Efficient multi-physics field modeling method and system for substrate integrated waveguide filter

Abstract

The invention discloses an efficient multi-physical field modeling method and system for a substrate integrated waveguide filter, and belongs to the field of multi-physical field joint modeling and simulation. Aiming at the problem that the efficiency is insufficient when a traditional modeling method is used for processing a specific structure of the integrated waveguide, the invention innovatively provides a solution strategy customized for multi-physics field coupling of the integrated waveguide. Based on a periodic through hole array of an integrated waveguide, a resonant cavity and a coupling structure characteristic, adaptive subdomain division guided by physical topology is carried out. A finite element separation interconnection technology is introduced, and a global computing domain is divided into a plurality of sub-domains. A Lagrange multiplier specially used for processing electromagnetic, heat and force field data transmission is introduced into a sub-domain interface, and the coupling precision is ensured. According to the method, on the premise of keeping high fidelity, the solving efficiency of a large-scale multi-physical field problem is remarkably improved, and a core technical support is provided for rapid evaluation and optimization design of the performance and reliability of the integrated waveguide filter.

Description

Technical Field

[0001] This invention belongs to the field of multiphysics simulation technology for microwave devices, and in particular, it provides an efficient multiphysics modeling method for substrate integrated waveguide filters. Background Technology

[0002] Substrate integrated waveguide (SIW) filters, as core passive devices in modern microwave and millimeter-wave communication systems, are widely used in base stations, satellite communications, and radar systems due to their significant advantages such as high quality factor, low insertion loss, high power capacity, and ease of planar integration. As systems evolve towards higher frequencies, higher power densities, and miniaturization, SIW filters face severe multi-physics coupling challenges under high-power operation: Joule heating generated by conductor and dielectric losses causes temperature rise, leading to changes in the material's dielectric constant and conductivity; uneven temperature distribution further induces thermal stress and structural deformation, causing micrometer-level changes in the filter cavity geometry. This coupling chain of "electromagnetic loss—temperature rise—thermal stress deformation—electromagnetic performance degradation" significantly causes filter center frequency drift, bandwidth changes, and deterioration of out-of-band rejection, directly threatening the system's stability and reliability.

[0003] Traditional design methods typically rely on sequential single-physics simulations or rough estimations based on empirical formulas. While the former can guarantee a certain level of accuracy, it requires manual data transfer between different software platforms, resulting in a cumbersome process. Furthermore, the computational cost of full-wave 3D electromagnetic simulation combined with thermal and mechanical analysis is extremely high, making it difficult to support large-scale parametric optimization design. The latter, while fast, cannot accurately characterize complex nonlinear coupling effects, leading to excessive design margins or substandard actual performance. In recent years, while multiphysics coupling simulation tools based on commercial software can achieve automated analysis, their use of general-purpose solvers and mesh generation strategies often results in low computational efficiency when dealing with SIW filters with periodic metallized vias, complex cavity structures, and strong local coupling characteristics. This is due to the large number of meshes and coarse handling of interface conditions, limiting their practicality, especially in electrically large designs or designs requiring rapid iteration.

[0004] To improve computational efficiency, the split-interconnect method has been introduced into the multiphysics analysis framework. This method divides the global domain into multiple subdomains for parallel solution, effectively reducing the scale of a single solution. However, existing methods are mostly general split-interconnect strategies, and their subdomain partitioning is often based on simple geometric rules, failing to fully utilize the unique physical structure of SIW filters (such as the equivalent sidewalls formed by via arrays, the energy concentration region of the resonant cavity, and the local thermally sensitive region) and field coupling paths (the sequentiality and locality of electromagnetic→thermal→mechanical). This leads to problems such as unreasonable subdomain interface settings, large waiting overhead for synchronization of solutions to various physics fields, and insufficient accuracy of interface data transfer, so that the overall solution efficiency still fails to reach the "minute-level" or "second-level" response level required for rapid engineering design and optimization.

[0005] Therefore, the industry urgently needs a specialized modeling method that can deeply integrate the physical characteristics of SIW filters and significantly improve the efficiency of multiphysics coupling analysis, so as to achieve rapid and accurate evaluation and optimization of filter performance and reliability under limited computing resources. Summary of the Invention

[0006] The purpose of this invention is to overcome the bottlenecks of low efficiency, lack of optimization for device physical characteristics in existing multiphysics modeling methods for substrate integrated waveguide filters, and coarse handling of thermo-mechanical field coupling. It proposes a customized and efficient multiphysics modeling method for SIW filters, the core of which lies in the electromagnetic-thermal-mechanical three-region decomposition and the asynchronous relay solution driven by coupling.

