an important index for evaluating the riding comfort of the automobile. Various manufacturers in China are invested with great efforts and cost to solve the problem of sound quality in the automobile, and are subject to the reasons of long experimental test period, difficult determination of problem sources, high manufacturing cost of test equipment and the like, and simulation methods are often adopted to predict the sound field (distribution) in the automobile, so that the sound quality in the automobile is determined.

In car acoustic simulations, the core problem is how to solve the partial differential equation describing the sound field of the interior space of the car to be solved quickly and accurately. The method can be solved by a finite element method at present, namely, a partial differential equation is expressed by a finite element equation, and then the finite element equation is solved to obtain the sound field of the inner space of the automobile. In order to make the resulting sound field sufficiently accurate, penalty parameters may be added to the original finite element equation for constraining the accuracy of the resulting sound field. Then, the finite element equation with the penalty parameter added can be solved to obtain the sound field of the interior space of the automobile.

However, the added penalty parameter is usually a parameter optimized based on a two-dimensional scene (i.e., the current internal penalty finite element method is only called as perfect theoretical analysis and application on a two-dimensional problem), so that the three-dimensional space in the automobile needs to be converted into a two-dimensional plane, the plane is taken as a region to be solved, and a finite element equation added with the penalty parameter is solved to obtain a sound field on the plane. The above-mentioned process is repeated, so that a sound field on at least one plane can be obtained, and then the sound field of the internal space of the automobile can be estimated based on the sound field on at least one plane. Therefore, since the existing penalty parameters are limited to two-dimensional scenes, the sound field of the three-dimensional space inside the automobile needs to be estimated through the sound field of at least one plane in the space, the calculation cost of the calculation mode is high (the sound fields of a plurality of planes need to be repeatedly solved), and the calculation error is large (the estimated sound field of the automobile interior space is often not accurate enough).

In order to solve the above-mentioned problems, the embodiments of the present application provide a partial differential equation solving method, which may be implemented by an algorithm framework (fig. 1 is a schematic diagram of the algorithm framework provided in the embodiments of the present application) as shown in fig. 1, and it should be noted that the algorithm framework is schematically described with a target object as an acoustic simulation scene of an automobile, but the target object to which the algorithm framework is applicable is not limited, for example, the target object may also be an object whose interior is a three-dimensional space, such as a room, a sound box, or the like. As shown in fig. 1, the algorithm framework comprises the following steps:

(1) A three-dimensional model of the target object is constructed, for example, a three-dimensional model of an automobile is acquired by software such as CAD, or the like.

(2) The internal space of the three-dimensional model of the target object is divided, for example, for the internal space of the three-dimensional model of the automobile, the space occupied by the seat may be determined as one three-dimensional space, the space occupied by the door may be determined as another three-dimensional space, the space occupied by the center console may be determined as another three-dimensional space, and so on, so that the space within the three-dimensional model of the automobile may be divided into a plurality of three-dimensional spaces.

(3) For any one of the three-dimensional spaces that has been divided, the three-dimensional space may be meshed so that the three-dimensional space may include a plurality of meshes, each of the meshes typically including a plurality of mesh points, so that the three-dimensional space also includes a plurality of mesh points.

(4) Boundary conditions of partial differential equations describing sound field distribution of the three-dimensional space are acquired.

(5) And solving a partial differential equation for describing sound field distribution of the three-dimensional space on the boundary condition to obtain the sound field of the three-dimensional space.

(6) Determining an error based on the calculated sound field of the three-dimensional space, and if the error is greater than or equal to a preset threshold, repartitioning the internal space of the three-dimensional model of the target object based on the error to adjust the size of the three-dimensional space, and recalculating the adjusted sound field of the three-dimensional space until the error is less than the preset threshold (i.e., re-executing steps (2) to (6)). For example, after obtaining the sound field of the space occupied by the seat, an error may be calculated based on the sound field, and if the error is too large, the size of the space occupied by the seat may be readjusted, and the sound field of the new space may be recalculated until the error satisfies the condition.

To further understand the algorithm framework described above, the algorithm framework is further described below in conjunction with FIG. 2. Fig. 2 is a schematic flow chart of a partial differential equation solving method according to an embodiment of the present application, as shown in fig. 2, the method includes:

201. a three-dimensional model of the target object is acquired.

