A rapid reanalysis method of substrate multiplexed electrodes based on regional decomposition

Abstract

The application provides a substrate multiplexing electrode rapid reanalysis method based on region decomposition, relates to the technical field of simulation and design of surface acoustic wave devices, and comprises the following steps: according to geometric parameters and material parameters of a substrate region, performing dimensionless pretreatment on the substrate region, and obtaining a substrate region interface operator through cascade calculation; storing substrate region interface operators with different lengths in a cascade operator library; according to new electrode design parameters, judging whether the substrate region interface operator needs to be reconstructed, if not, reusing an existing substrate region interface operator from the cascade operator library, and if yes, quickly cascading new substrate region interface operators by using operator materials in the cascade operator library. Through the region decomposition strategy of offline pretreatment of the substrate region and online update of the electrode region, the application realizes rapid reanalysis in iterative design of an electrode structure, and improves the simulation efficiency and calculation stability of a surface acoustic wave device.

Description

Technical Field

[0001] This invention relates to the field of surface acoustic wave device simulation and design technology, and in particular to a rapid reanalysis method for substrate-reusable electrodes based on region decomposition. Background Technology

[0002] Surface acoustic wave (SAW) devices are widely used in modern wireless communication, sensing, and RF front-end systems due to their compact structure, good frequency selectivity, and relatively low manufacturing cost. As communication standards develop towards higher frequencies, wider bandwidths, and multi-mode multi-frequency operation, the structural design of SAW devices is becoming increasingly complex, particularly in terms of electrode layout, material combination, and boundary conditions, exhibiting a trend towards diversification and aperiodicity. Currently, performance prediction of SAW devices largely relies on numerical simulation methods such as the finite element method. These methods can effectively describe piezoelectric coupling effects, multilayer material structures, and complex boundary conditions, and are therefore widely used in the design and optimization of devices such as resonators and filters. However, when the device model includes intricate electrode structures, thick multilayer substrates, or large apertures, the overall model has a high degree of freedom, resulting in significant computational overhead for matrix assembly, storage, and solution, thus affecting simulation efficiency.

[0003] In engineering practice, the design of SAW devices often requires repeated adjustments to electrode parameters, such as electrode thickness, finger width, spacing, number, or arrangement. During this process, the substrate and some basic structures often remain unchanged, while the electrode area needs to be updated frequently. Traditional methods usually require rebuilding the entire model and performing a complete finite element solution after each modification of electrode parameters. This process involves a large amount of repetitive calculations, which increases time costs and resource consumption, and to some extent restricts the efficiency of design iteration.

[0004] Under the domain decomposition framework, when dividing the device into multiple sub-regions for coupled solution, some numerical processing challenges are also faced. For example, there may be mismatches in the interface meshes between different sub-regions. If not handled properly, it may affect the accuracy of variable transfer between regions. In addition, the simulation of SAW devices involves the coupling of displacement field and electric field. The magnitude difference of different physical quantities in the system matrix is ​​large, which may lead to an increase in the matrix condition number, thereby affecting the stability or convergence speed of the solution. Summary of the Invention

[0005] This invention provides a fast reanalysis method for substrate-reusable electrodes based on domain decomposition. By employing a domain decomposition strategy of offline preprocessing of the substrate domain and online updating of the electrode domain, it enables rapid reanalysis in the iterative design of electrode structures, thereby improving the simulation efficiency and computational stability of surface acoustic wave devices.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: In a first aspect, a rapid reanalysis method for substrate-reusable electrodes based on domain decomposition is provided, the method comprising: Step 1: Divide the solution domain of the surface acoustic wave device into the substrate domain and the electrode domain; Step 2: Based on the geometric and material parameters of the substrate domain, perform dimensionless preprocessing on the substrate domain, and obtain the substrate domain interface operator through cascade calculation. Store the substrate domain interface operators of different lengths into the cascade operator library. Step 3: Based on the new electrode design parameters, determine whether the substrate domain interface operator needs to be reconstructed. If it does not need to be reconstructed, reuse the existing substrate domain interface operator from the cascaded operator library. If it needs to be reconstructed, use the operator materials in the cascaded operator library to quickly cascade and obtain a new substrate domain interface operator. Step 4: Based on the new electrode design parameters, establish an electrode domain model using air-filled modeling, and perform secondary partitioning on the air-filled model. Then, obtain a new electrode domain interface operator through parallel condensation operation and cascade splicing operation. Step 5: Determine whether the interface mesh of the substrate domain interface operator and the new electrode domain interface operator matches. If they match perfectly, perform assembly and solution. If they do not match perfectly, construct the interface transfer matrix through Mortar projection. Use the interface transfer matrix to complete the interface coupling assembly and solution. After obtaining the solution of the interface degree of freedom, further restore the solution of the internal degree of freedom to obtain the overall response of the device.

[0007] In a second aspect, a computer-readable storage medium storing a program that, when executed by a processor, implements the method.

[0008] The above-described solution of the present invention has at least the following beneficial effects: By dividing the solution domain into a substrate domain and an electrode domain, and performing dimensionless preprocessing and cascaded calculations on the substrate domain, a reusable cascaded operator library is constructed. This eliminates the need to repeatedly solve the substrate domain during electrode parameter iterative optimization, reducing redundant computations and improving the overall modeling and simulation efficiency of surface acoustic wave (SAW) devices. A substrate domain interface operator reuse and rapid reconstruction strategy is adopted. Existing operator materials can be directly called or cascaded for substrate structures of different lengths, avoiding the need to solve the substrate field from scratch in each design iteration, thus reducing computational resource consumption. The electrode domain employs air-filled modeling and undergoes secondary partitioning and parallel condensation operations, shortening the generation time of electrode domain interface operators and enabling rapid reanalysis of the electrode structure. Finally, an interface transfer matrix is ​​constructed using Mortar projection to address interface mesh mismatch issues, improving adaptability to complex electrode topologies and variable parameter designs. Attached Figure Description

[0009] Figure 1This is a schematic flowchart of a rapid reanalysis method for substrate-reusable electrodes based on region decomposition provided by an embodiment of the present invention.

[0010] Figure 2 This is a two-dimensional schematic diagram of the interface between the electrode domain and the substrate domain.

[0011] Figure 3 This diagram illustrates the definition of the basic unit cell of the substrate domain and its hierarchical cascade tree.

[0012] Figure 4 This is a schematic diagram of the splicing of two basic units in the substrate domain.

[0013] Figure 5 This is a schematic diagram of the forces acting at the corners of basic unit blocks A and B.

[0014] Figure 6 To select operator materials from the cascaded operator library.

[0015] Figure 7 This is a schematic diagram of an air-filled electrode domain.

[0016] Figure 8 This is a schematic diagram of the secondary partitioning strategy for the electrode domain.

[0017] Figure 9 This is a schematic diagram of the secondary condensation process in the electrode domain subdomain.

[0018] Figure 10 This is a schematic diagram of the IDT and reflective grating grouping in the DMS model.

[0019] Figure 11 This is a comparison of the S-parameters of a rapid reanalysis method for substrate-reusable electrodes based on domain decomposition and the finite element method.

[0020] Figure 12 A comparison of S-parameters for DMS models with different electrode structures. Detailed Implementation

[0021] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0022] like Figure 1 As shown, embodiments of the present invention propose a rapid reanalysis method for substrate-reusable electrodes based on domain decomposition, the method comprising the following steps: Step 1: Divide the solution domain of the surface acoustic wave device into the substrate domain and the electrode domain; Step 2: Based on the geometric and material parameters of the substrate domain, perform dimensionless preprocessing on the substrate domain, and obtain the substrate domain interface operator through cascade calculation. Store the substrate domain interface operators of different lengths into the cascade operator library. Step 3: Based on the new electrode design parameters, determine whether the substrate domain interface operator needs to be reconstructed. If it does not need to be reconstructed, reuse the existing substrate domain interface operator from the cascaded operator library. If it needs to be reconstructed, use the operator materials in the cascaded operator library to quickly cascade and obtain a new substrate domain interface operator. Step 4: Based on the new electrode design parameters, establish an electrode domain model using air-filled modeling, and perform secondary partitioning on the air-filled model. Then, obtain a new electrode domain interface operator through parallel condensation operation and cascade splicing operation. Step 5: Determine whether the interface mesh of the substrate domain interface operator and the new electrode domain interface operator matches. If they match perfectly, perform assembly and solution. If they do not match perfectly, construct the interface transfer matrix through Mortar projection. Use the interface transfer matrix to complete the interface coupling assembly and solution. After obtaining the solution of the interface degree of freedom, further restore the solution of the internal degree of freedom to obtain the overall response of the device.

[0023] In this embodiment of the invention, by dividing the solution domain into a substrate domain and an electrode domain, and performing dimensionless preprocessing and cascaded calculations on the substrate domain, a reusable cascaded operator library is constructed. During iterative optimization of electrode parameters, it is unnecessary to repeatedly solve the substrate domain, reducing redundant computations and improving the overall modeling and simulation efficiency of surface acoustic wave devices. A substrate domain interface operator reuse and rapid reconstruction strategy is adopted. For substrate structures of different lengths, existing operator materials can be directly called or cascaded, avoiding the need to solve the substrate field from scratch in each design iteration, thus reducing computational resource consumption. The electrode domain adopts air-filled modeling and undergoes secondary partitioning and parallel condensation operations, shortening the generation time of electrode domain interface operators and enabling rapid reanalysis of the electrode structure. An interface transfer matrix is ​​constructed using Mortar projection to handle interface mesh mismatch issues, improving the adaptability to complex electrode topologies and variable parameter designs.

