Multi-physics coupling analysis system and method based on universal PDE solving base

Abstract

The invention relates to a multi-physics coupling analysis system and method based on a universal PDE solving base. The system comprises a general PDE solving base which is used for managing cooperative work among modules, providing a standardized interface, loading an electromagnetic model plug-in, a thermal model plug-in and a structural mechanical model plug-in according to acquired configuration file information, integrating the plug-ins and a core module through the standardized interface, constructing each physical field solving module, and solving each physical field solving module; selecting operators configured in a physical field solving module from a discrete operator library, discretizing the physical model to obtain a linear equation set, and solving the linear equation set to obtain a physical field result; and the adapter is used for acquiring the physical field result of the coupling region during each iteration, performing parameter conversion and space alignment, updating the physical model parameters in each physical field solving module based on the coupling response result, and outputting each physical field result when the iteration is stopped. By adopting the system, the solving efficiency and flexibility of the multi-physics coupling analysis system can be improved.

Description

Technical Field

[0001] The present application relates to the technical field of multi-physics field coupling analysis, and in particular to a multi-physics field coupling analysis system and method based on a general PDE solution base. Background Art

[0002] With the rapid development of information technology in the field of scientific computing and engineering simulation, the numerical solution technology of partial differential equations (PDE) has become a key means to solve many complex physical problems. In this process, some traditional PDE solution software frameworks have gradually been formed, which have played an important role in the early research of physical problems.

[0003] These traditional PDE solving software frameworks have certain characteristics. They are usually designed and developed for specific types of physical problems or specific algorithms, and are relatively professional in terms of functionality. For example, some software focuses on structural mechanics analysis, and its internal algorithms and data structures are optimized around the calculation of structural fields; others focus on single physical field problems such as heat conduction or electromagnetic field calculations. When faced with relatively simple and single physical problems, these traditional frameworks can provide relatively accurate solutions with their professionalism.

[0004] However, with the continuous advancement of modern science and technology, especially in high-end engineering fields such as supercomputer development, the complexity of physical problems has shown an exponential growth. Traditional PDE solving software frameworks have exposed many serious problems. In supercomputer development, the coupling problem of electromagnetic-thermal-structural multi-physics fields is involved. For example, electromagnetic fields are generated in the circuit system of supercomputers, which induce Joule heat, and Joule heat causes thermal deformation of the structure. This complex coupling relationship requires the interaction of multiple physical fields to be considered simultaneously. However, when dealing with such multi-physics field coupling problems, traditional frameworks are difficult to quickly integrate calculation modules of different physical fields due to their difficulty in functional expansion. Every time faced with new physical field coupling requirements, a large amount of code modification and recompilation are required, resulting in extremely low calculation efficiency. On the other hand, the adaptability of traditional frameworks is limited, and it is easy to make mistakes when dealing with diversified physical problems. In the scenario of supercomputer development, which has extremely high safety requirements, incorrect calculation results may lead to serious consequences. Due to the inability to efficiently handle multi-physics field coupling problems, traditional frameworks often require a large amount of repeated calculations and unnecessary intermediate data storage during the calculation process, which increases development costs and resource consumption. Summary of the invention

[0005] Based on this, it is necessary to provide a multi-physical field coupling analysis system and method based on general PDE to solve the above technical problems.

[0006] A multi-physics field coupling analysis system for solving a base based on a general PDE, the system comprising:

[0007] A general PDE solving base and adapter; the PDE solving base includes a core module, a plug-in management module and a numerical calculation module;

[0008] The core module is used to manage the collaborative work between modules and provide a standardized interface;

[0009] The plug-in management module is used to load the electromagnetic model plug-in, the thermal model plug-in and the structural mechanics model plug-in respectively according to the acquired configuration file information, complete the integration of the plug-in and the core module through the standardized interface, and construct the corresponding electromagnetic field solution module, thermal solution module and structural solution module;

[0010] The numerical calculation module includes a discrete operator library, a numerical discretizer and a linear system solver. The numerical discretizer is used to select corresponding operators from the discrete operator library according to the configuration information in the electromagnetic field solution module, the thermal solution module and the structural solution module, and discretize the physical model to obtain the corresponding linear equation group. The linear system solver is used to solve each linear equation group to obtain the electromagnetic field result, the thermal field result and the structural mechanics field result.