In this embodiment, when an acoustic simulation experiment needs to be performed on the inside of the target object, a three-dimensional model of the target object may be constructed first. For example, when it is necessary to analyze the sound field distribution of the interior space of the automobile, a three-dimensional model of the automobile (which may also be referred to as an automobile model) may be constructed by simulation software such as CAD. Then, solving the sound field of the interior space of the automobile is equivalent to solving the sound field of the interior space of the automobile model.

202. The three-dimensional model internal space of the target object is divided into a target three-dimensional space and a remaining three-dimensional space based on characteristic information of the target object, the characteristic information including a plurality of materials of the target object and/or a plurality of functions of the target object.

After the three-dimensional model of the target object is obtained, the characteristic information of the target object can be further obtained, and the characteristic information of the target object can comprise information such as a plurality of materials of the target object and/or a plurality of functions of the target object. After the feature information of the target object is obtained, the internal space of the three-dimensional model of the target object can be divided into a plurality of three-dimensional spaces based on the feature information of the target object, wherein the plurality of three-dimensional spaces comprise the target three-dimensional space to be solved currently and the rest three-dimensional spaces, and the plurality of three-dimensional spaces just form the internal space of the three-dimensional model of the target object, namely, for any three-dimensional space, at least one three-dimensional space is connected around the internal space.

For example, after the automobile model is obtained, the materials of various components in the automobile, that is, the seat of the automobile is made of leather, the door is made of metal, the center console is made of plastic, glass or the like, so that the space occupied by the seat can be determined as one three-dimensional space, the space occupied by the door is determined as another three-dimensional space, the space occupied by the center console is determined as another three-dimensional space, and the like in the internal space of the automobile model, and thus, the space in the three-dimensional model of the automobile can be divided into a plurality of three-dimensional spaces. For example, after the automobile model is obtained, the functions of each component in the automobile, namely, the functions of the seat of the automobile are used for a user to ride, the functions of the door are used for the user to get in and out of the automobile, the center console is used for the user to issue instructions and the like, so that the space occupied by the seat can be determined as one three-dimensional space, the space occupied by the door is determined as another three-dimensional space, the space occupied by the center console is determined as another three-dimensional space and the like in the internal space of the automobile, and therefore, the space in the three-dimensional model of the automobile can be divided into a plurality of three-dimensional spaces and the like.

203. And meshing the target three-dimensional space so that the target three-dimensional model comprises N grid points, wherein the length of the edge connected with the N grid points is smaller than a preset first threshold value, and N is more than 1.

After the target three-dimensional space is obtained, the target three-dimensional space can be subjected to grid division, namely, the whole target three-dimensional space is divided into M grids with certain sizes, and M is a positive integer greater than 1. For example, each of the M meshes may be a triangular patch, that is, each mesh has three mesh points, and any two adjacent mesh points have a common mesh point and a common side, so that after dividing the entire target three-dimensional space into M mesh points having a certain size, the target three-dimensional space includes N mesh points, where the i-th mesh point is connected to a plurality of sides (it can be seen that N mesh points are connected to a plurality of sides), i=1, 2, …, N is a positive integer greater than 1, and N is not equal to M.

It should be noted that the sizes of the M grids are uniformly determined according to a preset grid division granularity, that is, the edges connected by the N grid points are smaller than a preset first threshold (the first threshold is usually small enough, and is related to the preset grid division granularity, and the size of the first threshold can be set according to actual requirements, and is not expanded here).

To further understand the meshing described above, the meshing is further described below in conjunction with FIG. 3 a. Fig. 3a is a schematic diagram of a mesh provided in an embodiment of the present application, and as shown in fig. 3a, it is assumed that the target three-dimensional space is divided into M meshes, where the M meshes are all regular triangles. Of the M grids, 12 grids among them are taken for schematic illustration, and the 12 grids have 13 grid points. For grid point 1, 6 sides are connected (i.e., grid point 1 is connected to grid point 2, grid point 3, grid point 4, grid point 5, grid point 6, and grid point 7, respectively), and these 6 sides are of equal length. Likewise, the edges to which the remaining grid points are connected are of equal length, and will not be described here again.

