A frequency-independent automatic matching layer method for fast modeling and simulation of acoustic and vibro-acoustic coupling problems

Abstract

The application discloses a frequency-independent automatic matching layer method for fast modeling simulation of acoustic and vibro-acoustic coupling problems, and belongs to the cross field of computational acoustics and numerical methods, and comprises the following steps: step 1, a physical domain model is established, and a perfect matching layer grid is automatically generated, and a round corner transition is arranged at a sharp corner; step 2, a complex space coordinate transformation is established, an absorption function and an integral function thereof are constructed; step 3, a standard finite element framework is established, a frequency-independent global system matrix is assembled, and a final system equation is obtained; step 4, an acoustic or vibro-acoustic coupling finite element-perfect matching layer formula is constructed, and near-field or far-field physical quantities of the acoustic or vibro-acoustic coupling problem are obtained; and step 5, the frequency-independent characteristics of the perfect matching layer and adaptive multi-point second-order Krylov subspace reduction are combined to realize fast solving. According to the application, the system matrix is assembled once to realize full-band reuse, the calculation cost is reduced, and the low-frequency precision, geometric adaptability and far-field prediction capability are improved.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of computational acoustics and numerical methods, and in particular relates to a frequency-independent automatic matching layer method for rapid modeling and simulation of acoustic and vibratory coupling problems. Background Technology

[0002] Numerical simulation of external acoustic and vibration-acoustic coupling systems is of great significance in various engineering applications such as high-speed aircraft, acoustic sensors, and marine infrastructure. The physical domain of many sound wave propagation problems is unbounded, and it is impossible to directly discretize the entire infinite space using the finite element method. In order to use the finite element method, the infinite computational domain must be truncated into a computational domain of finite size. After truncation, non-physical reflection waves will be generated at the artificial boundary, affecting the internal calculation results. There are three mainstream solutions: absorbing boundary condition method; infinite element method; and perfect matching layer method.

[0003] The perfectly matched layer method has been well-developed due to its flexibility, accuracy, and ease of numerical implementation, and has been successfully applied to industrial simulations of Helmholtz external acoustic problems and vibration-acoustic coupling problems. By applying complex stretching to spatial coordinates to absorb emitted sound waves, the performance of the perfectly matched layer method depends on the absorption function, which typically involves free parameters. Using an unbounded absorption function has proven to be a very effective approach, and by setting specific parameters to the sound velocity of the fluid medium, it avoids any adjustment of the free perfectly matched layer parameters.

[0004] Despite the attractiveness and effectiveness of the perfectly matched layer method, it still faces challenges in frequency sweep analysis: most absorption functions are frequency-dependent, and its performance at low frequencies is insufficient compared to the high-frequency range, especially when the matched layer is placed close to the scattering target. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a frequency-independent automatic matching layer method for rapid modeling and simulation of acoustic-vibration coupling problems, comprising: Based on the boundary mesh data of the physical domain, a perfectly matched layer mesh covering the scatterer or structure is generated, and rounded transitions are set at geometric sharp corners to make the normal vector change continuously along the boundary. Complex spatial coordinates are established based on the perfectly matched layer mesh, the frequency is fixed to the middle frequency of the analysis band, an absorption function independent of frequency is constructed, and the complex spatial coordinates are stretched along the normal direction. A finite element framework is established based on the stretched complex spatial coordinates. A frequency-independent global system matrix is ​​assembled and boundary conditions are applied to obtain the final system equations. Based on the final system equations, construct the finite element-perfectly matched layer formulation of acoustic or vibratory-acoustic coupling to obtain the near-field or far-field physical quantities of the acoustic or vibratory-acoustic coupling problem. The final system equations are solved using an adaptive multi-point second-order Krylov subspace reduction method. The expansion point position and order are automatically determined through cross-validation of the double-reduction model, and the solution is applied to the perfectly matched layer to complete the attenuation matching of the sound wave within the perfectly matched layer.

[0006] Optionally, generating a perfectly matching layer mesh covering the scatterer or structure includes: An unbounded acoustic field is constructed based on the Helmholtz equation and radiation conditions, and a perfectly matched layer is constructed to truncate the unbounded acoustic field. After meshing the unbounded acoustic field, the mesh data on the outer boundary is obtained. The normal vector is calculated based on the grid data on the outer boundary. For vertices at corner points, the weighted average of the normal vectors of adjacent cells is taken. For second-order nodes at the midpoint of an edge, the average of the normal vectors of the two endpoints of that edge is taken. Based on the normal vector, a perfectly matched layer is generated by stretching outward at equal intervals along the normal direction of each node, and the mesh cell type of the perfectly matched layer generated by stretching is defined as a format that matches the internal computational domain.