[0011] When the system performs electromagnetic-thermal-structural multi-physics field coupling analysis, the adapter obtains the electromagnetic field results, thermal field results and structural mechanics field results of the coupling area in each iteration step and performs parameter conversion and spatial alignment to obtain coupling response results, and updates the physical model parameters in each physical field solution module based on the coupling response results until the iteration stop condition is met, and then outputs the current electromagnetic field results, thermal field results and structural mechanics field results.

[0012] A multi-physics field coupling analysis method for solving a base based on a general PDE, the method comprising:

[0013] Load the electromagnetic model plug-in, thermal model plug-in and structural mechanics model plug-in respectively according to the acquired configuration file information, complete the integration of the plug-in and the core module through the standardized interface, and build the corresponding electromagnetic field solution module, thermal solution module and structural solution module;

[0014] According to the configuration information in the electromagnetic field solution module, the thermal solution module and the structural solution module, the corresponding operator is selected from the discrete operator library, the physical model is discretized to obtain the corresponding linear equation group, and each linear equation group is solved to obtain the electromagnetic field results, thermal field results and structural mechanics field results;

[0015] In the electromagnetic-thermal-structural multi-physics field coupling analysis, the electromagnetic field results, thermal field results and structural mechanics field results of the coupling area are obtained in each iterative step, and parameter conversion and spatial alignment are performed to obtain the coupling response results. The physical model parameters in each physical field solution module are updated based on the coupling response results until the iteration stop condition is met, and the current electromagnetic field results, thermal field results and structural mechanics field results are output.

[0016] The above-mentioned multi-physics coupling analysis system and method based on the general PDE solution base, through a highly modular design, enables the electromagnetic, thermal and structural modules to have independent functions and interfaces, which is convenient for development, testing, optimization and expansion. The system adopts a standardized interface to ensure efficient coupling between different physical modules, supports rapid integration of new physical modules, and meets diverse solution requirements. Through the separated coupling calculation method, each physical field module is calculated independently and iteratively coupled, thereby improving the calculation efficiency and providing optimization space for each module. At the same time, the system can be flexibly adjusted according to specific coupling problems, supports dynamic expansion, and simplifies the process of functional optimization and adjustment. The system of the present invention has good scalability, adaptability and efficiency, can effectively solve complex electromagnetic-thermal-structural coupling problems, and improve solution efficiency and flexibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a structural block diagram of a multi-physics field coupling analysis system for solving a base based on a general PDE in one embodiment;

[0018] Figure 2 A schematic diagram of a base structure for solving a general PDE in an embodiment;

[0019] Figure 3 A schematic diagram of model solution of an electromagnetic field solution module in one embodiment;

[0020] Figure 4 A schematic diagram of electromagnetic-thermal-structural coupling calculation in one embodiment;

[0021] Figure 5 A schematic diagram of discrete space alignment in one embodiment;

[0022] Figure 6 A schematic diagram of real-time data transmission direction in an embodiment;

[0023] Figure 7 A schematic diagram of an iterative solution process in an embodiment;

[0024] Figure 8 It is a flowchart of a multi-physics coupling analysis method for solving a base based on a general PDE in an embodiment. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0026] In one embodiment, Figure 1 As shown, a multi-physics field coupling analysis system based on a general PDE solution base is provided, including:

[0027] General PDE solving base and adapter; PDE solving base includes core module, plug-in management module and numerical calculation module;

[0028] The core module is used to manage the collaboration between modules and provide standardized interfaces;

[0029] The plug-in management module is used to load the electromagnetic model plug-in, thermal model plug-in and structural mechanics model plug-in according to the acquired configuration file information, integrate the plug-in with the core module through the standardized interface, and build the corresponding electromagnetic field solution module, thermal solution module and structural solution module;

[0030] The numerical calculation module includes a discrete operator library, a numerical discretizer and a linear system solver. The numerical discretizer selects corresponding operators from the discrete operator library according to the configuration information in the electromagnetic field solver module, the thermal solver module and the structural solver module, and discretizes the physical model to obtain the corresponding linear equations. The linear system solver solves each linear equation to obtain electromagnetic field results, thermal field results and structural mechanics field results.