[0024] In a preferred embodiment of the present invention, step 1 above, which divides the solution domain of the surface acoustic wave device into a substrate domain and an electrode domain, may include: In this embodiment of the invention, the core physical characteristic of the surface acoustic wave (SAW) device is the coupling effect between the piezoelectric solid mechanical field and the electrostatic field. The global physical model covers the entire geometric space of the device and includes two types of core physical fields: one is the piezoelectric coupling field existing inside the piezoelectric substrate, and the other is the pure electrostatic field and solid mechanical field existing in the metal electrode and the surrounding filling medium. The layered topological characteristics of the device's physical structure are analyzed. The physical structure of the SAW device is divided into two stacked parts. The lower layer is the piezoelectric substrate structure that undertakes the functions of SAW propagation and piezoelectric energy conversion, including a piezoelectric functional layer and a bottom perfectly matched layer. The upper layer is the metal electrode structure that undertakes the functions of electrical excitation and signal output, including discrete components such as interdigital transducers, reflective gratings, and busbar electrodes. The two types of structures have a unique common contact interface in space, with no spatial overlap or geometric discontinuity, which is the natural geometric boundary for the solution domain division.

[0025] The mathematical definition and geometric partitioning of the solution domain are performed, based on the core principle of the domain decomposition method, to solve the entire solution domain of the surface acoustic wave device. A rigorous mathematical partitioning is performed, dividing the piezoelectric substrate structure into two independent sub-domains that transfer physical quantities only through a common interface. The complete geometric and physical space corresponding to the piezoelectric substrate structure is defined as the substrate domain, denoted as... The complete geometric and physical space corresponding to the metal electrode structure and the air-filled medium is defined as the electrode domain, denoted as... The global solution domain satisfies the geometric coverage relation. The only intersection of the two domains is the common coupling interface. ,Right now This interface is the interface through which mechanical and electrical physical quantities are transferred between the substrate domain and the electrode domain, and it is also the core carrier for subsequent interface coupling.

[0026] For the partitioned subdomains, adapted dimensionless discrete system equations are established. Based on the differences in physical properties between the substrate and electrode domains, finite element discrete equations conforming to multiphysics laws are constructed. All equations adopt the standard form after global dimensionless preprocessing, eliminating the magnitude differences of different physical quantities and laying a numerical foundation for subsequent operator generation and coupled solution. For a discrete system where the substrate domain is a piezoelectric coupling medium domain, and both solid-state mechanical fields and piezoelectric coupled electrostatic fields exist simultaneously, its dimensionless finite element discrete system formula is: ,in The dimensionless stiffness matrix of the substrate domain characterizes the mechanical stiffness properties of the piezoelectric substrate. is the dimensionless piezoelectric coupling matrix in the substrate domain, characterizing the piezoelectric coupling effect between the displacement field and the electric field; The dimensionless dielectric matrix of the substrate domain characterizes the dielectric properties of the piezoelectric substrate. The vector of the substrate domain displacement degrees of freedom; The substrate domain potential is the degree of freedom vector; This represents the substrate domain force load vector; The substrate domain charge load vector; This is the transpose of the piezoelectric coupling matrix, and the formula fully describes the piezoelectric multiphysics coupling relationship in the substrate domain.

[0027] Electrode domain The electrode domain is modeled using an air-filled method, with solid mechanical fields existing only in the metal electrode region. The entire domain is covered by an electrostatic field, and there is no piezoelectric coupling effect. Its dimensionless finite element discrete system is a block diagonal structure. ,in It is a dimensionless stiffness matrix for the electrode domain, which only characterizes the mechanical properties of the metal electrode; is the dimensionless dielectric matrix of the electrode domain, characterizing the overall dielectric properties of the metal electrode and the air-filled region; 0 is the zero matrix, characterizing the absence of piezoelectric coupling terms in the electrode domain. This is the displacement degree of freedom vector of the electrode domain; The potential vector of the electrode domain is the degree of freedom vector. This represents the force load vector in the electrode domain. For the charge load vector of the electrode domain, this formula is adapted to the core feature of the separation of the physical field of the electrode domain.

[0028] Define the physical constraint rules for the coupling interface. After the partitioning is complete, at the common coupling interface... The pre-set weakly continuous physical constraints of mechanical force balance and electrical charge conservation satisfy the integral form. ,in , These are the interpolated approximations of the physical quantities at the interfaces of the substrate domain and the electrode domain, respectively. The Mortar check function is used to ensure the stable transfer of physical quantities between the two domains, which is suitable for the coupled solution requirements of subsequent non-matching meshes.

[0029] The validity of the solution domain partitioning was verified. The partitioned substrate and electrode domains completely covered the entire geometric space of the device, with no structural gaps or spatial overlaps. The discrete system formulas of the two domains were completely matched with their physical properties. The geometric position, degree of freedom definition, and physical constraints of the coupling interface all met the numerical solution requirements of the domain decomposition method. After the verification was passed, the process of partitioning the solution domain of the surface acoustic wave device into the substrate and electrode domains was officially completed.

[0030] In a preferred embodiment of the present invention, step 2 above, which involves performing dimensionless preprocessing on the substrate domain based on its geometric and material parameters, obtaining substrate domain interface operators through cascaded calculations, and storing substrate domain interface operators of different lengths into a cascaded operator library, may include: In this embodiment of the invention, step 220 involves constructing a substrate basic unit data structure based on the geometric and material parameters of the substrate domain, and performing dimensionless preprocessing on the substrate basic unit data structure based on the multiphysics coupling characteristics in the material parameters to obtain standardized basic unit data. Specifically, this includes: constructing a geometric topology data structure for the substrate basic units; determining the geometric boundaries and stacked structures of two types of substrate basic units based on the geometric parameters of the substrate domain; the first type is unit 0, which includes a piezoelectric layer and its bottom perfectly matched layer (PML); and the second type is unit 1, which is a pure perfectly matched layer (PML). The two types of basic units are then subjected to fine meshing to determine the topological relationships of the mesh nodes, the geometric boundary range of the units, and the interlayer contact relationships. A substrate basic unit geometric topology data structure containing mesh topology, geometric dimensions, and boundary attributes is constructed to ensure that the structure completely reproduces the physical geometry of the basic units.

[0031] The material parameter mapping and integration of the substrate basic unit involves mapping the material parameters of the substrate domain one by one to the geometric topology data structure of unit 0 and unit 1 according to the material layer type, realizing the association between geometric information and material information. Specifically, the elastic parameters, dielectric parameters, piezoelectric parameters, and density parameters corresponding to the piezoelectric layer and PML layer are assigned to the corresponding geometric mesh in the basic unit, and the damping parameters are assigned to the global mesh to characterize the energy loss characteristics. After integration, a complete substrate basic unit data structure containing geometric topology information and material physical information is formed. This structure is the original data foundation for dimensionless preprocessing.

[0032] The selection and constraint of global dimensionless reference constants, considering the multi-physics coupling characteristics of the substrate's basic unit, and to balance the magnitude difference between the displacement field and the electric field and improve the ill-conditioned nature of subsequent matrix solutions, involves selecting a set of global dimensionless reference constants, including characteristic elastic constants. Characteristic dielectric constant Characteristic piezoelectric constant Feature density Characteristic frequencies Characteristic length To ensure that the mechanical energy term and the electrical energy term remain in balance on a numerical scale, a constraint relationship is imposed on the reference constant. = Based on the general parameter characteristics of surface acoustic wave device simulation, the fixed value of the reference constant is determined. , , , , , .

[0033] The dimensionless transformation of the substrate basic unit data structure, based on a selected global dimensionless reference constant, sequentially performs dimensionless transformation processing on the spatial coordinates, frequencies, and various material parameters in the substrate basic unit data structure. The dimensionless transformation of spatial coordinates and frequencies makes the actual spatial coordinates... Actual frequency with dimensionless spatial coordinates Dimensionless frequency Satisfy transformation relationship , The coordinates and geometric dimensions of all mesh nodes in the basic unit geometric topology data structure are replaced with dimensionless quantities; the dimensionless transformation of material parameters makes the actual elastic parameters... Actual dielectric parameters Actual piezoelectric parameters Actual density parameters With dimensionless elastic parameters Dimensionless dielectric parameters Dimensionless piezoelectric parameters Dimensionless density parameter Satisfy the unified mapping relationship All material parameters in the basic unit data structure are replaced with dimensionless quantities; for non-piezoelectric elastic layers, their piezoelectric parameters are naturally zero, and the above dimensionless mapping framework remains applicable.

[0034] The generation and integration of standardized basic unit data involves the full integration of geometric topology data and material physics data after dimensionless transformation, updating them to the original substrate basic unit data structure, removing the original dimensional data, and forming standardized basic unit data containing only dimensionless information. This data eliminates the magnitude differences of different physical quantities under multi-physics coupling, providing standardized data input for finite element discretization and condensed computation.

[0035] Step 221 involves discretizing and condensing the standardized basic unit data using finite element or other numerical methods to obtain basic unit interface operators characterizing the boundary mechanical and electrical properties of the basic units, and defining these basic unit interface operators as operator materials. Specifically, this includes: finite element multiphysics discretization of the standardized basic units; based on the standardized basic unit data and combined with the multiphysics control equations of the piezoelectric coupling of the surface acoustic wave device, performing finite element discretization on units 0 and 1 respectively; substituting the dimensionless material parameters of the standardized basic units into the finite element shape function matrix; and sequentially assembling to obtain the dimensionless stiffness matrix. piezoelectric coupling matrix Dielectric matrix Determine the boundary force load vector based on the mechanical and electrical boundary conditions of the basic unit. With boundary charge load vector Integrating the above matrices with the load vectors, a structure containing displacement degrees of freedom is constructed. With electric potential degree of freedom A standardized basic unit finite element discrete system is used to realize the numerical representation of the multi-physics field of the basic unit.