[0007] Optionally, complex spatial coordinates are established and a frequency-independent absorption function is constructed, including: Set up a reference coordinate system, establish an expression for complex spatial coordinates, and use interpolation to interpolate the boundary normal vector to obtain the complex coordinate stretching expression and dimensionless thickness coordinates. The frequency-independent absorption function includes preset parameters. C ,and C greater than the speed of sound c The frequency is fixed at the middle frequency of the analysis band, and the absorption function and its integral function are constructed. The integral of the absorption function at the singularity is processed using numerical integration.

[0008] Optionally, a finite element framework is established and a frequency-independent global system matrix is ​​assembled, including: Discretization is performed using the Galerkin method, and weight functions with the same shape function are selected. A standard Jacobian matrix is ​​constructed for the physical domain, and a complex Jacobian matrix is ​​constructed for the perfectly matched layer domain. Based on the complex Jacobian matrix, a global stiffness matrix and a global mass matrix are constructed, and the frequency response equation is obtained after applying boundary conditions.

[0009] Optionally, when establishing the finite element framework and assembling the global system matrix, velocity potential is used instead of sound pressure as the basic unknown in the acoustic domain, so that the coupled system matrix is ​​transformed into a symmetric matrix.

[0010] Optionally, when obtaining near-field or far-field physical quantities for acoustic or vibratory coupling problems, the boundary of the perfectly matched layer is used as the Kirchhoff integral surface. The sound pressure and normal derivative on this boundary are used to extrapolate the sound pressure at any point in the far field using the Kirchhoff surface integral formula.

[0011] Optionally, when dealing with full-space problems, a full-space Green's function is used for far-field extrapolation; when dealing with half-space problems, a half-space Green's function is introduced for far-field extrapolation.

[0012] Optionally, the final system equations are solved using an adaptive multi-point second-order Krylov subspace reduction method, including: Two different sets of extension points are selected, and the two sets of extension points are symmetrically distributed on both sides of the middle complex frequency point. The second-order Arnoldi algorithm is used to construct two independent reduced-order models respectively. Calculate the relative error of the transfer function of the two independent reduced-order models, and compare the maximum difference with a preset threshold. If the termination criterion is met, it is determined that both reduced-order models have converged. If the termination criterion is not met, new extension points are added, and the newly generated orthogonal basis is orthogonalized and merged with the previous orthogonal basis to form two updated sets of reduced-order models until convergence.

[0013] Optionally, the expression for the final acoustic problem system equation is: ; Where K is the global stiffness matrix. i Dummy unit ω Let be the angular frequency, C be the damping matrix, M be the global mass matrix, p be the unknown nodal sound pressure vector, and F be the load vector.

[0014] Optionally, the expression for the final system equations of the vibration-acoustic coupling problem is: [K+ iω C- ω 2 M]x=F; Where x is an unknown vector.

[0015] Optionally, the complex Jacobian matrix is ​​obtained from real coordinates to complex coordinates in a two-dimensional problem by the chain rule; in a three-dimensional problem, the complex Jacobian matrix is ​​decomposed into the product of the reference Jacobian matrix and the perfectly matched layer Jacobian matrix.

[0016] Compared with the prior art, the present invention has the following advantages and technical effects: 1. This invention develops a frequency-independent automatic matching layer technique for rapid modeling and simulation of acoustic and vibratory coupling problems, to solve the problem of high computational cost in external acoustic and vibratory coupling systems. This method combines the geometric flexibility of a perfect matching layer with the computational efficiency of a frequency-independent framework, enabling accurate and efficient modeling of an infinite acoustic domain. Compared to traditional frequency-dependent perfect matching layer methods that require recalculation and assembly of the system matrix at each frequency point, this invention only requires one matrix assembly and decomposition in full-band sweep analysis, significantly reducing computation time.