It should be understood that the example shown in fig. 3a is only schematically illustrated by using regular triangles with the same size for M grids, and is not limited to the size of the M grids in the present application, for example, as shown in fig. 3b (fig. 3b is another schematic diagram of the grids provided in the embodiment of the present application), the M grids may be different triangles, or the M grids may be different quadrilaterals, or the like.

204. And acquiring a partial differential equation, wherein the partial differential equation is used for describing the sound field of the target three-dimensional space to be solved.

After the mesh division of the target three-dimensional space is completed, a partial differential equation for describing the sound field of the target three-dimensional space to be solved can be obtained, and the value range (also called as a region to be solved) of the partial differential equation is used as the target three-dimensional space. It should be noted that, the sound field distribution of the internal space of the three-dimensional model of the target object may be described by the same partial differential equation, so that the partial differential equation may be used to describe not only the sound field of the target three-dimensional space to be solved, but also the sound fields of the remaining three-dimensional spaces to be solved. However, when the partial differential equation is used for describing the sound field of the rest three-dimensional space to be solved, the value range of the partial differential equation is the rest three-dimensional space.

For example, let the partial differential equation describing the sound field of the target three-dimensional space to be solved be the helmholtz (helmholtz) equation, which can be expressed by the following equation:

Au(p _i )+k ² u(p _i )＝0，p _i ∈Ω _i (1)

in the above, p _i An ith grid point of N grid points of the target three-dimensional space; u (p) _i ) For the ith grid point p _i Sound waves on the upper surface; k is the wave number of the sound wave; omega shape _i The method is a value range (to-be-solved area), namely a target three-dimensional space. Wherein the ith grid point p _i Can be expressed as p _i ＝(x _i ，y _i )。

205. And converting the partial differential equation to obtain a first finite element equation, wherein the first finite element equation comprises penalty parameters of N grid points, the penalty parameters of the ith grid point are obtained based on coordinates of the ith grid point and preset sound wave incidence angles, and i=1, 2, … and N.

After the partial differential equation is obtained, the partial differential equation can be converted based on an internal penalty finite element method to obtain a first finite element equation, wherein the first finite element equation comprises penalty parameters of N grid points, the penalty parameters of the N grid points are all known parameters, and the penalty parameters of the i grid point are calculated based on the coordinates of the i grid point and a preset sound wave incident angle in the N grid points. Specifically, the penalty parameter for the ith grid point may be obtained by:

(1) Because the existing penalty parameters are only applicable to two-dimensional scenes, penalty parameters applicable to three-dimensional scenes need to be acquired. First, the partial differential equation is converted based on the internal penalty finite element method, so as to obtain a second finite element equation (which can be understood as an original finite element equation), where the second finite element equation contains the penalty parameters to be solved (i.e., the penalty parameters in the second finite equation are unknown). Then the second finite element equation needs to be analyzed and solved to optimize the penalty parameters for the three-dimensional scene.

Still as in the above example, equation (1) is converted by the interior penalty finite element method into the following second finite element equation:

in the above-mentioned method, the step of,operators of the internal penalty finite element method; v (p) _i ) For the ith grid point p _i Acoustic wave u (p) _i ) Wave velocity, wave number v (p _i ) Can be set according to actual demands, and is regarded as a known quantity; q is an imaginary unit (which may also be represented by a conventional imaginary unit representation "i"); j (u (p) _i )，v(p _i ) To contain the ith grid point p _i Penalty parameter gamma of (2) _i Is an unknown quantity; f is a source term in a Helmholtz equation, and the value is 0; g is a parameter related to the coordinates of the grid point, and can be set according to the actual requirement, as a known quantity, for example, when the ith grid point p is analyzed at present _i The value of g is equal to the ith grid point p _i Correspondingly, when the rest grid points are analyzed, the value of g corresponds to the rest grid points. It can be seen that if the ith grid point p is to be determined _i Penalty parameter gamma of (2) _i It is necessary to solve for J (u (p _i )，v(p _i ) Is a value of (2).