[0007] The technical solution for achieving the objective of this invention is as follows: On one hand, an efficient multiphysics modeling method for substrate-integrated waveguide filters is provided, the method comprising the following steps:

[0008] Step 1, Physical Topology-Guided Multi-Level Domain Decomposition: Based on the physical structure and field distribution characteristics of the substrate-integrated waveguide filter, the global computational domain is first decomposed into electromagnetic, thermal, and mechanically dominant regions according to the dominant physical processes. Further, within each dominant region, based on the field gradient, energy concentration, and coupling strength, each region is further divided into multiple non-overlapping subdomains, forming the electromagnetic dominant region Ω. E Thermally critical region Ω T The key area of ​​force Ω M ;

[0009] Step 2, asynchronous relay solution by region: Construct local field solvers for each subdomain and execute the asynchronous solution process;

[0010] Step 3, Multi-field coupling interface processing based on Lagrange multipliers: Lagrange multipliers are introduced into the interfaces of the three subdomains of electromagnetic-thermal, thermal-mechanical, and mechanical-electromagnetic, respectively, and constraint equations are constructed to realize the conservation of power loss to heat flux, temperature field to thermal strain, displacement field to electromagnetic mesh deformation, and high-fidelity data transfer.

[0011] Step 4, Iterative Convergence and Result Output: Repeat steps 2 and 3 until each physical field solution satisfies the preset convergence criterion, and output the multi-physics coupling results including electric field distribution, temperature field, stress field and displacement field.

[0012] Furthermore, in step 1, the electromagnetic dominance region Ω E The propagation channel and resonant cavity region are covered between the equivalent waveguide walls formed by the array of metallized vias; the thermally critical region Ω T The high-heat-generating region covers areas with significant dielectric and conductor losses; the force-critical region ΩM It covers areas with significant mechanical support points, constraint boundaries, and thermal stress gradients.

[0013] Furthermore, step 2 specifically includes:

[0014] Solve the vector wave equation in the electromagnetic dominant subdomain, extract the loss power density and transfer it to the corresponding thermally critical subdomain;

[0015] Solve the heat conduction equation in the thermal key domain, extract the temperature distribution and transfer it to the corresponding force key domain;

[0016] The thermoelastic equations are solved in a coupled manner within the force-critical subdomain, the displacement field is extracted and fed back to the affected electromagnetic dominant subdomain, triggering its mesh update and electromagnetic re-solution.

[0017] Furthermore, in step 2, the vector wave equation is solved using the vector finite element method in the electromagnetic key domain, the heat conduction equation is solved using the scalar finite element method in the thermal key domain, and the equilibrium and geometric equations are solved using the structural finite element method in the force key domain.

[0018] Furthermore, the construction of the Lagrange multipliers in step 3 is customized for different interface types: at the electromagnetic-thermal interface, the Lagrange multipliers are used to force the flux conservation of the loss power density at the interface; at the thermo-mechanical interface, the Lagrange multipliers are used to realize the coupling mapping of the temperature field to the thermal strain field; at the force-electromagnetic interface, the Lagrange multipliers are used to accurately map the structural displacement field to the node coordinate update of the electromagnetic grid.

[0019] Furthermore, in step 4, the convergence criterion is constructed based on the residual norms of each physical field and the interface propagation error, thereby achieving stable convergence of the full-field coupled solution.

[0020] On the other hand, a high-efficiency multiphysics modeling system for substrate-integrated waveguide filters is provided, the system comprising sequentially executed:

[0021] The first module is used to realize the multi-level region decomposition guided by physical topology: based on the physical structure and field distribution characteristics of the substrate integrated waveguide filter, the global computational domain is first decomposed into electromagnetic dominant region, thermal dominant region and force dominant region according to the dominant physical process; further, within each dominant region, according to the field gradient, energy concentration and coupling strength, each region is divided into multiple non-overlapping subdomains, forming electromagnetic dominant region ΩE, thermal critical region ΩT and force critical region ΩM.

[0022] The second module is used to implement asynchronous relay solution in different regions: it builds local field solvers for each subdomain and executes the asynchronous solution process;

[0023] The third module is used to realize multi-field coupling interface processing based on Lagrange multipliers: Lagrange multipliers are introduced into the interfaces of the three subdomains of electromagnetic-thermal, thermal-mechanical, and mechanical-electromagnetic, respectively, and constraint equations are constructed to realize the conservation of power loss to heat flux, temperature field to thermal strain, displacement field to electromagnetic grid deformation, and high-fidelity data transmission.

[0024] The fourth module is used to achieve iterative convergence and result output: the second and third modules are executed cyclically until each physical field solution meets the preset convergence criterion, and the multi-physics coupling results, including electric field distribution, temperature field, stress field and displacement field, are output.