[0017] 2. This invention introduces rounded corners to address the discontinuity of interface curvature, thereby improving numerical accuracy and reducing errors associated with sharp geometric abrupt changes. Compared with traditional automatic matching layer methods without rounded corners, this invention significantly reduces the computational complexity of the Jacobian matrix while improving numerical stability and ease of implementation.

[0018] 3. This invention uses velocity potential instead of sound pressure as the basic unknown in the acoustic domain, making all the matrices of the coupled system symmetric matrices. This symmetry transformation allows large-scale sparse linear equation systems to call efficient symmetric solvers, significantly reducing memory requirements and solution time compared to the original asymmetric system.

[0019] 4. This invention directly uses the boundary of the perfectly matched layer as the integration surface of the Kirchhoff surface integral formula, and extrapolates the sound pressure distribution at any point in the far field using the sound pressure and normal derivative values ​​obtained on this boundary. Since the integration surface is located at the intersection of the perfectly matched layer and the physical domain, its extrapolation accuracy is better than the traditional scheme that uses the surface of the scatterer as the integration surface. At the same time, this invention introduces the mirror method half-space Green's function for the half-space problem, which can automatically satisfy the sound pressure release boundary conditions without additional discrete modeling, and unifies the full-space and half-space problems into the same computational framework.

[0020] 5. This invention fully utilizes the frequency independence property of the system matrix, constructs two independent reduced-order models based on the second-order Arnoldi algorithm, and uses the relative error of the transfer functions of the two models as the convergence criterion. It can adaptively determine the position and order of the expansion point without knowing the true error, thus achieving a good balance between computational efficiency and accuracy. Attached Figure Description

[0021] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a typical sound wave scattering problem; Figure 3This is a schematic diagram of the two-dimensional problem truncated computational domain grid and automatic matching layer according to an embodiment of the present invention; Figure 4 This is a comparison chart of the acoustic scattering calculation results with and without rounded corner transitions in this embodiment of the invention with and without analytical solutions; Figure 5 The diagram shows the acoustic scattering calculation results of different convex polygon truncated boundaries in this embodiment of the invention; Figure 6 This is a comparison diagram of a traditional matching layer and a frequency-independent automatic matching layer according to an embodiment of the present invention; Figure 7 This is a comparison chart of the absolute sound pressure levels of the method in this embodiment and commercial software. Figure 8 This is a comparison diagram of the solid part of sound compression in the embodiment of the present invention and commercial software; Figure 9 This is a comparison chart of the sound pressure frequency response curves of the method in this embodiment of the invention and commercial software. Detailed Implementation

[0022] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0023] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0024] Example 1 like Figure 1 As shown, this embodiment provides a frequency-independent automatic matching layer method for rapid modeling and simulation of acoustic and vibratory coupling problems, including: Based on the boundary mesh data of the physical domain, a perfectly matched layer mesh covering the scatterer or structure is generated, and rounded transitions are set at geometric sharp corners to make the normal vector change continuously along the boundary. Complex spatial coordinates are established based on the perfectly matched layer mesh, the frequency is fixed to the middle frequency of the analysis band, an absorption function independent of frequency is constructed, and the complex spatial coordinates are stretched along the normal direction. A finite element framework is established based on the stretched complex spatial coordinates. A frequency-independent global system matrix is ​​assembled and boundary conditions are applied to obtain the final system equations. Based on the final system equations, construct the finite element-perfectly matched layer formulation of acoustic or vibratory-acoustic coupling to obtain the near-field or far-field physical quantities of the acoustic or vibratory-acoustic coupling problem. The final system equations are solved using an adaptive multi-point second-order Krylov subspace reduction method. The expansion point position and order are automatically determined through cross-validation of the double-reduction model, and the solution is applied to the perfectly matched layer to complete the attenuation matching of the sound wave within the perfectly matched layer.

[0025] Specifically, the following steps are included: S1: Construct a general external propagation region; Generating a perfectly matched layer mesh covering a scatterer or structure includes: constructing an unbounded acoustic field based on the Helmholtz equation and radiation conditions, and constructing a perfectly matched layer to truncate the unbounded acoustic field; after meshing the unbounded acoustic field, obtaining the mesh data on the outer boundary; calculating the normal vector based on the mesh data on the outer boundary; for vertices at corner points, taking the weighted average of the normal vectors of adjacent cells; for second-order nodes at the midpoint of an edge, taking the average of the normal vectors of the two endpoints of that edge; and generating a perfectly matched layer by stretching it outward at equal intervals along the normal direction of each node based on the normal vectors, and defining the cell type of the stretched perfectly matched layer mesh as a format matching the internal computational domain.