For penalty parameters applicable to two-dimensional scenes, the value of the penalty parameter can be selected by the following process:

based on fig. 3a, grid point 1 may be selected for analysis, let grid point 1 be the origin, and the side length of the regular triangle be h, and by performing simple calculation on equation (2), a third finite element equation (i.e., the finite element equation at grid point 1) may be obtained as follows:

in the above, gamma ₁ Penalty parameter for grid point 1, u ₁ 、u ₂ 、...、u ₁₃ These are unknown quantities for the acoustic waves at grid points 1 to 13, respectively.

Assume thatSatisfy equation (4), where (x) _i ，y _i ) Is the ith grid point p _i Coordinates of->Is the discrete wave number, θ is the ith grid point p _i Acoustic wave u on _i In formula (4), i=1, 2, …,13. Note t=kh, < >>Will be the ith grid point p _i Is substituted into the ith grid point p _i Acoustic wave u on _i And the following discrete wavenumber equation can be obtained from equation (3):

ideally, discrete wavenumbers are desiredThe closer to wavenumber k, i.e. +. >The smaller the better. Using the hidden function theorem, differential median theorem, and F (t, t, θ, γ) ₁ ) Taylor (taylor) expansion at t=0, can be obtained:

it should be noted that the number of the substrates,t ⁸ multiplied "()" represents t ⁸ The many parameters multiplied are represented by "()" because they are complex and have little effect in the subsequent reasoning. Based on equation (5), the following progressive relationship can be obtained:

let a (gamma) ₁ ) =0, and let b (γ ₁ θ) is minimum for all angles of incidence θ, the penalty parameter γ 'for grid point 1 can be solved' _i . The penalty parameter acquisition process described above may also be performed for the remaining grid points, so that penalty parameters applicable to each grid point of the two-dimensional scene may be obtained.

Based on the process of obtaining the penalty parameter suitable for the two-dimensional scene, and as long as kh is made small enough (for example, kh is made to be less than or equal to 1, i.e., the edge connected by the grid points is set to be small enough), the second finite element equation shown in the formula (2) can be solved by using a numerical method in the three-dimensional scene (i.e., the subsequent steps (2) to (4)), so as to obtain the penalty parameter suitable for the three-dimensional scene.

(2) After the second finite element equation is obtained, calculation may be performed based on the coordinates of the ith grid point and a preset sound wave incident angle (the incident angle may be selected according to actual requirements, which is not limited herein), so as to obtain a predicted sound wave of the ith grid point.

Still as in the example above, equation (2) may be modified to a system of linear equations:

(A+J(γ _i ))U＝F (7)

in the above formula, U is U (p) in formula (2) _i )，U＝e ^qk (x _i cosθ+y _i sin theta); a is as defined in formula (2)k ² (u(p _i )，v(p _i ) And qk (p) _i )，v(p _i )) _Γ The three items extract UThe obtained product; f is a group represented by the formula (2) (F, v (p) _i ))、(g，v(p _i )) _Γ The two items are obtained by extracting U; j (gamma) _i ) To combine J (u (p) _i )，v(p _i ) Obtained by extracting U.

In formula (7), only U and J (γ) _i ) Is an unknown quantity. To estimate the value of U, a preset sound wave incident angle theta' can be obtained and substituted into U (q, k, x _i And y _i All of known amounts), the i-th grid point p is obtained _i And predicted sound wave U'.

(3) After obtaining the predicted sound wave of the ith grid point, substituting the predicted sound wave of the ith grid point into the second finite element equation to obtain the penalty parameter of the ith grid point, wherein the penalty parameter of the ith grid point is usually a vector, the vector comprises a plurality of identical subparameters (as a plurality of elements of the vector), and the subparameters are in one-to-one correspondence with a plurality of edges connected with the ith grid point. Likewise, for the remaining grid points, the same operations as performed for the ith grid point may be performed, so that the penalty parameters for the N grid points may be obtained.