[0036] The global degree of freedom of the standardized basic unit is divided into two categories: internal degree of freedom and boundary degree of freedom. The internal degree of freedom is the displacement and potential of the grid nodes inside the geometric space of the basic unit, and the boundary degree of freedom is the displacement and potential of the grid nodes on the geometric boundary of the basic unit. The boundary degree of freedom includes the left and right boundary degrees of freedom of the basic unit (for subsequent cascading and splicing) and the top boundary degree of freedom (for subsequent coupling with the electrode domain).

[0037] Based on the Schur complement condensation operation, internal degrees of freedom are eliminated. For the partitioned degree-of-freedom system, the Schur complement condensation operation is performed. Through matrix transformation and elimination, the internal degrees of freedom of the normalized basic unit are eliminated, retaining only the boundary degrees of freedom, resulting in the boundary condensation system of the basic unit. The matrix expression of this system is as follows: The extraction and calibration of the basic unit interface operator: The boundary condensation system obtained by the Schur complement condensation operation is the basic unit interface operator. This operator is only related to the boundary degree of freedom of the basic unit, and fully characterizes the mechanical and electrical coupling characteristics of the displacement field and electric field at the boundary of the basic unit, and is not related to the internal degree of freedom. The above finite element discretization and condensation operation are performed on unit 0 and unit 1 respectively to obtain the basic unit interface operator of unit 0 and the basic unit interface operator of unit 1. These two types of interface operators are uniformly defined as the operator material of recursive cascade operation.

[0038] Step 222 involves recursively cascading the operator materials according to the actual length requirements of the surface acoustic wave (SAW) device to obtain complete substrate domain interface operators with different total length configurations. The complete substrate domain interface operators and their corresponding length identifiers are then categorized and stored in the cascaded operator library. Specifically, this includes: determining the basic unit combination sequence based on the actual requirements of the SAW device; determining the basic unit combination sequence of the substrate domain based on the geometric design requirements of the SAW device to be simulated, such as the total propagation length and aperture size, combined with the basic length parameters of unit 0 and unit 1. This sequence clarifies the splicing order, number of splicing operations, and splicing position of the operator materials, and also determines the top boundary degree of freedom range of the cascaded substrate domain (the interface coupled with the electrode domain), ensuring that the total length of the cascaded substrate domain completely matches the actual geometric requirements of the SAW device; and designing corresponding basic unit combination sequences for SAW devices with different total propagation lengths to provide a basis for generating complete substrate domain interface operators with multiple length configurations.

[0039] The recursive cascade operation of operator materials realizes the splicing and fusion of basic units. Based on a defined sequence of basic unit combinations, a recursive splicing and cascade operation is performed on the operator materials. The core is to eliminate the common interface degrees of freedom of adjacent basic units through Schur complement condensation operation, thereby achieving the fusion of multiple basic units. Specifically, the initial splicing unit is defined by selecting the first two operator materials in the combination sequence as the initial splicing units, denoted as block A and block B, respectively. The left and right boundary degrees of freedom of block A and the left and right boundary degrees of freedom of block B are defined. The right boundary of block A and the left boundary of block B are the common interface between the two units, and the degrees of freedom of the common interface are denoted as . Physical constraints are imposed at the common interface, including both mechanical and electrical constraints, which mechanically satisfy the force equilibrium condition. That is, the forces at the common interface of block A and the common interface of block B are equal in magnitude and opposite in direction, and electrically satisfy the conditions of continuous electric potential and conservation of charge; by eliminating the degrees of freedom at the common interface, boundary equations for blocks A and B are constructed respectively, thus eliminating the degrees of freedom at the common interface. As the internal degrees of freedom of the new unit after splicing, these internal degrees of freedom are eliminated by Schur condensation operation, resulting in a spliced ​​new unit interface operator that retains only the degrees of freedom of the left, right, and top boundaries of the new unit. Recursively splicing is then performed, using the spliced ​​new unit interface operator as a new splicing unit. According to the basic unit combination sequence, the above-mentioned common interface definition, physical constraint application, and internal degree of freedom elimination operations are performed with the next operator material. This process is recursively iterated until the cascade operation of all operator materials in the combination sequence is completed, resulting in a complete substrate domain interface operator corresponding to the actual length of the surface acoustic wave device. This operator retains only the top boundary degree of freedom of the coupling between the substrate domain and the electrode domain, eliminating the internal degrees of freedom of the other boundaries, and fully characterizing the boundary mechanical and electrical coupling characteristics of the entire substrate domain.

[0040] The generation of complete substrate domain interface operators with different total length configurations is achieved by calling the corresponding basic unit combination sequence to perform the above recursive cascade operation on the operator material for different propagation direction total length requirements of surface acoustic wave devices. This results in multiple sets of complete substrate domain interface operators with different total length configurations. Each set of operators corresponds one-to-one with the total length of the specific substrate domain propagation direction and retains the top boundary degree of freedom coupled with the electrode domain, thus meeting the simulation requirements of surface acoustic wave devices of different sizes.

[0041] The length identifier information of the complete substrate domain interface operator is added. A unique length identifier information is added to each group of complete substrate domain interface operators. This information includes key contents such as the total length of the substrate domain propagation direction, the basic unit combination method, the mesh generation accuracy, and the number of degrees of freedom of the top boundary. This realizes the association between the operator and the geometric dimensions of the substrate domain and provides an identifier basis for the rapid retrieval and reuse of the operator.

[0042] The cascaded operator library is categorized, stored, and initialized. An offline storage structure for the cascaded operator library is built, and data is categorized and stored according to the properties of the operators. The first category is the original operator material, namely the basic unit interface operators of unit 0 and unit 1; the second category is the complete substrate domain interface operators with different total length configurations. Each group of complete operators is bound to its corresponding length identifier information before storage. During storage, a secondary classification is performed according to the basic unit type to ensure convenient operator retrieval. After storing all operators and identifier information, the cascaded operator library is initialized, providing offline data support for the reuse and reconstruction of substrate domain interface operators in electrode iterative design.

[0043] By structuring and dimensionless preprocessing of substrate basic units, the magnitude differences of different physical quantities in multiphysics coupling are balanced. Operator materials are extracted through Schur complement condensation operations, decomposing the computation of large-scale substrate domains into the computation of small-scale basic units, reducing the computational pressure and memory overhead of a single operation. Based on the recursive cascade operation of operator materials, complete substrate domain interface operators with different length configurations can be quickly generated to adapt to the simulation requirements of SAW devices of different sizes. The classified storage of the cascaded operator library realizes the offline caching of substrate domain interface operators.

[0044] In a preferred embodiment of the present invention, step 3 above, which involves determining whether the substrate domain interface operator needs to be reconstructed based on the new electrode design parameters, if reconstruction is not required, then reusing the existing substrate domain interface operator from the cascaded operator library; if reconstruction is required, then rapidly cascading new substrate domain interface operators using operator materials from the cascaded operator library, may include: In this embodiment of the invention, step 330 involves parsing the new electrode design parameters and extracting the total length information of the substrate domain required at present. The total length information of the substrate domain is then matched and compared one by one with the length identifier information stored in the cascaded operator library to obtain the comparison results. Specifically, this includes: systematic parsing and feature classification of the new electrode design parameters. The system receives a complete set of newly input electrode design parameters, which fully covers all electrode iterative design-related parameters such as electrode thickness, electrode finger width, electrode finger spacing, number of electrode fingers, electrode arrangement, total size of device propagation direction, size of device aperture direction, and electrode metallization rate. The parameter set is then subjected to dimensional parsing and feature classification. The parameters are divided into two categories: electrode domain-specific parameters, parameters that only affect the electrode domain structure, such as electrode thickness and finger width, which are geometric parameters associated with the substrate domain, and parameters that are related to the size of the substrate domain, such as total size of device propagation direction and size of aperture direction. Unrelated redundant parameters are removed, and the effective parameter set is retained.

[0045] The accurate extraction and geometric verification of the total length information of the substrate domain is based on the substrate domain associated geometric parameters in the effective parameter set. The core geometric parameters of the substrate domain required for the current simulation are extracted through geometric correlation calculation, including the total length of the substrate domain in the propagation direction. This length is completely consistent with the total dimension of the device in the propagation direction after electrode iteration and forms a geometric match with the dimension of the substrate domain aperture direction. At the same time, it is verified whether the extracted total length of the substrate domain conforms to the geometric design specifications of the substrate domain of the surface acoustic wave device, ensuring that the length value has no logical deviation, forming a unique total length information of the substrate domain in the propagation direction. This information is the core basis for operator matching.

[0046] The cascaded operator library is retrieved and its length identifier information is extracted. The offline cascaded operator library, which has been initialized and stored, is retrieved. This operator library adopts a two-layer storage structure of original operator material area + complete substrate domain interface operator area. The complete substrate domain interface operator area stores complete substrate domain interface operators with different length configurations, and each operator is bound to a unique structured length identifier information. This identifier information includes core matching fields such as total length of substrate domain propagation direction, meshing accuracy, number of degrees of freedom of coupling interface, and basic unit combination method. All operators in the complete substrate domain interface operator area are traversed, and the structured length identifier information corresponding to each operator is enumerated and extracted one by one to form a length identifier information set.