[0026] Specifically, construct a finite-domain geometric object that is completely enclosed by boundaries, and immerse the entire object in an acoustic medium at the speed of sound. c and mass density ρ In an infinite field, factors are omitted for all time-dependent quantities. ,in i It is a virtual unit; ω It is the angular frequency in rad / s. t It is time. For scattering problems, the target is affected by incident waves from the background plane. The function; utilizing the principle of field superposition, the total sound pressure p Equal to the known incident field and unknown scattering field The sum. The steady-state dynamic behavior in the external acoustic domain is governed by the scalar Helmholtz equation in the frequency domain, which is expressed as: ; in Represents the Laplace operator; r represents the point position vector; k = ω / c It is the wave number; Q (r) denotes the source term. The second equation is the Sommerfeld radiation condition, which ensures that sound energy must be radiated outward at infinity without being reflected back into the computational domain.

[0027] Figure 2 This is a schematic diagram of a typical sound wave scattering problem, where the scattering body is... VIts surface Γ has an unbounded region outside, and the matching layer truncates the unbounded region to form a bounded computational domain Ω. dom The automatic matching layer region is Ω. pml , Γ int To match the inner boundary of the layer, Γ ext To match the outer boundary of the layer. p I For incident sound waves, p S It is a scattered sound wave.

[0028] S2: Establish complex spatial coordinates and construct the absorption function; Specifically, establishing complex spatial coordinates and constructing a frequency-independent absorption function includes: setting a reference coordinate system, establishing an expression for the complex spatial coordinates, and interpolating the boundary normal vector using interpolation to obtain the complex coordinate stretching expression and dimensionless thickness coordinates; the frequency-independent absorption function includes preset parameters. C ,and C greater than the speed of sound c The frequency is fixed at the middle frequency of the analysis band, and the absorption function and its integral function are constructed; numerical integration is used to process the integral of the absorption function at the singularity.

[0029] S201: Perform complex coordinate stretching; For complex coordinate stretching by introducing an imaginary part into the actual position vector, the formula is: ; in For dimensionless parameters, their definition is: ; The optimal absorption function for the perfectly matched layer is the classic logarithmic absorption function, whose integral expression is: ; Its absorption function expression is: ; S202 constructs the absorption function; In order to break frequency dependence, let = ,in , The median frequency of the frequency band is expressed as follows: ; This makes the matrix required for calculation independent of frequency, thus reducing the amount of computation.

[0030] Furthermore, a new absorption function is proposed, whose integral expression is: ; The expression for the absorption function is: ; in C It should be much greater than the propagation speed. c， The sound waves will be trapped in the perfectly matched layer domain and will not be reflected back into the inner computational domain, where... The ratio was determined through convergence analysis.

[0031] S3 establishes a perfectly matched layer finite element form; Specifically, establishing a finite element framework and assembling a frequency-independent global system matrix includes: discretizing using the Galerkin method, selecting weight functions identical to the shape functions, constructing a standard Jacobian matrix for the physical domain, and constructing a complex Jacobian matrix for the perfectly matched layer domain; constructing a global stiffness matrix and a global mass matrix based on the complex Jacobian matrix, and obtaining the frequency response equation after applying boundary conditions.

[0032] S301: Construct the Jacobian matrix; The equation for the perfectly matched layer region can be written in standard form as follows: ; Essentially, it is an analytic continuation of the Helmholtz equation into complex space coordinates, where sound waves attenuate; among which, vector operators are used for two-dimensional problems. The superscript T denotes transpose; the resulting matrix is ​​the Jacobian matrix of the transformation from real Cartesian coordinates to complex Cartesian coordinates, and its expression in the two-dimensional problem is: ; Each element in the list is obtained using the chain rule, and the result is: ; ; For a three-dimensional problem, the Jacobian matrix expression is: ; ; 3D Jacobian Matrix The elements in can be solved in a manner similar to that in a two-dimensional Jacobian matrix.

[0033] The final system equations for the acoustic problem are then constructed, and their expression is: ; Where K is the global stiffness matrix, M is the global mass matrix, C is the damping matrix, p is the unknown nodal sound pressure vector, and F is the force vector derived from external loads. Finally, the frequency response equation is obtained, and its expression is: ; Where L is the output distribution vector.