Still as in the above example, the ith grid point p is obtained _i After the predicted sound wave U 'is obtained, U' can be substituted into the formula (7) to solve J (gamma) _i '), and then the ith grid point p can be obtained _i Penalty parameter gamma of (2) _i ′，γ _i ′＝(γ _i1 ′，γ _i2 ' y., wherein γ _i1 ' ith grid point p _i Penalty parameters (i.e., the aforementioned sub-parameters) corresponding to the first edge of the connection, γ _i2 ' ith grid point p _i Penalty parameters corresponding to the second edge of the connection, etc., as can be seen, γ _i A certain element in' corresponds to a certain edge to which the ith grid point is connected. Similarly, the same operations can be performed for the remaining grid points, and the penalty parameters of N grid points, i.e., gamma ₁ ′，γ ₂ ′，....γ _N ′。

(4) After penalty parameters of the N grid points are obtained, the penalty parameters to be solved can be replaced by penalty parameters of the N grid points in the second finite element equation, so as to obtain a first finite element equation (i.e., a finite element equation with known penalty parameters).

206. And solving the first finite element equation to obtain the sound field of the target three-dimensional space.

After the first finite element equation is determined, the first finite element equation can be solved on the boundary condition of the partial differential equation to obtain the sound field of the target three-dimensional space. It should be noted that the conventional boundary conditions are often limited to the following problems, resulting in poor calculation accuracy and performance: (1) the target three-dimensional space may be an irregular space; (2) When the wave number of the sound wave is too high, the finite element equation with the added penalty parameter cannot be adapted. Thus, the present embodiment provides a novel DtN boundary condition as the boundary condition of the partial differential equation:

The novel DtN boundary condition is that a first difference value is equal to a second difference value, the first difference value is the difference between a first DtN boundary condition of a partial differential equation and the partial differential equation, the second difference value is the difference between a second DtN boundary condition of the partial differential equation and the partial differential equation, the value range of the new boundary condition is the superposition area between the target three-dimensional space and the rest three-dimensional space, the value range of the first DtN boundary condition is the target three-dimensional space, and the value range of the second DtN boundary condition is the rest three-dimensional space.

Still as in the example above, a first DtN boundary condition is obtained:

in the above-mentioned method, the step of,for the ith grid point p on the boundary of the three-dimensional space of the target _i Acoustic wave u (p) _i ) Derivative in the normal direction; n is the DtN operator on the boundary; />Is the boundary of the three-dimensional space of the target.

Next, a second DtN boundary condition is obtained:

in the above, Ω _j The other three-dimensional space adjacent to the target three-dimensional space;for the j-th grid point p on the boundary of the rest three-dimensional space _j Acoustic wave u (p) _j ) Derivative in the normal direction.

Then, equation (8) is written asLet formula (9) be +.>Equation (1) is denoted as Su (p) _i ) Based on formula (1), su (p) _j ). Then the new DtN boundary conditions are:

In the above-mentioned method, the step of,is the coincidence region between the boundary of the target three-dimensional space and the boundary of the rest three-dimensional space.

After the novel DtN boundary condition is obtained, the first finite element equation can be solved on the boundary condition to obtain the sound field of the target three-dimensional space.

207. And calculating based on the sound field of the target three-dimensional space to obtain an error between the sound field of the target three-dimensional space and the real sound field of the target three-dimensional space.

208. And if the error is greater than or equal to a preset second threshold value, adjusting the size of the target three-dimensional space to obtain a new boundary condition of the partial differential equation, wherein the value range of the new boundary condition is the superposition area between the adjusted target three-dimensional space and the adjusted rest three-dimensional space.

209. And solving the first finite element equation on the new boundary condition to obtain a new sound field of the target three-dimensional space.

After the sound field of the target three-dimensional space is obtained, feedback adjustment can be performed based on the sound field until the final sound field of the target three-dimensional space is obtained, wherein the feedback adjustment process is as follows:

(1) And calculating the sound field of the target three-dimensional space by using a preset error indicator (also known as a preset error calculation formula), so as to obtain the error between the sound field of the target three-dimensional space and the real sound field of the target three-dimensional space.