[0031] When the system performs electromagnetic-thermal-structural multi-physics field coupling analysis, the adapter obtains the electromagnetic field results, thermal field results, and structural mechanics field results of the coupling area in each iteration step and performs parameter conversion and spatial alignment to obtain the coupling response results. The physical model parameters in each physical field solution module are updated based on the coupling response results until the iteration stop condition is met, and the current electromagnetic field results, thermal field results, and structural mechanics field results are output.

[0032] In this embodiment, the PDE solving base can meet the solving requirements of different types of partial differential equations, and provide a unified interface and data structure to facilitate the integration and expansion of different physical modules. The electromagnetic, thermal and structural modules adopt a highly modular design, and each module has independent functions and interfaces. This not only facilitates the development, testing and optimization of a single module, but also allows for flexible combination and expansion according to the needs of different problems. An extensible interface is designed for each physical module, so that new physical modules can be easily integrated into the solving framework. The compatibility of data exchange and numerical methods is fully considered in the interface design to ensure that different modules can be efficiently coupled for calculation.

[0033] The separated coupling calculation method is adopted to carry out the calculation of electromagnetic, thermal and structural three physical fields in different modules, and realize the coupling of multiple physical fields through iterative solution. This method not only improves the calculation efficiency, but also facilitates the independent optimization and control of the calculation of each physical field.

[0034] In the above-mentioned multi-physics field coupling analysis system based on the general PDE solution base, through a highly modular design, the electromagnetic, thermal and structural modules have independent functions and interfaces, which are convenient for development, testing, optimization and expansion. The system adopts a standardized interface to ensure efficient coupling between different physical modules, supports rapid integration of new physical modules, and meets diverse solution requirements. Through the separated coupling calculation method, each physical field module is calculated independently and iteratively coupled, thereby improving the calculation efficiency and providing optimization space for each module. At the same time, the system can be flexibly adjusted according to specific coupling problems, supports dynamic expansion, and simplifies the process of functional optimization and adjustment. The system of the present invention has good scalability, adaptability and efficiency, can effectively solve complex electromagnetic-thermal-structural coupling problems, and improve solution efficiency and flexibility.

[0035] In one embodiment, Figure 2 The schematic diagram of the general PDE solving base structure shown in the figure, the discrete operator library includes a variety of discretized mathematical operators; the mathematical operators are used to discretize continuous partial differential equations; the numerical discretizers include finite element method and finite volume method.

[0036] like Figure 2As shown in the figure, first, the two basic algorithms, the finite element method and the finite volume method, are modularly encapsulated. The finite element method has advantages in dealing with complex geometries and multiple boundary conditions, while the finite volume method performs well in conservation. Through modular encapsulation, the two algorithms can be developed, tested and optimized independently, while working together when needed. Providing a standardized interface for the physical field solver is one of the core features of this base. This interface is carefully designed with clear input and output specifications. For the input part, it can receive relevant parameters of different physical models such as electromagnetics, heat, and structural mechanics, including geometric descriptions, material properties, boundary condition settings, etc. Through this interface, different physical models can easily interact with the solver base without worrying about the complexity of the underlying algorithm. When the physical model is connected to the solver base through the interface, the base can discretize these models into large linear systems. For electromagnetic problems, by discretizing the Maxwell equations, a linear system of equations is obtained to describe the distribution of the electromagnetic field. In thermal problems, discretization is performed based on the heat conduction equation, and a linear system of equations is also obtained to determine the temperature field. Structural mechanics problems are discretized based on the mechanical equilibrium equation. Finally, an iterative method is used to solve these large linear systems. The iterative method has the advantages of high computational efficiency and relatively small memory requirements. By continuously iterating and updating the solution vector, the true solution is gradually approached. During the iteration process, the convergence criterion is used to determine whether the required accuracy has been achieved. If not, the iteration continues; once the convergence condition is met, the final physical field solution is output. Such a solution process not only ensures the accuracy of the calculation, but also improves the computational efficiency. Based on the general PDE solution base, the design and calculation of various physical field solution modules such as electromagnetic field, heat, and structural mechanics will be based on a unified interface and platform. In the above way, electromagnetic, thermal, and structural solution modules are designed based on the finite element method and the finite volume method, which provides a reliable foundation for multi-physical field coupling calculations. These physical field modules can perform data interaction and coupling calculations through integrated separate coupling adapters.