[0034] S302: Construct the global system matrix and the final system equations; By using arbitrary weight functions Multiplying the results, integrating over the region, and then applying the divergence theorem, we obtain the relevant variational form of the equation, which is expressed as: ; The latter two terms are weakly enforced boundary conditions and continuity constraints, respectively. The boundary conditions specified on the outer boundary of the perfectly matched layer can be of Dirichlet, Neumann, or Robin type; this specific choice has little impact. This invention uses homogeneous Neumann conditions, thus eliminating the former. For the latter, when combined with the variational equations of the internal computational domain, the two terms are equal in magnitude and opposite in direction, thus canceling each other out and ensuring the continuity requirement. Its expression is: .

[0035] Furthermore, the two regions are discretized using non-overlapping elements. The unknown sound pressure in each element is approximated as a linear combination of a polynomial basis function multiplied by the unknown values ​​of the field variables at the grid nodes. The polynomial basis function is chosen as the weight function, and the same function is used to interpolate the element geometry, forming an isoparametric mapping from the physical element to the reference element. Since the polynomial basis function is not a direct function of Cartesian coordinates but a function of natural coordinates, its range varies depending on the element type. Using the chain rule of differentiation, a 2×2 Jacobian matrix is ​​derived for the two-dimensional problem, and its expression is as follows: ; For the three-dimensional problem, the 3×3 Jacobian matrix is ​​derived, and its expression is as follows: ; For the perfectly matched layer, an additional transformation is required to connect the differentials in the complex Cartesian coordinate system with those in the Cartesian coordinate system. This invention uses quadrilateral elements from a two-dimensional problem to delineate the perfectly matched layer region. This choice also facilitates the use of the standard Gaussian quadrature algorithm. Numerical integration formulas are used to avoid the singular integral problem that occurs in unbounded absorbing functions. The stiffness matrix and mass matrix are: ; ; in yes Determinant; Operator yes ; It is the number of Gaussian integration points. This is the total number of Gaussian integration points; These are weighting coefficients; It is related to physical units Corresponding reference unit; , , These are the shape function matrix, the Jacobian matrix, and the Jacobian determinant, respectively, at the integration points. Evaluation; After assembly, the global stiffness matrix and global mass matrix can be obtained, and their expressions are: ; ; The final system of linear algebraic equations is expressed as follows: ; in, s = iω , It is the global stiffness matrix. These are global quality matrices, and they are all frequency-independent matrices; It is the sound pressure vector of an unknown node; It is a complex force vector originating from external load terms; and Let represent the total number of elements in the truncated region discretization and the total number of elements used in the perfect matching layer, respectively. The system transfer function is: ; Where L is the output distribution vector used to select a certain degree of freedom.

[0036] S4 is based on far-field sound pressure extrapolation of perfectly matched inner-layer boundaries; S401 uses rounded corners to simplify the Jacobian matrix; The Jacobian matrix in the three-dimensional problem derived from S3 is J=J ref •J pml ,in: ; ; Furthermore, by creating rounded corners at all sharp corners at the interface between the perfectly matched layer and the computational domain, the calculation of the distance between the two endpoints of the perfectly matched layer is eliminated, ensuring that the thickness of the perfectly matched layer is consistent and that the interface normal vector is continuous, thus simplifying the calculation of the Jacobian matrix. ; ; .

[0037] S402 eliminates asymmetry; When establishing the finite element framework and assembling the global system matrix, velocity potential is used instead of sound pressure as the basic unknown in the acoustic domain, so that the coupled system matrix is ​​transformed into a symmetric matrix.

[0038] Specifically, to eliminate the asymmetry of the coefficient matrix in the structural acoustic coupling equation, the scalar fluid velocity potential is used instead of sound pressure as the fundamental unknown in the acoustic domain, and its expression is as follows: After variable substitution, the final expression for the system equations of the vibration-acoustic coupling problem is: [K+ iω C- ω 2 M]x=F; ; Where K, C, and M are the global stiffness matrix, damping matrix, and mass matrix, respectively, all of which are symmetric matrices; K s C s and M s These are the stiffness matrix, damping matrix, and mass matrix of the structural components, K. a C a and M a These are the acoustic stiffness matrix, damping matrix, and mass matrix; C as and C sa Let be the coupling matrix, and ; ρ a The density of the sound field medium; It is the total number of degrees of freedom of the vibratory acoustic finite element model, that is x is an unknown vector, containing the unknown displacement vector u and the unknown velocity potential vector. F is the load vector, which includes the structural load vector F. s Harmony acoustic part load vector F a .