(2) It may be determined whether the error is greater than or equal to a preset second threshold (the magnitude of the second threshold may be set according to actual needs, which is not limited herein). If the error is less than the second threshold, the resulting sound field of the target three-dimensional space may be considered acceptable. If the error is greater than or equal to the preset second threshold, the obtained sound field of the target three-dimensional space is considered to be unqualified, the size (dimension) of the target three-dimensional space needs to be readjusted, and correspondingly, the sizes of other adjacent spaces of the target three-dimensional space are also adjusted, so that the new type DtN boundary condition needs to update the value range, and the updated value range of the new type DtN boundary condition is as follows: and a superposition area between the adjusted target three-dimensional space and the adjusted rest three-dimensional space.

(3) And solving the first finite element equation again on the updated novel DtN boundary condition to obtain a new sound field of the target three-dimensional space.

(4) And (3) repeatedly executing the steps (1) to (3) based on the new sound field of the target three-dimensional space until the error is smaller than a second threshold value, and obtaining the final sound field of the target three-dimensional space.

In addition, a simulation experiment may be performed by using a car of a certain model, where the experimental results are shown in fig. 4 to 7 (fig. 4 is a schematic diagram of the simulation experimental results provided by the embodiment of the present application, fig. 5 is another schematic diagram of the simulation experimental results provided by the embodiment of the present application, fig. 6 is another schematic diagram of the simulation experimental results provided by the embodiment of the present application, and fig. 7 is another schematic diagram of the simulation experimental results provided by the embodiment of the present application), and it should be noted that, when the simulation experiment is performed, the car may be divided into four parts to perform the simulation experiment, and the experimental results are respectively the main driving part, the left rear position, the right rear position and the auxiliary driving part of the car, where fig. 4 shows the difference between the experimental effect of the sound field distribution of the main driving part of the car (the experiment performed based on the method provided by the embodiment of the present application) and the standard effect, fig. 5 shows the difference between the experimental effect of the sound field distribution of the left rear position of the car (the experiment performed based on the method provided by the embodiment of the present application) and the standard effect, and fig. 6 shows the difference between the experimental effect of the sound field distribution of the right rear position of the car (experiment result of the experiment performed by the method provided by the embodiment of the present application) and the standard effect.

As can be seen from the comparison results shown in fig. 4 and fig. 7, the experimental effect of the sound field distribution obtained by the method provided in the embodiment of the present application has little difference from the standard effect of the sound field distribution, and the experimental effect and the standard effect of the sound field distribution are almost fitted, so that enough excellent performance can be obtained.

Furthermore, the embodiment of the application also provides a novel DtN boundary condition which is suitable for three-dimensional spaces with various shapes, and can be adapted to a finite element equation added with penalty parameters when solving the problem of high wave numbers, thereby being beneficial to improving the calculation precision and performance.

The above is a detailed description of the partial differential equation solving equation provided in the embodiment of the present application, and the partial differential equation solving apparatus provided in the embodiment of the present application will be described below. Fig. 8 is a schematic structural diagram of a partial differential equation solving apparatus according to an embodiment of the present application, as shown in fig. 8, where the apparatus includes:

the first obtaining module 801 is configured to obtain a partial differential equation, where the partial differential equation is used to describe a sound field of a target three-dimensional space to be solved, the target three-dimensional space includes N grid points, a length of a side connected with the N grid points is smaller than a preset first threshold, and N is greater than 1;

the conversion module 802 is configured to convert the partial differential equation to obtain a first finite element equation, where the first finite element equation includes penalty parameters of N grid points, and the penalty parameters of the i grid point are obtained based on coordinates of the i grid point and a preset sound wave incident angle, i=1, 2, …, N;

And the first solving module 803 is configured to solve the first finite element equation to obtain a sound field of the target three-dimensional space.

In one possible implementation, the conversion module 802 is configured to: converting the partial differential equation to obtain a second finite element equation, wherein the second finite element equation comprises a penalty adding parameter to be solved; calculating based on the coordinates of the ith grid point and a preset sound wave incidence angle to obtain a predicted sound wave of the ith grid point; substituting the predicted sound wave of the ith grid point into a second finite element equation to obtain a penalty parameter of the ith grid point, wherein the penalty parameter of the ith grid point comprises a plurality of same subparameters, and the subparameters are in one-to-one correspondence with a plurality of edges; and in the second finite element equation, replacing the penalty parameters to be solved with the penalty parameters of the N grid points to obtain a first finite element equation.