[0025] On the other hand, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement an efficient multiphysics modeling method for the substrate integrated waveguide filter.

[0026] On the other hand, a computer-readable storage medium is provided on which a computer program is stored, which, when executed by a processor, implements an efficient multiphysics modeling method for the substrate-integrated waveguide filter.

[0027] Compared with the prior art, the present invention has the following significant advantages:

[0028] (1) By decomposing the electromagnetic-thermal-mechanical regions, the optimal reduction of the solution scale and complexity of each physical field is achieved, which greatly reduces the amount of computation per solution.

[0029] (2) The asynchronous relay solution mechanism significantly reduces the idle waiting time of the process and improves the overall computational efficiency.

[0030] (3) The customized interface multiplier ensures the accuracy and physical conservation of cross-regional data transfer and guarantees the fidelity of coupled analysis.

[0031] (4) This invention provides an efficient and accurate dedicated tool for the collaborative design and rapid optimization of the performance, thermal management and mechanical reliability of SIW filters.

[0032] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0033] Figure 1 This is a flowchart of an efficient multiphysics modeling method for a substrate-integrated waveguide filter in one embodiment.

[0034] Figure 2 This is a schematic diagram of substrate-integrated waveguide modeling in one embodiment.

[0035] Figure 3This is a schematic diagram comparing the distribution of waveguide field on the xoz surface of a substrate integrated in one embodiment, wherein... Figure 3 (a) in the figure represents the simulation results of the method of the present invention. Figure 3 (b) in the figure represents the COMSOL simulation results.

[0036] Figure 4 This is a schematic diagram comparing the distribution of the thermal field on the xoz surface of a substrate-integrated waveguide in one embodiment, wherein... Figure 4 (a) in the figure represents the simulation results of the method of the present invention. Figure 4 (b) in the figure represents the COMSOL simulation results.

[0037] Figure 5 This is a schematic diagram comparing the Von der Waals equivalent stress distribution of a substrate-integrated waveguide in one embodiment, wherein... Figure 5 (a) shows the simulation results of the method of the present invention. Figure 5 (b) COMSOL simulation results.

[0038] Figure 6 This is a schematic diagram comparing the S11 parameters before and after thermal deformation in one embodiment. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0040] It should be noted that if the embodiments of the present invention involve descriptions such as "first" and "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" and "second" may explicitly or implicitly include at least one of those features. Furthermore, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0041] In one embodiment, combined Figure 1 This paper provides an efficient multiphysics modeling method for substrate-integrated waveguide filters, the method comprising the following steps:

[0042] Step 1, Physical Topology-Guided Multi-Level Domain Decomposition: Based on the physical structure and field distribution characteristics of the substrate-integrated waveguide filter, the global computational domain is first decomposed into electromagnetic, thermal, and mechanically dominant regions according to the dominant physical processes. Further, within each dominant region, based on the field gradient, energy concentration, and coupling strength, each region is further divided into multiple non-overlapping subdomains, forming the electromagnetic dominant region Ω. E Thermally critical region Ω T The key area of ​​force Ω M ;

[0043] Here, the key physical characteristics of the SIW filter are automatically identified first. Unlike existing technologies, this invention first decomposes the global computational domain into three primary regions based on the dominant physical processes: an electromagnetic-dominated region, a thermal-dominated region, and a mechanical-dominated region. Based on this, according to the field distribution characteristics within each region (such as energy concentration, loss density, and stress gradient), each primary region is further divided into multiple non-overlapping subdomains.

[0044] Step 2, asynchronous relay solution by region: Construct local field solvers for each subdomain and execute the asynchronous solution process;

[0045] Step 3, Multi-field coupling interface processing based on Lagrange multipliers: Lagrange multipliers are introduced into the interfaces of the three subdomains of electromagnetic-thermal, thermal-mechanical, and mechanical-electromagnetic, respectively, and constraint equations are constructed to realize the conservation of power loss to heat flux, temperature field to thermal strain, displacement field to electromagnetic mesh deformation, and high-fidelity data transfer.

[0046] Step 4, Iterative Convergence and Result Output: Repeat steps 2 and 3, monitor the solution residuals of each subdomain and the interface propagation error until each physical field solution meets the preset convergence criterion, and output the multi-physics coupling results including electric field distribution, temperature field, stress field and displacement field.

[0047] Furthermore, in one embodiment, in step 1, the electromagnetically dominant region Ω E The propagation channel and resonant cavity region are covered between the equivalent waveguide walls formed by the array of metallized vias; the thermally critical region Ω T The high-heat-generating region covers areas with significant dielectric and conductor losses; the force-critical region Ω M It covers areas with significant mechanical support points, constraint boundaries, and thermal stress gradients.