[0039] S403 far-field extrapolation; When obtaining near-field or far-field physical quantities for acoustic or vibratory-acoustic coupling problems, the boundary of the perfectly matched layer is used as the Kirchhoff integral surface. The sound pressure and normal derivative at this boundary are then extrapolated using the Kirchhoff surface integral formula to obtain the sound pressure at any point in the far field. For full-space problems, a full-space Green's function is used for far-field extrapolation; for half-space problems, a half-space Green's function is introduced for far-field extrapolation.

[0040] Specifically, the inner boundary of the perfectly matched layer is selected as the Kirchhoff integral surface. Based on the sound pressure and normal derivative on the inner boundary of the perfectly matched layer, the sound pressure at any point in the far field is extrapolated using the Kirchhoff surface integral formula, and its expression is: ; in G The Green's function can be a free-space Green's function or a half-space Green's function. When dealing with full-space problems, the full-space Green's function is used, and its expression is: ; When dealing with half-space problems, we introduce the half-space Green's function, whose expression is: ; in, yes The mirror point.

[0041] S5 model order reduction; Using the perfect matching layer calculation method of this invention, the system matrix only needs to be assembled once. The multi-point matrix matching algorithm is used for projective model order reduction. In the projective model order reduction, the position of the expansion point (outer loop process) and the order corresponding to each expansion point (inner loop process) need to be automatically selected by an adaptive process, and the error is estimated to construct a compact order reduction model.

[0042] Furthermore, the final system equations are solved using an adaptive multi-point second-order Krylov subspace reduction method, including: selecting two different sets of extension points, which are symmetrically distributed on both sides of the intermediate complex frequency point; constructing two independent reduced-order models using the second-order Arnoldi algorithm; calculating the relative error of the transfer function of the two independent reduced-order models; comparing the maximum difference with a preset threshold; if the termination criterion is met, it is determined that both reduced-order models have converged; if the termination criterion is not met, new extension points are added, and the newly generated orthogonal basis is orthogonalized and merged with the previous orthogonal basis to form two updated reduced-order models, until convergence.

[0043] S501: Select two different sets of extension points, which are symmetrically distributed at the intermediate complex frequency point. Around the perimeter, each group contains several staggered extension points, and the two reduced-order models must converge across the entire frequency range.

[0044] S502: Applying the second-order Arnoldi algorithm to efficiently obtain the transfer functions of two reduced-order models. and The two reduced-order models are completely independent, allowing for parallel computation.

[0045] S503: Compare two transfer functions to calculate their relative error, expressed as follows: ; For accuracy cross-validation, the maximum error value is compared with a specified threshold TOL. If the termination criterion is met, i.e. If the result is positive, both reduced-order models will converge. Otherwise, the number of expansion points needs to be increased until convergence.

[0046] S504: If the maximum error Then it is necessary to consider three possible scenarios. Within the region, determine the locations of two new expansion points for the next iteration. Then, at each new expansion point, run the second-order Arnoldi algorithm again, merging and orthogonalizing their orthogonal bases with those from the previous iteration to obtain two new global orthogonal bases. This process is used to obtain two convergent reduced-order models.

[0047] S505: Repeat steps S403 and S404 continuously until the error converges across the entire frequency range of interest. .

[0048] The following explanation is based on the accompanying drawings: like Figure 3 The diagram shown is a schematic diagram of the two-dimensional problem truncation computational domain grid and automatic matching layer according to an embodiment of the present invention. Figure 3 The left side shows a schematic diagram of a traditional truncated computational domain mesh without rounded corners. Figure 3 The right side shows a schematic diagram of the truncated computational domain mesh and automatic matching layer of the present invention after rounded corner transition. It shows the specific form of meshing the physical computational domain with triangular elements and meshing the perfect matching layer with quadrilateral elements. The comparison shows that the rounded corner transition makes the perfect matching layer uniform in thickness at the corners and the normal vector changes continuously.