[0047] The total length information of the substrate domain is matched and compared with the length identifier information at the field level. The extracted total length information of the substrate domain propagation direction is compared with each identifier information in the length identifier information set through multi-field, layer-by-layer precise comparison. First, the core total length value of the substrate domain propagation direction is compared. After the values ​​are completely consistent, auxiliary matching fields such as mesh subdivision accuracy and number of degrees of freedom of the coupling interface are further compared to ensure that the geometric and numerical characteristics of the operator match the current requirements. The results of each comparison are recorded one by one, including matched fields, unmatched fields, and matching status (complete match / partial match / no match). Finally, a structured comparison result is generated, which includes the overall matching status, the unique identifier of the completely matched item (if any), and the reason for the unmatch (if none). This result has only two core states: there is a completely matched length identifier information in the cascaded operator library, or there is no completely matched length identifier information in the cascaded operator library.

[0048] Step 331: Obtain a reconstruction judgment instruction based on the comparison results. If the judgment instruction indicates that the length identifier information has a complete match, locate and read the complete substrate domain interface operator corresponding to the complete match in the cascaded operator library, and use the read complete substrate domain interface operator as the reused substrate domain interface operator. Specifically, this includes: generating a structured reconstruction judgment instruction based on the comparison results. According to the structured comparison results output in step 330, automatically generate a structured reconstruction judgment instruction that corresponds one-to-one with the matching state. This instruction contains three core fields: core judgment result (reuse substrate domain interface operator / reconstruct substrate domain interface operator), matching item association information (if it is a reuse state, it contains the unique identifier of the complete match; if it is a reconstruction state, it contains an explanation of no complete match), and execution requirements (directly call / start the reconstruction process). The instruction and the comparison results are completely traceable, unambiguous, and can be directly executed.

[0049] In the state of complete matching, if the core judgment result of the reconstruction judgment instruction is to reuse the substrate domain interface operator, then the unique identifier of the matching item in the instruction is used as the search keyword to call the index mapping table of the cascaded operator library. This table establishes a one-to-one correspondence between the unique identifier of the length identifier information and the storage address of the operator in the library. The corresponding storage address is quickly matched through the unique identifier, and the accurate positioning of the target complete substrate domain interface operator is completed in the complete substrate domain interface operator area, ensuring that the positioned operator is completely matched with the current simulation requirements.

[0050] The full data reading and boundary agglomeration system verification of the target operator were performed. Based on the located storage address, all data of the target complete substrate domain interface operator were fully read. This operator is the boundary agglomeration system obtained through Schur complement agglomeration and cascade operations. The corresponding core formula in the document is as follows: In the formula, The stiffness matrix is ​​the dimensionless stiffness matrix of the substrate domain, which characterizes the mechanical properties of the substrate domain boundary. The dimensionless piezoelectric coupling matrix of the substrate domain characterizes the coupling relationship between the boundary displacement field and the electric field. The dielectric matrix is ​​the dimensionless dielectric matrix of the substrate domain, which characterizes the electrical properties of the substrate domain boundary. The boundary displacement degree of freedom vector of the coupling interface between the substrate domain and the electrode domain; The boundary potential degree of freedom vector at the coupling interface between the substrate domain and the electrode domain; This represents the boundary force load vector at the substrate domain coupling interface; The boundary charge load vector of the substrate domain coupling interface is used to verify the integrity of the read operator data. The matrix dimension, vector length, and topological information are checked to ensure they are complete and without missing or distorted data. If the verification passes, proceed to the next step; otherwise, the data is retrieved and verified again.

[0051] The calibration and verification of the reused substrate domain interface operator involves formally marking the complete substrate domain interface operator that has passed integrity verification as the substrate domain interface operator that can be directly reused in the current simulation process, and completing the usage calibration of the operator, marking the matching basis, retrieval time, data characteristics and other information of the operator; the calibrated reused operator does not require any matrix correction, feature adjustment or recalculation, and can be directly used as fixed input data for solving the coupling assembly of the substrate domain and electrode domain, thus completing the operator reuse process of this step.

[0052] Step 332: If the instruction indicating length identifier information does not have a complete match, then the required basic unit combination sequence is decomposed according to the currently required total substrate domain length information, and multiple basic unit interface operators corresponding to the basic unit combination sequence are retrieved from the cascade operator library as cascade operator materials; specifically, this includes: confirming the constraint conditions for the decomposition of the total substrate domain length, using the currently required total substrate domain propagation direction length information extracted in step 330 as the target parameter, first clarifying the decomposition constraint conditions of the substrate basic units, including basic unit type constraints (only using the two types of substrate basic units pre-stored in the cascade operator library). The decomposition process is as follows: Unit 0 is the basic unit containing the piezoelectric layer and its bottom perfectly matched layer (PML), and Unit 1 is the basic unit of the pure perfectly matched layer. Both are normalized units that have been dimensionless and Schur-complemented. Geometric topological constraints (the two ends of the substrate domain along the propagation direction must be Unit 1 to match the arrangement requirements of the perfectly matched layer, and the middle region must be Unit 0 to match the main structure of the piezoelectric layer) and length adaptation constraints (the total length of the decomposed basic units is completely consistent with the total length of the target substrate domain, with no length deviation). All decomposition operations strictly follow the above constraints to ensure the rationality and effectiveness of the decomposition results.

[0053] The precise decomposition of the total length of the target substrate domain and the generation of the basic unit combination sequence are achieved by layer-by-layer precise decomposition of the total length of the target substrate domain in the propagation direction based on the confirmed decomposition constraints. The number of units 0 and 1 used, the splicing order along the propagation direction of the substrate domain, and the specific splicing position of each unit are calculated. At the same time, the connection relationship between adjacent units is clarified (such as the connection between unit 1 and unit 0, and the connection between unit 0 and unit 0). Based on the decomposition results, a standardized basic unit combination sequence is generated. This sequence is a structured sequence containing core fields such as sequence number, unit position index, unit type, number of units, connection characteristics of adjacent units, and total length verification results. The total length of the sequence completely matches the total length of the target substrate domain and conforms to the geometric topology rules of the substrate domain.

[0054] The targeted retrieval and consistency verification of basic unit interface operators are based on standardized basic unit combination sequences. The retrieval is performed by entering the original operator material area of ​​the cascaded operator library. According to the unit type and quantity in the sequence, the corresponding basic unit interface operator is retrieved (unit 0 corresponds to the retrieved basic unit interface operator for unit 0, and unit 1 corresponds to the retrieved basic unit interface operator for unit 1). Both types of basic unit interface operators satisfy the substrate domain boundary condensation system formula, denoted as _____ for unit 0. Unit 1 is In the formula, the subscripts 0 and 1 represent unit 0 and unit 1, respectively. The meaning of each parameter is consistent with that of the interface operator of the complete substrate domain. It only represents the boundary characteristics of a single basic unit. The consistency verification of the basic unit interface operator is performed to check whether the type and number of the operator are completely consistent with the requirements of the basic unit combination sequence, and whether the boundary condensation system data of the operator is complete and valid. If the verification is successful, proceed to the next step; if it fails, it is re-retrieved and verified.

[0055] The process of marking and constructing the material set for the operators to be cascaded involves uniformly marking all basic unit interface operators that have passed consistency verification as materials for the operators to be cascaded, and assigning each material a unique material number corresponding to the unit position index in the basic unit combination sequence, thus establishing a one-to-one mapping relationship between the materials for the operators to be cascaded and the basic unit combination sequence. All marked materials for the operators to be cascaded are then integrated to form a structured material set for the operators to be cascaded. This material set serves as the sole input data for subsequent recursive cascade operations, and the arrangement order of the materials is completely consistent with the splicing order of the basic unit combination sequence.

[0056] Step 333: Perform recursive cascading operations on the materials to be cascaded according to the order of the basic unit combination sequence. Use the intermediate interface operator of the previous stage as the input data of the next stage to continuously synthesize the matrix until the synthesis of all materials to be cascaded is completed. Use the final synthesis result as the new complete substrate domain interface operator. Specifically, this includes: preprocessing and initialization of iteration parameters for recursive cascading operations. Before performing recursive cascading operations, preprocess the structured set of materials to be cascaded to confirm that the boundary condensation system of all materials to be cascaded is a dimensionless standardized form, and that the rules for defining degrees of freedom and the matrix dimension specifications are completely unified. At the same time, initialize the iteration parameters of recursive cascading, including the current iteration number (initial value is 1), the current input operator (initial value is empty), the number of remaining materials to be cascaded (initial value is the total number of materials in the set of materials to be cascaded), and the intermediate interface operator storage area (initialized to empty), to make full preparations for recursive cascading operations.

[0057] The first cascade operation is executed as follows: When the current iteration number is 1, the first two cascaded operator materials are selected from the set of materials to be cascaded, denoted as block A and block B, respectively, as the initial splicing units for the first cascade. The specific execution process is as follows: Boundary degrees of freedom are defined, with left, right, and top boundary degrees of freedom defined for blocks A and B. The top boundary degree of freedom is the interface degree of freedom for subsequent coupling with the electrode domain and is retained throughout the process without participating in internal degree of freedom elimination. The right boundary of block A and the left boundary of block B are the common interface of the two units, and the degree of freedom of this common interface is defined as follows. .

[0058] Physical constraints are applied at the common interface, including both mechanical and electrical constraints, which mechanically satisfy the force equilibrium condition. ,in Let A be the force load vector of the common interface of block A. The force load vector at the common interface of block B ensures the balanced transmission of interface forces; electrically, it satisfies the conditions of continuous electric potential and conservation of charge, ensuring the continuous transmission of the electric field at the interface.

[0059] Boundary condensation system construction and internal degree of freedom elimination: Construct boundary condensation systems for blocks A and B respectively. Block A Block B Increase the freedom of the public interface As the internal degree of freedom of the new unit after splicing, this internal degree of freedom is eliminated by the Schur complement condensation operation, thus completing the matrix synthesis of the two initial units.