[0048] Specifically:

[0049] Electromagnetic dominant subdomain set Ω E The electromagnetic energy concentration area is covered and finely discretized using high-order vector basis functions.

[0050] thermal key subdomain set ΩT It receives loss data from the electromagnetically dominant region, covering high-loss dielectric and conductor regions, and performs high-resolution thermal analysis independently.

[0051] The set of force key subfields Ω M It receives temperature data from the thermally critical subdomain, covering mechanical constraint points, supporting structures, and areas of thermal stress concentration, and performs independent structural mechanics analysis.

[0052] Background subdomain set Ω B For substrate regions where the field changes gradually, a simplified treatment using low-order basis functions is employed.

[0053] Furthermore, in one embodiment, step 2 specifically includes:

[0054] Solve the vector wave equation in the electromagnetic dominant subdomain, extract the loss power density and transfer it to the corresponding thermally critical subdomain;

[0055] Solve the heat conduction equation in the thermal key domain, extract the temperature distribution and transfer it to the corresponding force key domain;

[0056] The thermoelastic equations are solved in a coupled manner within the force-critical subdomain, the displacement field is extracted and fed back to the affected electromagnetic dominant subdomain, triggering its mesh update and electromagnetic re-solution.

[0057] Preferably, in some embodiments, in step 2, the vector wave equation is solved using the vector finite element method in the electromagnetic key subdomain, the heat conduction equation is solved using the scalar finite element method in the thermal key subdomain, and the equilibrium equation and geometric equation are solved using the structural finite element method in the force key subdomain.

[0058] This step proposes constructing local field solvers for each subdomain and executing a directional asynchronous solution process from electromagnetic to thermal to force and back to electromagnetic. In the electromagnetic-dominant subdomain, the vector wave equation is solved, the loss power density is extracted, and directionally transferred to the associated thermally critical subdomain. Once the thermally critical subdomain obtains all the necessary boundary heat sources, it immediately triggers the solution of its internal heat conduction equations, extracts the temperature distribution, and directionally transfers it to the associated force-critical subdomain. Based on the received temperature field, the force-critical subdomain couples and solves the thermoelastic equations, extracts the displacement field, and feeds it back only to the electromagnetic-dominant subdomain affected by its deformation, triggering the update and re-solution of that part of the electromagnetic mesh. This process breaks down the barriers of traditional synchronous solutions, enabling on-demand scheduling of computational resources.

[0059] Furthermore, in one embodiment, in step 3, to achieve accurate and conserved transfer of cross-regional data in the asynchronous process, the construction of the Lagrange multiplier is customized for different interface types: at the electromagnetic-thermal interface, the Lagrange multiplier is used to force the flux conservation of loss power density at the interface; at the thermo-mechanical interface, the Lagrange multiplier is used to realize the coupling mapping of the temperature field to the thermal strain field; at the force-electromagnetic interface, the Lagrange multiplier is used to accurately map the structural displacement field to the node coordinate update of the electromagnetic grid.

[0060] Furthermore, in one embodiment, the convergence criterion in step 4 is constructed based on the residual norms of each physical field and the interface propagation error, thereby achieving stable convergence of the full-field coupled solution.

[0061] In one embodiment, the efficient multiphysics modeling method for substrate integrated waveguide filters described in this invention will be further described in detail below.

[0062] Step 1: Multi-level domain decomposition and subdomain partitioning guided by physical topology. Based on the physical structure of the substrate-integrated waveguide filter, the global computational domain is decomposed into multiple levels. According to the dominant physical processes, the global domain is divided into three major functional regions: the electromagnetically dominant region Ω. E Thermally critical region Ω T Ω, key force area M The continuity of electric and magnetic fields is ensured by employing the Robin transport condition at the interface between adjacent subdomains.

[0063] Robin's transfer conditions:

[0064] (1)

[0065] In the formula, It is the unit outward normal vector of the boundary of the i-th subdomain. The electric field strength in the i-th subdomain curl, It is a coefficient related to boundary characteristics. It is a known field source or equivalent current term on the boundary. Representing the boundary of the i-th subdomain, this formula, through a combination of the electric field curl and the electric field itself, describes the constraint relationship that the electric field at the boundary of the i-th subdomain must satisfy.

[0066] Step 2 involves constructing the governing equations and finite element discretization schemes for each physical field, obtaining the finite element matrix equations for electromagnetic and thermal fields. The partial differential form of Maxwell's equations is then processed according to constitutive relations. as well as , , and Let these represent the magnetic permeability, permittivity, and conductivity of the medium, respectively. Eliminating these values ​​from the equation... The vector wave equation for the magnetic field:

[0067] (2)

[0068] in, and Represents relative permeability and relative permittivity, respectively. and Let represent the wavenumber and characteristic impedance of free space, respectively. Calculate the Joule heat loss power density as a heat source.