[0049] like Figure 4 The figure shown is a comparison between the acoustic scattering calculation results with and without rounded corner transitions in an embodiment of the present invention and the analytical solution. Figure 4 The results of acoustic scattering calculated using the method of this invention with rounded corners and the traditional method without rounded corners are compared with the analytical solution. As can be seen from the figure, the calculation result with rounded corners matches the analytical solution better, which verifies that the present invention can effectively improve numerical accuracy and reduce errors related to sharp geometric changes by setting rounded corners at geometric sharp corners.

[0050] like Figure 5 The figure shown is a diagram of the acoustic scattering calculation results of different convex polygon truncated boundaries according to an embodiment of the present invention. Figure 5 The acoustic scattering calculation results of the method of the present invention are presented when using triangular, quadrilateral, hexagonal, octagonal, circular, and elliptical truncated boundaries. As can be seen from the figure, all calculation results agree well for different convex polygonal truncated boundaries, which verifies that the method of the present invention has good geometric adaptability and calculation accuracy for truncated boundaries with different geometric shapes.

[0051] like Figure 6 The diagram shown is a schematic diagram of the truncated computational domain grid and automatic matching layer for a two-dimensional complex underwater vehicle problem according to an embodiment of the present invention. Figure 6 The differences between the traditional frequency-dependent perfect matching layer and the frequency-independent automatic matching layer of this invention were compared from multiple dimensions, including the number of degrees of freedom in the truncated region and the geometric adaptability of the perfect matching layer. The comparison results show that the frequency-independent automatic matching layer of this invention requires fewer degrees of freedom in the truncated region and is more adaptable to complex geometries, thus broadening the applicability of the traditional perfect matching layer.

[0052] like Figure 7 The figure shown is a comparison of the absolute sound pressure levels of the method in this embodiment and commercial software. Figure 7 The distribution cloud maps or curves of the absolute sound pressure values ​​calculated using the method of this invention and using commercial software are given respectively. The comparison results show that the calculation results of the method of this invention are in good agreement with the results of commercial software. At the same time, the number of degrees of freedom of the truncated calculation domain of the method of this invention is much smaller than that of commercial software, which verifies that the method of this invention has higher calculation efficiency while ensuring calculation accuracy.

[0053] like Figure 8 The figure shown is a comparison diagram of the sound compression solid part of the method of the present invention and commercial software. Figure 8 The acoustic compaction cloud diagrams or curves obtained by the method of this invention and by commercial software are presented respectively. The comparison results show that the calculation results of the method of this invention are in good agreement with the results of commercial software, which further verifies the calculation accuracy of the method of this invention. At the same time, the method of this invention has fewer degrees of freedom in the truncation region and higher calculation efficiency.

[0054] like Figure 9 The figure shown is a comparison of the sound pressure frequency response curves of the method in the embodiment of the present invention and those of commercial software. Figure 9 The sound pressure frequency response curves calculated using the method of this invention and commercial software over a wide frequency range are presented. As can be seen from the figure, the two curves match very well throughout the entire analysis frequency band, verifying the accuracy and effectiveness of the method of this invention in broadband acoustic analysis.

[0055] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A frequency-independent automatic matching layer method for rapid modeling and simulation of acoustic-vibration coupling problems, characterized in that, include: Based on the boundary mesh data of the physical domain, a perfectly matched layer mesh covering the scatterer or structure is generated, and rounded transitions are set at geometric sharp corners to make the normal vector change continuously along the boundary. Complex spatial coordinates are established based on the perfectly matched layer mesh, the frequency is fixed to the middle frequency of the analysis band, an absorption function independent of frequency is constructed, and the complex spatial coordinates are stretched along the normal direction. A finite element framework is established based on the stretched complex spatial coordinates. A frequency-independent global system matrix is ​​assembled and boundary conditions are applied to obtain the final system equations. Based on the final system equations, construct the finite element-perfectly matched layer formulation of acoustic or vibratory-acoustic coupling to obtain the near-field or far-field physical quantities of the acoustic or vibratory-acoustic coupling problem. The final system equations are solved using an adaptive multi-point second-order Krylov subspace reduction method. The expansion point position and order are automatically determined through cross-validation of the double-reduction model, and the solution is applied to the perfectly matched layer to complete the attenuation matching of the sound wave within the perfectly matched layer.