[0037] Specifically, Figure 3The schematic diagram of model solution of the electromagnetic field solution module shown in the figure shows that for the electromagnetic field solution module, the model grid file of the electromagnetic problem to be solved is first prepared externally, and the physical parameters and solution parameters of the electromagnetic model are set through the configuration file (yaml file); after the program is started, the core module (Base module) in the PDE solution base starts to work, first calling the command line parameter parsing module to read the configuration file path input by the command line, and then the PDE solution base completes the reading of the configuration file and the model grid file by calling the parallel communication and file IO modules. According to the settings in the configuration file, the PDE solution base dynamically loads the electromagnetic model plug-in and its related components, completes the integration of the plug-in and the core module, and constructs the electromagnetic field solution module. The electromagnetic model in the electromagnetic field solution module is a mathematical model established for electromagnetic problems, and the mathematical model is established based on the Maxwell equations. The electromagnetic field solution module extracts the curl operator (▽×) and the vector dot multiplication operator (·) from the discretized operator library of the PDE base according to the Herm-Hertz equation in the mathematical model, and combines the operators to form a complete discrete equation through operator overloading, completing the finite element discretization of the electromagnetic mathematical model and obtaining a linear equation group describing the electromagnetic field distribution. With the help of the linear system solver in the PDE solution base, the linear equation group is solved to obtain the electromagnetic field intensity on each unit. Electromagnetic problems are usually described by Maxwell's equations. Specifically, a mathematical model of the electromagnetic problem is first established, and the boundary conditions and initial conditions are determined. Then, the finite element method is used to discretize the solution area to obtain a set of linear equations. By solving this linear equation group, the electromagnetic field intensity on each unit can be obtained. Next, the distribution of the electromagnetic field at different time steps is updated. In the iterative process, the solution of the electromagnetic field is continuously adjusted until the convergence conditions are met.

[0038] For the thermal solution module, the finite volume method is used. Specifically, first, a mathematical model of the thermal problem is established, and the boundary conditions and initial conditions are determined. Then, the solution area is discretized using the finite volume method to obtain a set of linear equations. By solving this set of linear equations, the temperature value on each unit can be obtained. Next, the distribution of the thermal field at different time steps is updated to ensure the conservation of heat between different units. During the iteration process, the temperature solution is continuously adjusted until the convergence conditions are met.

[0039] For the structural solution module, the finite element method is used for discretization. The structure is divided into small units, and the stress and strain distribution on the unit is obtained by approximately solving the mechanical equilibrium equation on each unit. Specifically, a mathematical model of the structural problem is first established, and the boundary conditions and initial conditions are determined. Then, the structure is discretized using the finite element method to obtain a set of linear equations. By solving this linear equations, the displacement, stress and strain values ​​on each unit can be obtained. In the iterative process, the solution of the structure is continuously adjusted until the convergence conditions are met.