[0069] The steady-state thermal effect is analyzed using the finite element method (FEM), transforming the heat conduction equation into a partial differential equation form suitable for FEM. The heat conduction equation is shown below:

[0070] (3)

[0071] In the formula, Thermal conductivity, Let be the power density of the heat source. The transport boundary conditions and Lagrange multipliers are introduced at the interface of the subdomains to achieve coupling between them.

[0072] The third type of boundary condition is as follows:

[0073] (4)

[0074] In the formula, The initial temperature of the environment. The equation represents the convective heat transfer coefficient, which is given by the equation between the boundary and the surrounding environment and the ambient temperature, corresponding to the convective heat transfer in the heat transfer process.

[0075] The electric field affects the thermal field through the self-heating effect. Joule heating is analyzed, and the Joule heat power density is:

[0076] (5)

[0077] In the formula, p represents the Joule heat power per unit volume, E is the electric field intensity vector, and J is the current density vector. The dot product of the two corresponds to the power of electrical energy converted into heat energy. σ(T) is the conductivity as a function of temperature, describing the linear relationship between the current density J and the electric field E.

[0078] Thermal stress refers to the stress generated by constrained thermal deformation due to temperature changes, without the application of external force. Thermal strain caused by temperature changes includes:

[0079] (6)

[0080] in, Representing thermal strain, that is, the degree of deformation of a material due to temperature change alone, α(T) is the coefficient of thermal expansion as a function of temperature, ΔT is the amount of temperature change, and T is the current temperature of the material. ref That is the reference temperature.

[0081] Step 3 involves solving the problem based on the field coupling of asynchronous relay and Lagrange multipliers. In this step, the transport boundary conditions can be mathematically expressed using Dirichlet and Norman boundary conditions. In thermal analysis, the introduced Lagrange multipliers physically correspond to the equivalent heat flux at the subdomain interface:

[0082] (7)

[0083] The first equation In the second equation, n represents the temperature continuity condition at the interface. i and n j It is the unit outward normal vector of subdomains i and j on the interface. , These are the temperature gradients within the two subdomains, and the equation represents the normal continuity condition of heat flow at the interface.

[0084] In a stress field, the Lagrange multipliers correspond to the interfacial forces at the interface:

[0085] (8)

[0086] In the formula, the first equation The second equation represents the displacement continuity condition. , These are the stress tensors of the two subdomains. Equation (8) is the coupled boundary condition at the interface between the two adjacent subdomains, used to connect the deformation and stress relationship between the subdomains.

[0087] By introducing the aforementioned Lagrange multipliers, the system can establish a system of linear equations for each subdomain using finite element matrices. The equation system for the i-th subdomain is expressed as follows:

[0088] (9)

[0089] In the formula, It is a stiffness matrix. It is an unknown quantity to be determined. It is an internal load term. The second equation represents the load term corresponding to the boundary action, and expresses the boundary contribution as a matrix through the boundary integral of the weight function w. and The product form is used to construct a system of equations. Representing the Lagrange multiplier, this variable is only related to the degrees of freedom of nodes at the interface of adjacent subdomains. During the domain decomposition process, nodes located at the interface need to have two sets of numbers: one is a unified local number across subdomains, applicable to all boundary nodes; the other is an internal number determined based on the overall node order of the subdomain to which the node belongs.

[0090] In the overall system matrix, the last row and last column respectively represent the Dirichlet and Norman class boundary conditions applied at the subdomain interfaces. Subsequently, by eliminating the unknowns within each subdomain using Gaussian elimination, we obtain the Lagrange multiplier matrix equations that relate only to the unknowns at the interfaces:

[0091] (10)

[0092] in, and All of these are related to the Boolean matrix and the coefficient matrix of the subfield. In addition, It also relates to the right-hand vector of the subfield, and the terms of equation (10) can be specifically expanded as follows:

[0093] (11)

[0094] (12)

[0095] Thus, the Lagrange multipliers are obtained by solving equation (10). Then, it can be substituted back into the equation system (9) of each subdomain to obtain a simplified finite element equation system containing only the unknowns within the subdomains. In the equation, [F] is the global flexibility matrix, {p} is the global load vector; [K] is the global load vector. i [B] is the stiffness matrix of the i-th subdomain. i [b] is the correlation matrix between the subdomain and the whole. i [] is the internal load vector of the i-th subdomain. The formula assembles the local calculation results of multiple subdomains into a solution matrix and loads for the overall problem by summing the contributions of each subdomain, and is used for the unified solution of multi-domain problems. Solving this system of equations yields the physical field distribution of each subdomain, and then the field distribution result of the entire computational domain is obtained by synthesis.