2. The frequency-independent automatic matching layer method according to claim 1, characterized in that, Generate a perfectly matching layer mesh covering the scatterer or structure, including: An unbounded acoustic field is constructed based on the Helmholtz equation and radiation conditions, and a perfectly matched layer is constructed to truncate the unbounded acoustic field. After meshing the unbounded acoustic field, the mesh data on the outer boundary is obtained. The normal vector is calculated based on the grid data on the outer boundary. For vertices at corner points, the weighted average of the normal vectors of adjacent cells is taken. For second-order nodes at the midpoint of an edge, the average of the normal vectors of the two endpoints of that edge is taken. Based on the normal vector, a perfectly matched layer is generated by stretching outward at equal intervals along the normal direction of each node, and the mesh cell type of the perfectly matched layer generated by stretching is defined as a format that matches the internal computational domain.

3. The frequency-independent automatic matching layer method according to claim 1, characterized in that, Establish complex spatial coordinates and construct a frequency-independent absorption function, including: Set up a reference coordinate system, establish an expression for complex spatial coordinates, and use interpolation to interpolate the boundary normal vector to obtain the complex coordinate stretching expression and dimensionless thickness coordinates. The frequency-independent absorption function includes preset parameters. C ,and C greater than the speed of sound c The frequency is fixed at the middle frequency of the analysis band, and the absorption function and its integral function are constructed. The integral of the absorption function at the singularity is processed using numerical integration.

4. The frequency-independent automatic matching layer method according to claim 1, characterized in that, Establishing a finite element framework and assembling a frequency-independent global system matrix includes: Discretization is performed using the Galerkin method, and weight functions with the same shape function are selected. A standard Jacobian matrix is ​​constructed for the physical domain, and a complex Jacobian matrix is ​​constructed for the perfectly matched layer domain. Based on the complex Jacobian matrix, a global stiffness matrix and a global mass matrix are constructed, and the frequency response equation is obtained after applying boundary conditions.

5. The frequency-independent automatic matching layer method according to claim 4, characterized in that, When establishing the finite element framework and assembling the global system matrix, velocity potential is used instead of sound pressure as the basic unknown in the acoustic domain, so that the coupled system matrix is ​​transformed into a symmetric matrix.

6. The frequency-independent automatic matching layer method according to claim 1, characterized in that, When obtaining near-field or far-field physical quantities for acoustic or vibration-acoustic coupling problems, the boundary of the perfectly matched layer is used as the Kirchhoff integral surface. The sound pressure and normal derivative on this boundary are used to extrapolate the sound pressure at any point in the far field using the Kirchhoff surface integral formula.

7. The frequency-independent automatic matching layer method according to claim 6, characterized in that, When dealing with full-space problems, the full-space Green's function is used for far-field extrapolation; when dealing with half-space problems, the half-space Green's function is introduced for far-field extrapolation.

8. The frequency-independent automatic matching layer method according to claim 1, characterized in that, The final system equations are solved using an adaptive multi-point second-order Krylov subspace reduction method, including: Two different sets of extension points are selected, and the two sets of extension points are symmetrically distributed on both sides of the middle complex frequency point. The second-order Arnoldi algorithm is used to construct two independent reduced-order models respectively. Calculate the relative error of the transfer function of the two independent reduced-order models, and compare the maximum difference with a preset threshold. If the termination criterion is met, it is determined that both reduced-order models have converged. If the termination criterion is not met, new extension points are added, and the newly generated orthogonal basis is orthogonalized and merged with the previous orthogonal basis to form two updated sets of reduced-order models until convergence.

9. The frequency-independent automatic matching layer method according to claim 4, characterized in that, The final system equations include: The final system equation for the acoustic problem is expressed as follows: ； Where K is the global stiffness matrix. i Dummy unit ω Let be the angular frequency, C be the damping matrix, M be the global mass matrix, p be the unknown nodal sound pressure vector, and F be the load vector; The final system equation for the vibration-acoustic coupling problem is expressed as follows: [K+ iω C- ω 2 M]x=F; Where x is an unknown vector.

10. The frequency-independent automatic matching layer method according to claim 4, characterized in that, In a two-dimensional problem, the complex Jacobian matrix is ​​obtained by transforming from real coordinates to complex coordinates using the chain rule. In a three-dimensional problem, the complex Jacobian matrix is ​​decomposed into the product of the reference Jacobian matrix and the perfectly matched layer Jacobian matrix.

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