In one possible implementation, the first solving module 803 is configured to solve the first finite element equation on a boundary condition of the partial differential equation, to obtain a sound field of the target three-dimensional space; the boundary condition is a first difference value equal to a second difference value, the first difference value is a difference between a first DtN boundary condition of the partial differential equation and the partial differential equation, the second difference value is a difference between a second DtN boundary condition of the partial differential equation and the partial differential equation, the value range of the boundary condition is a superposition area between the target three-dimensional space and the rest three-dimensional space, the value range of the first DtN boundary condition is the target three-dimensional space, and the value range of the second DtN boundary condition is the rest three-dimensional space.

Fig. 9 is another schematic structural diagram of a partial differential equation solving apparatus according to an embodiment of the present application. As shown in fig. 9, one embodiment of an arbiter may include one or more central processing units 901, memory 902, input-output interfaces 903, wired or wireless network interfaces 904, and a power supply 905.

The memory 902 may be a transient memory or a persistent memory. Still further, the central processor 901 may be configured to communicate with the memory 902 to execute a series of instruction operations in the memory 902 on the partial differential equation solving device.

In this embodiment, the cpu 901 may execute the method steps in the embodiment shown in fig. 2 or fig. 8, which is not described herein.

In this embodiment, the specific functional module division in the central processor 901 may be similar to the division manner of the aforementioned modules such as the first acquisition module, the conversion module, the first solution module, the calculation module, the adjustment module, the second solution module, the second acquisition module, and the division module described in fig. 8, which is not repeated herein.

Embodiments of the present application also relate to a computer storage medium comprising computer readable instructions which, when executed, implement the method steps in the embodiments as shown in fig. 2 or fig. 8.

Embodiments of the present application also relate to a computer program product containing instructions which, when run on a computer, cause the computer to perform the method steps of the embodiments as shown in fig. 2 or fig. 8.

It will be clear to those skilled in the art that, for convenience and brevity of description, specific working procedures of the above-described systems, apparatuses and units may refer to corresponding procedures in the foregoing method embodiments, which are not repeated herein.

In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods may be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative, e.g., the division of the units is merely a logical function division, and there may be additional divisions when actually implemented, e.g., multiple units or components may be combined or integrated into another system, or some features may be omitted or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed with each other may be an indirect coupling or communication connection via some interfaces, devices or units, which may be in electrical, mechanical or other form.

The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

In addition, each functional unit in each embodiment of the present application may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit. The integrated units may be implemented in hardware or in software functional units.

The integrated units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present application may be embodied in essence or a part contributing to the prior art or all or part of the technical solution in the form of a software product stored in a storage medium, including several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.

Claims

1. A partial differential equation solving method, the method comprising:

acquiring a partial differential equation, wherein the partial differential equation is used for describing a sound field of a target three-dimensional space to be solved, the target three-dimensional space comprises N grid points, the length of a side connected with the N grid points is smaller than a preset first threshold value, and N is more than 1;

Converting the partial differential equation to obtain a first finite element equation, wherein the first finite element equation comprises penalty parameters of the N grid points, the penalty parameters of the ith grid point are obtained based on coordinates of the ith grid point and preset sound wave incidence angles, and i=1, 2, … and N;

and solving the first finite element equation to obtain the sound field of the target three-dimensional space.

2. The method of claim 1, wherein converting the partial differential equation to obtain a first finite element equation comprises:

converting the partial differential equation to obtain a second finite element equation, wherein the second finite element equation comprises a penalty adding parameter to be solved;

calculating based on the coordinates of the ith grid point and a preset sound wave incidence angle to obtain a predicted sound wave of the ith grid point;

substituting the predicted sound wave of the ith grid point into the second finite element equation to obtain a penalty parameter of the ith grid point, wherein the penalty parameter of the ith grid point comprises a plurality of same subparameters, and the subparameters are in one-to-one correspondence with a plurality of edges connected with the ith network point;

and in the second finite element equation, replacing the penalty parameter to be solved with the penalty parameters of N grid points to obtain a first finite element equation.