[0096] Step 4: Iterative Convergence and Result Output. For iterative convergence control, after each round of asynchronous relay solving, the residual norms of the three physical fields (electromagnetic, thermal, and mechanical) are calculated. Iterative convergence is then determined. Otherwise, using the latest geometry and field quantities as initial conditions, the process returns to step 2 to continue iterating.

[0097] In one embodiment, a high-efficiency multiphysics modeling system for substrate-integrated waveguide filters is provided, the system comprising sequentially executing:

[0098] The first module is used to implement a multi-level domain decomposition guided by physical topology: Based on the physical structure and field distribution characteristics of the substrate integrated waveguide filter, the global computational domain is first decomposed into an electromagnetic-dominated region, a thermal-dominated region, and a mechanical-dominated region according to the dominant physical processes; further, within each dominant region, based on the field gradient, energy concentration, and coupling strength, each region is divided into multiple non-overlapping subdomains, forming the electromagnetic-dominated region Ω. E Thermally critical region Ω T The key area of ​​force Ω M ;

[0099] The second module is used to implement asynchronous relay solution in different regions: it builds local field solvers for each subdomain and executes the asynchronous solution process;

[0100] The third module is used to realize multi-field coupling interface processing based on Lagrange multipliers: Lagrange multipliers are introduced into the interfaces of the three subdomains of electromagnetic-thermal, thermal-mechanical, and mechanical-electromagnetic, respectively, and constraint equations are constructed to realize the conservation of power loss to heat flux, temperature field to thermal strain, displacement field to electromagnetic grid deformation, and high-fidelity data transmission.

[0101] The fourth module is used to achieve iterative convergence and result output: the second and third modules are executed cyclically until each physical field solution meets the preset convergence criterion, and the multi-physics coupling results, including electric field distribution, temperature field, stress field and displacement field, are output.

[0102] Specific limitations regarding the efficient multiphysics modeling system for substrate-integrated waveguide filters can be found in the limitations of the efficient multiphysics modeling method for substrate-integrated waveguide filters described above, and will not be repeated here. Each module in the aforementioned efficient multiphysics modeling system for substrate-integrated waveguide filters can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0103] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements:

[0104] Step 1, Physical Topology-Guided Multi-Level Region Decomposition: Based on the physical structure and field distribution characteristics of the substrate integrated waveguide filter, the global computational domain is first decomposed into electromagnetic, thermal, and mechanically dominant regions according to the dominant physical processes. Furthermore, within each dominant region, based on the field gradient, energy concentration, and coupling strength, each region is divided into multiple non-overlapping subdomains, forming the electromagnetic dominant region ΩE, the thermally critical region ΩT, and the mechanically critical region ΩM.

[0105] Step 2, asynchronous relay solution by region: Construct local field solvers for each subdomain and execute the asynchronous solution process;

[0106] Step 3, Multi-field coupling interface processing based on Lagrange multipliers: Lagrange multipliers are introduced into the interfaces of the three subdomains of electromagnetic-thermal, thermal-mechanical, and mechanical-electromagnetic, respectively, and constraint equations are constructed to realize the conservation of power loss to heat flux, temperature field to thermal strain, displacement field to electromagnetic mesh deformation, and high-fidelity data transfer.

[0107] Step 4, Iterative Convergence and Result Output: Repeat steps 2 and 3 until each physical field solution satisfies the preset convergence criterion, and output the multi-physics coupling results including electric field distribution, temperature field, stress field and displacement field.

[0108] For specific limitations on each step, please refer to the limitations on the efficient multiphysics modeling method for substrate integrated waveguide filters mentioned above, which will not be repeated here.

[0109] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program being implemented when executed by a processor:

[0110] Step 1, Physical Topology-Guided Multi-Level Region Decomposition: Based on the physical structure and field distribution characteristics of the substrate integrated waveguide filter, the global computational domain is first decomposed into electromagnetic, thermal, and mechanically dominant regions according to the dominant physical processes. Furthermore, within each dominant region, based on the field gradient, energy concentration, and coupling strength, each region is divided into multiple non-overlapping subdomains, forming the electromagnetic dominant region ΩE, the thermally critical region ΩT, and the mechanically critical region ΩM.