[0060] The generation and verification of the first-level intermediate interface operator: After synthesis, a first-level intermediate interface operator is generated. This operator retains only the left boundary degree of freedom, right boundary degree of freedom, and top boundary degree of freedom of the new unit, and still satisfies the general formula of the substrate domain boundary condensation system. The effectiveness of the operator is verified by checking that the matrix is ​​not ill-conditioned, the degree of freedom is retained in accordance with the rules, and the total length matches the length after splicing. After the verification is passed, the operator is stored in the intermediate interface operator storage area, and the iteration parameters are updated at the same time (current iteration number +1, current input operator is a first-level intermediate interface operator, and the number of remaining materials to be cascaded -2).

[0061] The recursive cascading operation is executed cyclically. Based on the updated iteration parameters, it enters the cyclic recursive cascading stage, taking the current input operator as the new block A, and selecting the next block B from the set of block B to be cascaded. It repeats all operations from the first cascading operation, including defining boundary degrees of freedom, applying physical constraints to the common interface, constructing the boundary condensation system and eliminating internal degrees of freedom, and generating and verifying intermediate interface operators, to generate the next level intermediate interface operator. After each cascading operation is completed, the iteration parameters are updated (current iteration count +1, current input operator is the newly generated intermediate interface operator, remaining block B -1) until the remaining block B is 0, completing the splicing and synthesis of all block B materials.

[0062] The generation, verification, and calibration of the new complete substrate domain interface operator: When the remaining amount of material to be cascaded is 0, the final intermediate interface operator generated in the last cascade is used as the new complete substrate domain interface operator to meet the current total length requirement of the substrate domain. Its core formula remains the same. In the formula, the subscript This represents a new, complete substrate domain interface operator. Each parameter represents the boundary characteristic parameters of the cascaded global substrate domain, retaining only the top boundary degrees of freedom coupled to the electrode domain. The new operator undergoes comprehensive verification, including the matching of the total length of the substrate domain propagation direction with the target requirements, the effectiveness of the top coupling interface degrees of freedom, the numerical stability of the boundary condensation system, and the conformity of the geometric topology with the substrate domain design rules. Once all verification items pass, the new operator is calibrated, and information such as the operator's reconstruction basis, cascade number, and data characteristics are noted. This calibrated new operator fully characterizes the boundary mechanical and electrical coupling properties of the current substrate domain and can be directly used as input data for subsequent substrate domain and electrode domain coupling assembly solutions, completing the operator reconstruction process in this step.

[0063] By parsing parameters and matching lengths, the reuse of the substrate domain interface operator is maximized. When the operator needs to be reconstructed, it can be recursively synthesized based on prefabricated basic unit materials, reducing computation time and memory usage. At the same time, it can flexibly adapt to changes in the size of the substrate domain after electrode iteration, improving the overall efficiency of surface acoustic wave device design iteration.

[0064] In a preferred embodiment of the present invention, step 4 above, which involves establishing an electrode domain model using air-filled modeling based on the new electrode design parameters, performing secondary partitioning on the air-filled model, and obtaining a new electrode domain interface operator through parallel condensation operations and cascaded splicing operations, may include: In this embodiment of the invention, step 440 involves constructing an air-filled electrode domain model based on the new electrode design parameters. Specifically, this includes: electrode design parameter analysis and geometric feature extraction. The new electrode design parameters are systematically analyzed across the entire domain. After removing redundant parameters, the core parameters that determine the geometric shape of the electrode domain are extracted. The two-dimensional / three-dimensional geometric boundaries of all metal electrode structures, such as interdigital transducers (IDTs), reflectors, and busbars, are determined. These boundaries include the spatial position, size, gap distance between adjacent electrodes, and the range of blank areas on the outer edges of the electrodes. This forms an electrode geometric feature dataset, ensuring that the geometric features are completely consistent with the design parameters.

[0065] The construction of the geometric model of the metal electrode is based on the electrode geometric feature dataset. According to the physical structure rules of surface acoustic wave devices, a pure geometric model of the metal electrode is constructed, which completely reproduces the solid structure of all metal electrodes without geometric deviation or structural omission. This model is the core solid geometric foundation of the electrode domain.

[0066] The filling of air medium and the construction of a continuous physical domain address the interface coupling problem of discrete metal electrodes. The physical domain is completed for the geometric model of the metal electrodes. The gaps between the metal electrodes and the blank spaces on the outer edges of the electrodes are all defined as air medium regions. The air medium regions are seamlessly connected with the solid regions of the metal electrodes, forming a geometrically continuous and topologically complete electrode domain physical space. This eliminates the topological non-coherence problem caused by discrete electrodes and lays the geometric foundation for interface coupling.

[0067] The physical field of the electrode domain is partitioned and its parameters are assigned. The physical space is partitioned to separate the physical fields. One is the solid mechanical field (displacement degree of freedom), which covers only the metal electrode solid region and is used to describe the mass loading and mechanical boundary effects of the electrode. The air medium region does not participate in the assembly of the solid mechanical equations. The other is the electrostatic field (potential degree of freedom), which covers both the metal electrode solid region and the air medium region. It is used to apply electrode potential excitation and solve the global electrostatic field. Corresponding physical parameters are assigned to each field. The metal electrode region is assigned the elastic and density parameters of the electrode material, and the air medium region is assigned the dielectric parameter of air. At the same time, all physical parameters are subjected to dimensionless preprocessing consistent with the substrate domain to ensure that the parameter scale is consistent with the substrate domain.

[0068] Mesh generation and finite element discretization system construction: A refined mesh generation is performed on the continuous physical space of the air-filled electrode domain, with the mesh generation accuracy matching the mesh accuracy of the substrate domain coupling interface. Based on the meshed model, combined with the physical field partitioning definition and dimensionless physical parameters, finite element modeling of the air-filled electrode domain is completed. Its discrete system in the frequency domain has a block diagonal structure and no electromechanical coupling terms, as shown in the following formula: , where superscript The solid mechanical field representing the metal electrode unit. This represents the electrostatic field formed by the metal electrode and the air unit together; This is the dimensionless stiffness matrix, which only characterizes the mechanical properties of the metal electrode; is the dimensionless dielectric matrix, representing the electrical properties of the metal electrode in the air region; 0 is the zero matrix, representing the absence of electromechanical coupling terms; This is a displacement degree of freedom vector, which exists only in the metal electrode region; The potential is the degree of freedom vector, covering the region between the metal electrode and the air-filled area; For force load vector, This represents the charge load vector, thus completing the overall construction of the air-filled electrode domain model.

[0069] Step 441 involves a secondary partitioning process for the air-filled electrode domain model. This involves splitting the model along the propagation direction into multiple interconnected electrode subdomains, ensuring that each subdomain retains its interface with the substrate domain and the splicing boundaries between adjacent subdomains, resulting in a set of discrete electrode subdomains. Specifically, this includes: determining the core principles of secondary partitioning, including the principle of splitting along the propagation direction (the splitting direction must align with the propagation direction of the surface acoustic wave) and the physical characteristics of the adapter; the principle of no spatial overlap and no geometric omission (after merging, all the split electrode subdomains must be completely consistent with the geometric space and physical field range of the original electrode domain model); and the principle of complete boundary preservation (all the split electrode subdomains must retain their top interface with the substrate domain, while clear splicing boundaries are formed between adjacent electrode subdomains, providing a foundation for subsequent condensation and merging).

[0070] The planning of partition size and number is based on the total propagation direction length and meshing accuracy of the air-filled electrode domain model, combined with the hardware resource adaptability of parallel computing. The planning of the partition size and number of electrode subdomains ensures that the scale of each electrode subdomain is uniform and controllable, and that the degree of freedom scale of a single electrode subdomain is adapted to the efficiency requirements of Schur complement condensation operation, avoiding excessive computational pressure due to excessively large factor domain size or increased merging complexity due to excessively small size.

[0071] Precise splitting and subdomain construction along the propagation direction: According to the planned partition size and number, the air-filled electrode domain model is precisely split along the propagation direction in terms of geometry and physical field simultaneously. The original electrode domain model is divided into multiple interconnected independent regions, each of which is an electrode subdomain. During the splitting process, it is ensured that the top boundary of each electrode subdomain is an interface coupled to the substrate domain, and the geometric features, mesh distribution, and physical field parameters of the interface are consistent with the original model. The contact interface between adjacent electrode subdomains is defined as the splicing boundary, and the mesh nodes and degrees of freedom of the splicing boundary are marked.

[0072] The electrode subdomains are characterized and discretized. Each electrode subdomain is independently characterized and assigned a unique identifier. The boundary type (coupling interface with the substrate domain, splicing boundary with adjacent subdomains), geometric dimensions, field distribution, dimensionless parameters, and other core features of each subdomain are marked. All the calibrated electrode subdomains are then discretized, retaining the finite element mesh model, physical field parameters, and discrete system formulas of each subdomain. Finally, a set of discrete electrode subdomains that can be independently used for condensation calculations are obtained.

[0073] Step 442 involves independently performing the first condensation operation on each electrode subdomain. The internal degrees of freedom of each electrode subdomain are eliminated by Schur complement, resulting in boundary interface operators that retain only the splicing boundary degrees of freedom and the interface degrees of freedom for each electrode subdomain. Specifically, this includes: independent parallel initialization of the electrode subdomains, allocating all discrete electrode subdomains to parallel computing resources, independently initializing each electrode subdomain, and retrieving the finite element model, physical field parameters, and boundary feature information of each electrode subdomain to ensure that the calculation process of each subdomain is independent and free from data interference, thus laying the foundation for parallel condensation operations.