3. The method according to claim 1 or 2, wherein solving the first finite element equation to obtain the sound field of the target three-dimensional space comprises:

solving the first finite element equation on the boundary condition of the partial differential equation to obtain a sound field of the target three-dimensional space;

the boundary condition is a first difference value equal to a second difference value, the first difference value is a difference between a first DtN boundary condition of the partial differential equation and the partial differential equation, the second difference value is a difference between a second DtN boundary condition of the partial differential equation and the partial differential equation, the value range of the boundary condition is a superposition area between the target three-dimensional space and the rest three-dimensional space, the value range of the first DtN boundary condition is the target three-dimensional space, and the value range of the second DtN boundary condition is the rest three-dimensional space.

4. A method according to claim 3, wherein after said solving the first finite element equation to obtain the sound field of the target three-dimensional space, the method further comprises:

calculating based on the sound field of the target three-dimensional space to obtain an error between the sound field of the target three-dimensional space and the real sound field of the target three-dimensional space;

If the error is greater than or equal to a preset second threshold value, adjusting the size of the target three-dimensional space to obtain a new boundary condition of the partial differential equation, wherein the value range of the new boundary condition is a superposition area between the adjusted target three-dimensional space and the adjusted rest three-dimensional spaces;

and solving the first finite element equation on the new boundary condition to obtain a new sound field of the target three-dimensional space.

5. The method of any one of claims 1 to 4, wherein prior to the obtaining the partial differential equation, the method further comprises:

acquiring a three-dimensional model of a target object;

the three-dimensional model internal space is divided into a target three-dimensional space and other three-dimensional spaces based on the characteristic information of the target object, wherein the characteristic information comprises a plurality of materials of the target object and/or a plurality of functions of the target object.

6. A partial differential equation solving apparatus, the apparatus comprising:

the first acquisition module is used for acquiring a partial differential equation, wherein the partial differential equation is used for describing a sound field of a target three-dimensional space to be solved, the target three-dimensional space comprises N grid points, the length of a side connected with the N grid points is smaller than a preset first threshold value, and N is more than 1;

The conversion module is used for converting the partial differential equation to obtain a first finite element equation, the first finite element equation comprises penalty parameters of the N grid points, the penalty parameters of the ith grid point are obtained based on the coordinates of the ith grid point and preset sound wave incidence angles, and i=1, 2, … and N;

and the first solving module is used for solving the first finite element equation to obtain the sound field of the target three-dimensional space.

7. The apparatus of claim 6, wherein the conversion module is configured to:

8. The apparatus according to claim 6 or 7, wherein the first solving module is configured to solve the first finite element equation on a boundary condition of the partial differential equation to obtain a sound field of the target three-dimensional space;

9. The apparatus of claim 8, wherein the apparatus further comprises:

the computing module is used for computing based on the sound field of the target three-dimensional space to obtain an error between the sound field of the target three-dimensional space and the real sound field of the target three-dimensional space;

the adjusting module is used for adjusting the size of the target three-dimensional space if the error is larger than or equal to a preset second threshold value to obtain a new boundary condition of the partial differential equation, wherein the value range of the new boundary condition is an overlapping area between the adjusted target three-dimensional space and the adjusted rest three-dimensional spaces;

And the second solving module is used for solving the first finite element equation on the new boundary condition to obtain a new sound field of the target three-dimensional space.

10. The apparatus according to any one of claims 6 to 9, further comprising:

the second acquisition module is used for acquiring a three-dimensional model of the target object;

the dividing module is used for dividing the three-dimensional model internal space into a target three-dimensional space and other three-dimensional spaces based on the characteristic information of the target object, wherein the characteristic information comprises a plurality of materials of the target object and/or a plurality of functions of the target object.

11. A partial differential equation solving apparatus, the apparatus comprising a memory and a processor; the memory stores code, the processor being configured to execute the code, the partial differential equation solving means performing the method of any of claims 1 to 5 when the code is executed.

12. A computer storage medium storing one or more instructions which, when executed by one or more computers, cause the one or more computers to implement the method of any one of claims 1 to 5.

13. A computer program product, characterized in that it stores instructions that, when executed by a computer, cause the computer to implement the method of any one of claims 1 to 5.