[0111] Step 2, asynchronous relay solution by region: Construct local field solvers for each subdomain and execute the asynchronous solution process;

[0112] Step 3, Multi-field coupling interface processing based on Lagrange multipliers: Lagrange multipliers are introduced into the interfaces of the three subdomains of electromagnetic-thermal, thermal-mechanical, and mechanical-electromagnetic, respectively, and constraint equations are constructed to realize the conservation of power loss to heat flux, temperature field to thermal strain, displacement field to electromagnetic mesh deformation, and high-fidelity data transfer.

[0113] Step 4, Iterative Convergence and Result Output: Repeat steps 2 and 3 until each physical field solution satisfies the preset convergence criterion, and output the multi-physics coupling results including electric field distribution, temperature field, stress field and displacement field.

[0114] For specific limitations on each step, please refer to the limitations on the efficient multiphysics modeling method for substrate integrated waveguide filters mentioned above, which will not be repeated here.

[0115] As a specific example, the invention will be further verified and illustrated in one embodiment.

[0116] like Figure 2 As shown, this embodiment simulates a substrate integrated waveguide with the following dimensions: the distance between the two rows of metal vias. Spacing between adjacent metal vias Diameter of metal through hole Diode thickness The operating frequency of the incident plane wave is The wavelength is approximately ,from The incident wave is expressed as follows: , here The amplitude of the incident wave is given. The output port is truncated using a perfectly matched layer, the thickness of which is 1 / 4 wavelength. Regarding material properties, the relative permittivity of the dielectric substrate is given. Thermal conductivity is Specific heat capacity is The material density is Since a third type of boundary condition (i.e., a convection boundary condition) is to be used, the convective heat transfer coefficient is set to... The ambient temperature is The coefficient of thermal expansion is Young's modulus is Poisson's ratio is .

[0117] Figure 3 This structure was demonstrated in The electric field distribution on the xoz surface. It can be seen that... Figure 3 The two sub-figures in the diagram are highly consistent in terms of the spatial distribution and amplitude range of the electric field. The electric field energy is mainly concentrated in the waveguide region defined by the two rows of vias, exhibiting a typical standing wave mode. This characteristic originates from the equivalent electric wall formed by the periodic arrangement of the metal vias, thus achieving a waveguide mechanism similar to that of a traditional rectangular waveguide. The perfectly matched layer at the right end of the structure effectively absorbs the outgoing wave, avoiding interference from non-physical reflections on the field distribution within the cavity.

[0118] Based on the electromagnetic-thermal coupling mechanism, the electromagnetic loss in the dielectric substrate is converted into a heat source term and substituted into the heat conduction equation, which can be used to analyze the steady-state temperature distribution in the structure. Figure 4 The steady-state temperature field of the structure within the xoz cross section is presented. The temperature distribution intuitively reflects the local temperature rise caused by electromagnetic losses, and the heat source distribution follows the spatial distribution law of electromagnetic energy losses.

[0119] After obtaining the steady-state temperature field, the thermal stress response of the structure is further analyzed using a thermo-mechanical coupling model. Fixed constraints are applied to the xoy bottom surface and xoz symmetry plane of the substrate-integrated waveguide, and the von Mises equivalent stress distribution is obtained by solving, as shown below. Figure 5 As shown.

[0120] To quantitatively assess the impact of thermally induced deformation on electrical properties, the scattering parameter S11 of the structure was calculated in both the undeformed and thermally deformed states. The results are as follows: Figure 6 As shown in the figure, the comparison shows that thermal deformation significantly alters the resonant frequency and depth of the S11 curve, indicating that structural deformation has a substantial impact on the waveguide's matching characteristics, thus verifying the necessity of performing electromagnetic-thermal-mechanical multiphysics coupling modeling.

[0121] In summary, this invention innovatively proposes a solution strategy tailored for multiphysics coupling in integrated waveguides. Based on the periodic via array, resonant cavity, and coupling structure characteristics of the integrated waveguide, an adaptive subdomain partitioning guided by physical topology is performed. Finite element method (FEM) separation interconnection technology is introduced to divide the global computational domain into multiple subdomains. Lagrange multipliers specifically designed for handling electromagnetic, thermal, and force field data transfer are introduced at the subdomain interfaces to ensure coupling accuracy. This method significantly improves the solution efficiency of large-scale multiphysics problems while maintaining high fidelity, providing core technical support for the rapid evaluation and optimization design of the performance and reliability of integrated waveguide filters.

[0122] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention without departing from its spirit and scope should be included within the protection scope of the present invention.