[0074] The degrees of freedom of each electrode subdomain are divided independently into two categories: internal degrees of freedom and boundary degrees of freedom. The internal degrees of freedom are the displacement and potential degrees of freedom of the grid nodes within the geometric space of the electrode subdomain. The boundary degrees of freedom include two parts: the interface degrees of freedom that couple with the substrate domain and the splicing boundary degrees of freedom that connect with adjacent electrode subdomains. The internal degrees of freedom are the elimination objects in this condensation operation, and the boundary degrees of freedom are the core objects of subsequent operator merging and coupling.

[0075] Based on the first condensation operation of Schur complement, for each electrode subdomain, the Schur complement condensation operation is performed independently on its block diagonal structure finite element discretization system. Through matrix transformation and elimination operations, the internal degrees of freedom of the electrode subdomain are eliminated, retaining only the splicing boundary degrees of freedom and the interface degrees of freedom, resulting in the boundary condensation system of each electrode subdomain. This system is the boundary interface operator of the electrode subdomain. The discretization formula for air-filled electrode domains is used, and subdomain subscripts are added. The formula is In the formula, the subscript Representing the Each electrode subdomain; For the first The dimensionless stiffness matrix of each electrode subdomain; For the first The dimensionless dielectric matrix of each electrode subdomain; For the first The boundary displacement degree-of-freedom vector of each electrode subdomain includes only the displacement degree-of-freedom of the splicing boundary and the interface. For the first The boundary potential degree of freedom vector of each electrode subdomain includes only the potential degree of freedom of the splicing boundary and the interface. For the first Boundary force load vector of each electrode subdomain For the first Boundary charge load vectors of each electrode subdomain.

[0076] The validity verification and extraction of boundary interface operators are carried out by independently verifying the validity of the boundary interface operators obtained by Schur complement condensation operation for each electrode subdomain. The numerical stability of the matrix, the integrity of the preservation of boundary degrees of freedom, and the consistency of the characteristics of the operator with the original electrode subdomain are checked. After the verification is passed, the boundary interface operators of each electrode subdomain are extracted to form a set of boundary interface operators that correspond one-to-one with the discrete electrode subdomain.

[0077] Step 443: Merge the boundary interface operators of each electrode subdomain according to the splicing boundary between adjacent subdomains, and merge the common degrees of freedom on the splicing boundary into internal degrees of freedom to obtain the intermediate interface operator of the spliced ​​electrode domain; specifically, this includes: identifying the common degrees of freedom of the splicing boundary of adjacent subdomains, traversing the set of boundary interface operators of electrode subdomains, and identifying the common degrees of freedom on the splicing boundary of adjacent electrode subdomains according to the splicing relationship of the electrode subdomains along the propagation direction, including common displacement degrees of freedom and common potential degrees of freedom, to ensure that the geometric position and mesh node of the common degrees of freedom are completely corresponding, providing a basis for the continuous transmission of mechanical and electrical quantities between adjacent subdomains.

[0078] The boundary interface operators are integrated sequentially according to the arrangement order of the electrode subdomains in the original air-filled electrode domain model. The boundary interface operator matrices of each electrode subdomain are spatially aligned according to the topological relationship of the grid nodes to ensure that the common degrees of freedom of the splicing boundary of adjacent subdomains are in the corresponding positions in the matrix, thus satisfying the dimensional requirements of matrix merging.

[0079] The merging of common degrees of freedom and the redefinition of internal degrees of freedom: For the integrated boundary interface operator, the common degrees of freedom on the splicing boundary of adjacent subdomains are merged in a unified manner, and the merged common degrees of freedom are defined as the new internal degrees of freedom of the electrode domain. These degrees of freedom are the elimination objects for the subsequent second condensation operation. The interface degrees of freedom of the coupling between each electrode subdomain and the substrate domain are kept independent and intact, and are not involved in this merging operation, so as to ensure that the coupling solution with the substrate domain is not affected.

[0080] The generation of the intermediate interface operator of the electrode domain is based on the merging of common degrees of freedom and the redefinition of internal degrees of freedom. The integrated boundary interface operator matrix is ​​synthesized as a whole, and the spliced ​​intermediate interface operator of the electrode domain is obtained through matrix splicing and dimension adaptation. This operator is the boundary condensed system of the global electrode domain, which still maintains the block diagonal discrete system form in the document. It contains two types of degrees of freedom: one is the interface degree of freedom of all electrode subdomains that are uniformly coupled with the substrate domain, and the other is the internal degree of freedom of the newly defined spliced ​​boundary after merging. It fully characterizes the boundary mechanical and electrical properties of the merged electrode domain.

[0081] Step 444: Perform a second condensation operation on the spliced ​​electrode domain intermediate interface operator. Eliminate the internal degrees of freedom on the splicing boundary using Schur complement to obtain an electrode domain interface operator that retains the interface degrees of freedom coupled to the substrate domain. Specifically, this includes: separation of the degrees of freedom of the electrode domain intermediate interface operator. Separate the global degrees of freedom of the electrode domain intermediate interface operator into splicing boundary internal degrees of freedom and interface degrees of freedom. The splicing boundary internal degrees of freedom are the newly defined internal degrees of freedom after merging the common degrees of freedom in step 443, and the interface degrees of freedom are the top boundary degrees of freedom coupled to the substrate domain. This condensation operation only eliminates the splicing boundary internal degrees of freedom, while the interface degrees of freedom are fully retained throughout the process.

[0082] The second condensation operation based on Schur complement is performed. Using the block diagonal structure of the electrode domain's intermediate interface operator as a foundation, the Schur complement condensation operation is executed. Through matrix inversion and elimination transformations, the internal degrees of freedom of the splicing boundary are eliminated, condensing all global features of the electrode domain to the interface degrees of freedom coupled to the substrate domain. The corresponding electrode domain interface condensation equation is: Combining the block diagonal characteristics of air-filled electrode domains, the final result is an electrode domain boundary condensation system that retains only the interface degrees of freedom, as shown in the formula: In the formula, the subscript Represents the entire electrode domain; This is the dimensionless global stiffness matrix of the electrode domain, which only characterizes the mechanical properties of the interface. The overall dielectric matrix after the electrode domain is dimensionless is used to characterize only the electrical properties of the interface. The interface displacement degree of freedom vector for coupling the electrode domain and the substrate domain; The interface potential vector representing the coupling between the electrode domain and the substrate domain. This represents the force load vector at the electrode domain interface. This is the charge load vector at the electrode domain interface.

[0083] The generation and full-dimensional verification of the electrode domain interface operator: The electrode domain boundary condensation system obtained by the second Schur complement condensation operation, which retains only the degree of freedom of the interface coupled with the substrate domain, is defined as a new electrode domain interface operator. The operator is then subjected to full-dimensional validity verification, including the integrity of the interface degree of freedom, the numerical stability of the matrix, the consistency of the operator with the original air-filled electrode domain model, and the parameter scale matching with the interface coupled with the substrate domain. After all verification items pass, the final generation of the electrode domain interface operator is completed.

[0084] The feature calibration of the electrode domain interface operator involves calibrating the generated new electrode domain interface operator by labeling core information such as the electrode design parameters, secondary partitioning method, number of condensation operations, and number of interface degrees of freedom. This ensures that the operator can be directly coupled with the substrate domain interface operator, providing standardized input for subsequent mesh matching judgment and coupling solution.

[0085] By constructing an air-filled electrode domain model, the solid mechanical field and electrostatic field of the electrode domain are separated, reducing the numerical difficulty of Schur complement condensation calculation. By performing secondary partitioning along the propagation direction, the large-scale electrode domain is decomposed into multiple small-scale subdomains and parallel condensation calculation is performed, transforming a single large-scale Schur complement calculation into multiple small-scale independent calculations, reducing the peak memory and time consumption of online calculation, and improving the computational efficiency of electrode domain updates.

[0086] In a preferred embodiment of the present invention, step 5 above, determining whether the interface mesh of the substrate domain interface operator and the new electrode domain interface operator matches, if they match perfectly, performs assembly and solution; if they do not match perfectly, an interface transfer matrix is ​​constructed through Mortar projection, and the interface coupling assembly and solution are completed using the interface transfer matrix. After obtaining the solution for the interface degrees of freedom, the solution for the internal degrees of freedom is further restored to obtain the overall response of the device, which may include: In this embodiment of the invention, step 550 involves determining the interface of the electrode domain as the master interface and using the discrete degrees of freedom on the master interface as master variables; simultaneously, the interface of the substrate domain is determined as the slave interface, and the discrete degrees of freedom on the slave interface are used as slave variables; specifically, this includes: based on the characteristic that the substrate domain is fixed throughout and the electrode domain is iteratively updated, determining the interface of the electrode domain side as the master interface in the coupling interface between the substrate domain and the electrode domain (denoted as...). The interface on the substrate domain side is defined as the slave interface (denoted as...). The master and slave interfaces together constitute the complete coupling interface between the two domains of the surface acoustic wave device. Furthermore, they fit perfectly geometrically with no spatial offset.

[0087] Extract all discrete degrees of freedom on the main interface. These degrees of freedom are the interface degrees of freedom coupled to the electrode domain retained in the substrate domain interface operator, including displacement and potential degrees of freedom. Integrate them into the main variables, denoted as... , It is a column vector containing unknown mechanical and electrical quantities, which fully characterizes the physical state of the main interface.

[0088] Extract all discrete degrees of freedom on the side interface. These degrees of freedom are the interface degrees of freedom coupled to the substrate domain retained in the electrode domain interface operator, and also include displacement and potential degrees of freedom. Integrate them into a side variable, denoted as . , Physical quantity dimension and principal variables A perfect match, with the only difference being the distribution of discrete nodes in the grid.