Claims

1. A highly efficient multiphysics modeling method for substrate-integrated waveguide filters, characterized in that, The method includes the following steps: Step 1, Physical Topology-Guided Multi-Level Domain Decomposition: Based on the physical structure and field distribution characteristics of the substrate-integrated waveguide filter, the global computational domain is first decomposed into electromagnetic, thermal, and mechanically dominant regions according to the dominant physical processes. Further, within each dominant region, based on the field gradient, energy concentration, and coupling strength, each region is further divided into multiple non-overlapping subdomains, forming the electromagnetic dominant region Ω. E Thermally critical region Ω T The key area of ​​force Ω M ; Step 2, asynchronous relay solution by region: Construct local field solvers for each subdomain and execute the asynchronous solution process; Step 3, Multi-field coupling interface processing based on Lagrange multipliers: Lagrange multipliers are introduced into the interfaces of the three subdomains of electromagnetic-thermal, thermal-mechanical, and mechanical-electromagnetic, respectively, and constraint equations are constructed to realize the conservation of power loss to heat flux, temperature field to thermal strain, displacement field to electromagnetic mesh deformation, and high-fidelity data transfer. Step 4, Iterative Convergence and Result Output: Repeat steps 2 and 3 until each physical field solution satisfies the preset convergence criterion, and output the multi-physics coupling results including electric field distribution, temperature field, stress field and displacement field.

2. The efficient multiphysics modeling method for substrate integrated waveguide filters according to claim 1, characterized in that, In step 1, the electromagnetic dominance region Ω E The propagation channel and resonant cavity region are covered between the equivalent waveguide walls formed by the array of metallized vias; the thermally critical region Ω T The high-heat-generating region covers areas with significant dielectric and conductor losses; the force-critical region Ω M It covers areas with significant mechanical support points, constraint boundaries, and thermal stress gradients.

3. The efficient multiphysics modeling method for substrate integrated waveguide filters according to claim 1, characterized in that, Step 2 specifically includes: Solve the vector wave equation in the electromagnetic dominant subdomain, extract the loss power density and transfer it to the corresponding thermally critical subdomain; Solve the heat conduction equation in the thermal key domain, extract the temperature distribution and transfer it to the corresponding force key domain; The thermoelastic equations are solved in a coupled manner within the force-critical subdomain, the displacement field is extracted and fed back to the affected electromagnetic dominant subdomain, triggering its mesh update and electromagnetic re-solution.

4. The efficient multiphysics modeling method for substrate integrated waveguide filters according to claim 3, characterized in that, In step 2, the vector wave equation is solved using the vector finite element method in the electromagnetic key domain, the heat conduction equation is solved using the scalar finite element method in the thermal key domain, and the equilibrium and geometric equations are solved using the structural finite element method in the force key domain.

5. The efficient multiphysics modeling method for substrate integrated waveguide filters according to claim 1, characterized in that, In step 3, the construction of the Lagrange multiplier is customized for different interface types: at the electromagnetic-thermal interface, the Lagrange multiplier is used to force the flux conservation of the loss power density at the interface; at the thermo-mechanical interface, the Lagrange multiplier is used to realize the coupling mapping of the temperature field to the thermal strain field; at the force-electromagnetic interface, the Lagrange multiplier is used to accurately map the structural displacement field to the node coordinate update of the electromagnetic grid.

6. The efficient multiphysics modeling method for substrate integrated waveguide filters according to claim 1, characterized in that, In step 4, the convergence criterion is constructed based on the residual norms of each physical field and the interface propagation error, so as to achieve stable convergence of the full-field coupled solution.

7. A high-efficiency multiphysics modeling system for substrate-integrated waveguide filters based on the method of any one of claims 1 to 6, characterized in that, The system includes sequential execution of: The first module is used to realize the multi-level region decomposition guided by physical topology: based on the physical structure and field distribution characteristics of the substrate integrated waveguide filter, the global computational domain is first decomposed into electromagnetic dominant region, thermal dominant region and force dominant region according to the dominant physical process. Furthermore, within each dominant region, based on the field gradient, energy concentration, and coupling strength, each region is divided into multiple non-overlapping subdomains, forming the electromagnetic dominant region Ω. E Thermally critical region Ω T The key area of ​​force Ω M ; The second module is used to implement asynchronous relay solution in different regions: it builds local field solvers for each subdomain and executes the asynchronous solution process; The third module is used to realize multi-field coupling interface processing based on Lagrange multipliers: Lagrange multipliers are introduced into the interfaces of the three subdomains of electromagnetic-thermal, thermal-mechanical, and mechanical-electromagnetic, respectively, and constraint equations are constructed to realize the conservation of power loss to heat flux, temperature field to thermal strain, displacement field to electromagnetic grid deformation, and high-fidelity data transmission. The fourth module is used to achieve iterative convergence and result output: the second and third modules are executed cyclically until each physical field solution meets the preset convergence criterion, and the multi-physics coupling results, including electric field distribution, temperature field, stress field and displacement field, are output.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 6.

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