[0089] Feature-label the master / slave interface and its corresponding variables, and clarify the master / slave interface. From the side interface The geometric extent, mesh topology, and principal and secondary variables. Lateral variables The number of degrees of freedom and the types of physical quantities provide basic calibration information for subsequent Mortar projection coupling.

[0090] Step 551: Based on the geometry and mesh of the master-side interface and the slave-side interface, construct a Mortar test space between the master-side interface and the slave-side interface for applying weak continuity constraints; specifically, this includes: for the master-side interface and the slave-side interface... The geometry and mesh partitioning are analyzed globally to extract the mesh cell topology, node coordinates, shape function basis function types of the main side interface, as well as the mesh cell topology, node coordinates, shape function basis function types of the secondary side interface, to confirm the geometric fit between the two interfaces and the non-matching characteristics of the mesh discretization.

[0091] Based on variational principles, with the core objective of achieving weakly continuous constraints on master / slave variables, on the master-side interface... With the side interface The coupling interface formed Above, construct the Mortar test space, which is defined at the coupling interface. The function space on, denoted as .

[0092] Determine the Mortar test space The basis functions are configured such that their types match the shape function basis functions of the master / slave interface (e.g., both use linear or quadratic shape functions), and the support domain of the basis functions covers the entire coupled interface. Furthermore, it satisfies the constraints that the test function is continuous in the overlapping region of the non-matching mesh and satisfies the homogeneous boundary conditions at the interface boundary, thus ensuring the numerical convergence of the integral projection operation.

[0093] The completed Mortar test space Validation is performed by checking the completeness of its basis functions, the coverage of its supporting domain, and its compatibility with the shape functions of the master / slave interface. After the validation is passed, the validation space is used as the core carrier for subsequent master / slave variable integration and projection operations.

[0094] Step 552: Using the shape function matrices of the primary and secondary interfaces, perform integral projection operations on the primary and secondary variables in the Mortar test space to form a Mortar coupling matrix describing the constraint relationship between the primary and secondary variables; specifically, this includes defining the primary and secondary interfaces. The shape function matrix is From the side interface The shape function matrix is , With main variables Multiplying yields the interpolated approximation of the physical quantities at the main and side interfaces. , with side variables Multiplication yields an interpolated approximation of the physical quantities at the side interface. ,in , These represent the continuous distribution of displacement or potential on the master and slave interfaces, respectively.

[0095] In Mortar's test space Choose any test function Based on the weak continuity constraint principle of Mortar projection, at the coupling interface Weak continuity constraints are applied to the master / slave physical quantities, and the corresponding variational constraint formula is: This formula indicates that the integral of the difference in physical quantities between the master and slave interfaces on the Mortar test space is equal to 0, achieving physical quantity continuity in a weak sense and avoiding the strict requirements of strong continuity constraints on mesh matching.

[0096] The interpolated approximation of the physical quantities at the master and slave interfaces , Substituting into the weak continuity constraint formula above, and expanding, we get... Discretize the above integral and define the main-side coupling matrix. From the side coupling matrix ,in , They are respectively , The transpose of the matrix ultimately yields the discrete Mortar coupling matrix equation representing the master / slave variable constraint relationship in the document. In the formula, The Mortar coupling matrix is ​​the main-side matrix. The two are Mortar coupling matrices on the master / slave side, and together they constitute a set of Mortar coupling matrices describing the linear constraint relationship between the master / slave variables.

[0097] Step 553 involves performing matrix transformation and inversion on the Mortar coupling matrix to derive the interface transition matrix, where the principal variables represent the slave variables. Specifically, this includes: based on the numerical properties of the Mortar projection, the slave coupling matrix has been proven in the documentation. It exhibits good invertibility and is suitable for Mortar coupling matrix equations. Performing matrix transformations will reduce the side variables. When placed alone on the left side of the equation, we get To improve the stability of the numerical solution, Orthogonalization correction is performed, using The inverse matrix replaces the direct Finally, the interface transition matrix, in which the principal side variables represent the secondary side variables, is derived. Its formula is In the formula, For the side coupling matrix The transpose of the matrix, for and The inverse matrix of the product is obtained through this process, which effectively avoids numerical errors caused by direct inversion and improves the stability of the transition matrix.

[0098] The interface transition matrix is ​​completed based on the above formula. The calculation, A square matrix for dimension matching, the number of rows of which is equal to the number of side variables. The number of degrees of freedom, the number of columns equals the number of principal variables. The number of degrees of freedom, satisfying The mapping relationship enables a linear projection transformation from the principal variable to the dependent variable.

[0099] The calculated interface transition matrix Numerical verification is performed to check whether the matrix rank and condition number meet the requirements of numerical solution, ensuring the uniqueness and convergence of the mapping relationship.

[0100] Step 554: Embed the interface transfer matrix into the interface coupling framework composed of the substrate domain interface operator and the electrode domain interface operator, and eliminate the dependent variables through matrix operations to obtain the interface assembly equation including the principal variables; specifically, this includes: extracting the boundary condensation equation of the substrate domain interface operator, the general form of which is: ,in The substrate domain interface operator matrix includes the dimensionless stiffness matrix, piezoelectric coupling matrix, and dielectric matrix. The vector of degrees of freedom of the substrate domain interface, i.e., the variables from the side. , This is the load vector at the substrate domain interface, which includes force loads and charge loads.

[0101] Extracting the boundary condensation equation of the electrode domain interface operator, the interface condensation form of the air-filled electrode domain is as follows: ,in Let be the electrode domain interface operator matrix, and let be the stiffness and dielectric matrices of the block diagonal structure. The degree-of-freedom vector of the electrode domain interface, i.e., the principal variables. , This is the load vector at the electrode domain interface.

[0102] Mapping relationship of interface transition matrix Substituting into the electrode domain interface agglomeration equation, we obtain the substrate domain coupling equation after eliminating lateral variables. Based on the physical constraints of mechanical force balance and electrical charge conservation at the coupling interface of surface acoustic wave devices, the substrate domain interface condensation equation and the electrode domain coupling equation after eliminating secondary variables are assembled. After combining like terms, the document contains only primary secondary variables. Interface assembly equation In the formula, Interface transition matrix The transpose of the matrix, Let be the stiffness matrix of the overall coupled interface. Given the load vector of the overall coupled interface, this equation represents a single unknown system containing only principal variables, and is solved using the direct method.

[0103] Step 555: Numerically solve the interface assembly equations to obtain the unknowns on the main interface, and calculate the unknowns on the slave interface by back substitution using the interface transition matrix; specifically including: solving the interface assembly equations Numerical solutions were performed using the direct method to solve the system of linear equations. Triangular decomposition and back substitution of matrices were employed to obtain the numerical solutions for all discrete degrees of freedom on the main interface, denoted as... , It includes the specific values ​​of the displacement degree of freedom and the potential degree of freedom of the main interface.

[0104] Numerical solution of unknowns on the main interface Substitute the mapping formula into the interface transition matrix Perform matrix multiplication and back substitution to obtain the numerical solutions for the unknowns of all discrete degrees of freedom on the side interface, denoted as... ,Right now For the principal unknowns obtained by solving with unknowns from the side Physical consistency verification is performed to check whether the numerical magnitudes of displacement and potential conform to the physical characteristics of surface acoustic wave devices, and whether the mechanical force balance and electrical charge conservation conditions of the coupling interface are met. Once the verification is passed, it is determined as the final numerical solution of the interface unknowns.

[0105] Step 556: Based on the unknowns at the side interface and the main side interface, substitute them back into the internal degrees of freedom of the substrate domain and the electrode domain to solve the equations, thereby restoring all degrees of freedom of the substrate domain and the electrode domain to obtain the overall response of the surface acoustic wave device. Specifically, this includes extracting the internal degrees of freedom equation of the substrate domain, which is derived from the inverse process of the Schur-complementary condensation operation in the substrate domain. The document contains the internal degrees of freedom of the substrate domain. The back substitution formula is In the formula, Let be the stiffness matrix of the degrees of freedom within the substrate domain. This represents the load vector within the substrate domain. Let be the coupling matrix between the degrees of freedom inside the substrate domain and the degrees of freedom from the side interface, and let be the unknowns from the side interface. Substituting the values, we obtain the numerical solutions for all internal degrees of freedom of the substrate domain.

[0106] The equations for solving the internal degrees of freedom of the electrode domain are derived by reversing the two Schur-complementary condensation operations in the electrode domain. The back substitution formula is In the formula, Let be the stiffness matrix of the degrees of freedom within the electrode domain. This represents the load vector within the electrode domain. Let be the coupling matrix between the degrees of freedom inside the electrode domain and the degrees of freedom at the main interface, and let the unknowns at the main interface be denoted as . Substituting the values, we obtain the numerical solutions for all internal degrees of freedom of the electrode domain.

[0107] Restore all degrees of freedom of the substrate and electrode domains, and remove the substrate domain from the side interface degrees of freedom. With internal degrees of freedom By integrating these solutions, numerical solutions for the displacement and potential degrees of freedom across the entire substrate domain are obtained; the degrees of freedom at the main interface of the electrode domain are then integrated. With internal degrees of freedom By integrating these solutions, we obtain the numerical solutions for the displacement and potential degrees of freedom across the entire electrode domain. The degrees of freedom of the two domains together constitute the numerical solution for the global degrees of freedom of the surface acoustic wave device.

[0108] Based on the numerical solution of the device's global degrees of freedom, post-processing calculations are performed. According to the performance evaluation criteria of surface acoustic wave devices, core performance parameters such as admittance, S-parameters, resonant frequency, and bandwidth are calculated. These performance parameters are then integrated into the overall response of the surface acoustic wave device, fully characterizing the device's electrical and mechanical properties.

[0109] By defining the master-slave interface and variables, and constructing a weakly continuous constraint test space using Mortar projection, computational redundancy caused by mesh remapping is avoided. Based on the derivation of the formulas for the Mortar coupling matrix and the interface transfer matrix, accurate linear mapping of master-slave variables under mismatched meshes is achieved, ensuring the accuracy of physical quantity transfer at the coupling interface.

[0110] Embodiments of the present invention also provide a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform the method described above. All implementations in the above method embodiments are applicable to this embodiment and can achieve the same technical effects.

[0111] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A rapid reanalysis method for substrate-reusable electrodes based on domain decomposition, characterized in that, The method includes: Step 1: Divide the solution domain of the surface acoustic wave device into the substrate domain and the electrode domain; Step 2: Based on the geometric and material parameters of the substrate domain, perform dimensionless preprocessing on the substrate domain, and obtain the substrate domain interface operator through cascade calculation. Store the substrate domain interface operators of different lengths into the cascade operator library. Step 3: Based on the new electrode design parameters, determine whether the substrate domain interface operator needs to be reconstructed. If it does not need to be reconstructed, reuse the existing substrate domain interface operator from the cascaded operator library. If it needs to be reconstructed, use the operator materials in the cascaded operator library to quickly cascade and obtain a new substrate domain interface operator. Step 4: Based on the new electrode design parameters, establish an electrode domain model using air-filled modeling, and perform secondary partitioning on the air-filled model. Then, obtain a new electrode domain interface operator through parallel condensation operation and cascade splicing operation. Step 5: Determine whether the interface mesh of the substrate domain interface operator and the new electrode domain interface operator matches. If they match perfectly, perform assembly and solution. If they do not match perfectly, construct the interface transfer matrix through Mortar projection. Use the interface transfer matrix to complete the interface coupling assembly and solution. After obtaining the solution of the interface degree of freedom, further restore the solution of the internal degree of freedom to obtain the overall response of the device.

2. The zone-decomposition-based substrate multiplexed electrode fast reanalysis method according to claim 1, wherein, The electrode domain is the local area that needs to be updated and analyzed during the design iteration process, including metal electrodes. The substrate domain is the remaining area other than the electrode domain, including piezoelectric layers and other material layers.

3. The zone-decomposition-based substrate multiplexed electrode fast reanalysis method according to claim 2, wherein, Based on the geometric and material parameters of the substrate domain, a dimensionless preprocessing is performed on the substrate domain, and a substrate domain interface operator is obtained through cascaded calculation. Substrate domain interface operators of different lengths are stored in a cascaded operator library, including: Based on the geometric and material parameters of the substrate domain, a substrate basic unit data structure is constructed, and a dimensionless preprocessing is performed on the substrate basic unit data structure according to the multiphysics coupling characteristics in the material parameters to obtain standardized basic unit data. Standardized basic unit data is discretized and condensed using finite element or other numerical methods to obtain basic unit interface operators that characterize the boundary mechanical and electrical properties of basic units, and these basic unit interface operators are defined as operator materials. The operator materials are recursively cascaded according to the actual length requirements of the surface acoustic wave device to obtain complete substrate domain interface operators with different total length configurations. The complete substrate domain interface operators and their corresponding length identification information are classified and stored in the cascaded operator library.

4. The rapid reanalysis method for substrate-reusable electrodes based on domain decomposition according to claim 3, characterized in that, The geometric parameters include the thickness of each material layer, the overall size of the device, and the division size of the basic unit; the material parameters include elastic parameters, dielectric parameters, piezoelectric parameters, and damping parameters.

5. The zone-decomposition-based substrate multiplexed electrode fast reanalysis method according to claim 4, wherein, Based on the new electrode design parameters, determine whether the substrate domain interface operator needs reconstruction. If reconstruction is not required, reuse existing substrate domain interface operators from the cascaded operator library. If reconstruction is required, quickly cascade new substrate domain interface operators using operator materials from the cascaded operator library, including: The new electrode design parameters are analyzed and the required total length information of the substrate domain is extracted. The total length information of the substrate domain is matched and compared one by one with the length identifier information stored in the cascaded operator library to obtain the comparison results. Based on the comparison results, a reconstruction judgment instruction is obtained. If the judgment instruction indicates that there is a complete match in the length identification information, the complete substrate domain interface operator corresponding to the complete match in the cascaded operator library is located and read. The read complete substrate domain interface operator is used as the reused substrate domain interface operator. If the length identifier information indicated by the determination instruction does not have a complete match, the required basic unit combination sequence is decomposed according to the total length information of the substrate domain required at present, and multiple basic unit interface operators corresponding to the basic unit combination sequence are retrieved from the cascade operator library as cascade operator materials. The materials to be cascaded are recursively cascaded according to the order of the basic unit combination sequence. The intermediate interface operator of the previous stage is used as the input data of the next stage to continuously perform matrix synthesis until the synthesis processing of all materials to be cascaded is completed. The final synthesis result is used as a new complete substrate domain interface operator.

6. The zone-decomposition-based substrate multiplexed electrode fast reanalysis method according to claim 5, wherein, Based on the new electrode design parameters, an electrode domain model using air-filled modeling is established. This air-filled model is then subjected to secondary partitioning. New electrode domain interface operators are obtained through parallel condensation operations and cascaded splicing operations, including: An air-filled electrode domain model was constructed based on the new electrode design parameters; The air-filled electrode domain model is partitioned in two ways, dividing it into multiple interconnected electrode subdomains along the propagation direction. Each electrode subdomain retains the interface coupling with the substrate domain and the splicing boundary between adjacent subdomains, resulting in a set of discrete electrode subdomains. The first condensation operation is performed independently on each electrode subdomain. The internal degrees of freedom of each electrode subdomain are eliminated by Schur complement, resulting in a boundary interface operator that retains only the splicing boundary degrees of freedom and the interface degrees of freedom of each electrode subdomain. The boundary interface operators of each electrode subdomain are merged according to the splicing boundary between adjacent subdomains, and the common degrees of freedom on the splicing boundary are merged into internal degrees of freedom to obtain the intermediate interface operator of the spliced ​​electrode domain. A second condensation operation is performed on the intermediate interface operator of the spliced ​​electrode domain. The internal degrees of freedom on the splicing boundary are eliminated by Schur complement, resulting in an electrode domain interface operator that retains the interface degrees of freedom coupled with the substrate domain.

7. The zone-decomposition-based substrate multiplexed electrode fast reanalysis method according to claim 6, wherein, The intermediate interface operator of the electrode domain includes all interface degrees of freedom and the newly introduced internal degrees of freedom of the splicing boundary.

8. The zone-decomposition-based substrate multiplexed electrode fast reanalysis method according to claim 7, wherein, The interface mesh of the substrate domain interface operator and the new electrode domain interface operator is determined to match. If they match perfectly, assembly and solution are performed. If they do not match perfectly, an interface transfer matrix is ​​constructed using Mortar projection. The interface transfer matrix is ​​then used to complete the interface coupling assembly and solution. After obtaining the solution for the interface degrees of freedom, the solution for the internal degrees of freedom is further restored to obtain the overall response of the device, including: The interface of the electrode domain is defined as the master interface, and the discrete degrees of freedom on the master interface are used as master variables; at the same time, the interface of the substrate domain is defined as the slave interface, and the discrete degrees of freedom on the slave interface are used as slave variables. Based on the geometry and meshing of the main and secondary interfaces, a Mortar test space for applying weak continuity constraints is constructed between the main and secondary interfaces. Using the shape function matrix of the main side interface and the shape function matrix of the secondary side interface, integral projection operations are performed on the main side variables and the secondary side variables in the Mortar test space to form the Mortar coupling matrix used to describe the constraint relationship between the main side variables and the secondary side variables. By performing matrix transformation and inversion on the Mortar coupling matrix, the interface transition matrix, in which the main side variables represent the slave side variables, is derived. The interface transfer matrix is ​​embedded in the interface coupling framework composed of the substrate domain interface operator and the electrode domain interface operator. By eliminating the dependent variables through matrix operations, the interface assembly equation including the principal variables is obtained. Numerical solution of the interface assembly equation is performed to obtain the unknowns on the main interface, and the unknowns on the slave interface are obtained by back-substituting the interface transition matrix. Based on the unknowns at the main and secondary interfaces, the equations are solved by substituting them back into the internal degrees of freedom of the substrate and electrode domains, respectively, to restore all degrees of freedom of the substrate and electrode domains and obtain the overall response of the surface acoustic wave device.

9. The zone-decomposition-based substrate multiplexed electrode fast reanalysis method according to claim 8, wherein, Using the shape function matrices of the principal and slave interfaces, integral projection operations are performed on the principal and slave variables within the Mortar test space to form a Mortar coupling matrix describing the constraint relationship between the principal and slave variables, including: Based on the shape function matrix of the main and side interfaces and the Mortar test space, a weighted integral is performed on the shape function matrix of the main and side interfaces to obtain the first coupling matrix; Based on the shape function matrix of the side interface and the Mortar test space, a weighted integral is performed on the shape function matrix of the side interface to obtain the second coupling matrix; Based on the fact that the product of the first coupling matrix and the principal variable is equal to the product of the second coupling matrix and the slave variable, a weak continuity constraint equation is constructed between the principal and slave variables. Invert the second coupling matrix to obtain its inverse matrix; Multiply the inverse of the second coupling matrix by the first coupling matrix to obtain the interface transition matrix.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program that, when executed by a processor, implements the method as described in any one of claims 1 to 9.

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