[0040] like Figure 4 The electromagnetic-thermal-structural coupling calculation schematic diagram shown in the figure shows that when performing electromagnetic-thermal-structural coupling calculation, first, the case shape and boundary conditions are established: according to the electromagnetic-thermal-structural multi-physics field coupling application, it is divided into electromagnetic region, thermal region and structural region. Determine the geometric shape and boundary conditions of each region, such as setting current source and magnetic field boundary in the electromagnetic region; determining heat conduction boundary and initial temperature in the thermal region; setting fixed constraints and load boundaries in the structural region. There are interfaces between the regions, which constitute the coupling region. Next, construct discrete equations and determine the solver. Taking electromagnetics as an example, the finite element method is used to discretize the Maxwell equations through the discrete operators in the PDE solution base to obtain the linear equations describing the electromagnetic field distribution. With the help of the linear system solver in the PDE solution base, the linear equations are solved to obtain the electromagnetic field in the initial state. Through the PDE solution base's IO module, the temperature field of the thermal solution module and the calculation results of the displacement variables of the structural mechanics solution module are obtained at the same time, and it is judged whether the calculation results of the three modules meet the convergence conditions at the same time. If the conditions are met, the results are output and saved; if the conditions are not met, the results of the temperature field, electromagnetic field, and displacement variables are simultaneously input into the adapter, which completes the conversion and spatial alignment of physical parameters such as conductivity, magnetic permeability, thermal conductivity, and elastic modulus, and uses the adjusted conductivity, magnetic permeability, and other electromagnetic-related physical parameters as input to start a new round of calculations. It should be noted that at this time, the thermal solution module and the structural mechanics solution module must restart the calculation, and the corresponding physical parameters or state conditions must also be updated synchronously.

[0041] In one embodiment, the electromagnetic field results, thermal field results and structural mechanics field results of the coupling region are obtained in each iteration step, and parameter conversion and spatial alignment are performed to obtain the coupling response results, including: in each iteration step, the electromagnetic field results, thermal field results and structural mechanics field results of the coupling region are obtained; according to the equivalent conditions of the physical parameters in the coupling region, the representation forms of the electromagnetic field results, thermal field results and structural mechanics field results are converted to obtain the electromagnetic field results, thermal field results and structural mechanics field results after parameter equivalence, and then the discrete points of the electromagnetic-thermal coupling interface, the thermal-structural coupling interface and the structural-electromagnetic coupling interface are aligned to obtain the coupling response results.

[0042] In this embodiment, the physical parameters involved in the coupling simulation process are determined, such as electrical conductivity, thermal conductivity, elastic modulus, etc. Due to the different numerical solution mechanisms of different physical fields, the meanings and representations of these physical parameters in the three solution algorithms of electromagnetic, thermal, and structure are different. Therefore, according to the equivalent conditions of the physical parameters in each method, the representations of the physical parameters in different algorithms are converted to ensure the equivalence of the parameters in the electromagnetic-thermal-structural coupling solution process. For example, the conversion of electrical conductivity in electromagnetic calculations and Joule heat calculations, the conversion of thermal expansion coefficient in thermal calculations and structural calculations, etc. Figure 5 As shown in the diagram of discrete space alignment, since the discrete spaces of different physical fields may be inconsistent, it is necessary to align the different discrete spaces involved in the coupling region. Ensure the accuracy of data transfer and interaction at the electromagnetic-thermal and thermal-structural coupling interfaces. For example, the discrete points of the electromagnetic region and the thermal region at the coupling interface are aligned through the interpolation algorithm to ensure that the Joule heat calculated by the electromagnetic field can be accurately transferred to the thermal region for temperature calculation, and the displacement caused by thermal expansion can be accurately transferred to the structural region for stress and strain calculation.

[0043] In one embodiment, updating the physical model parameters in each physical field solution module based on the coupling response result includes: in each iteration step, real-time data transmission of the parameters and physical field information of the coupling region is performed to update the physical model parameters in each physical field solution module.

[0044] In this embodiment, if Figure 6 As shown in the diagram of real-time data transmission direction, when performing electromagnetic-thermal-structural multi-physics field coupling simulation, the adapter transmits the parameters and physical field information of the coupling area based on the time step. In each time step, the Joule heat calculated in the electromagnetic area is used as the heat source input of the thermal area, and the thermal expansion caused by the temperature distribution calculated in the thermal area is used as the load input of the structural area. The deformation of the structural area will affect the material properties (such as magnetic permeability) and boundary conditions (such as gap changes) of the electromagnetic area. Figure 7 The iterative solution process diagram shown in the figure shows that the discrete equations of the electromagnetic area, thermal area and structural area are iteratively solved according to the coupling solution package until convergence. Select a suitable numerical coupling method from the coupling solution package, such as explicit coupling or implicit coupling. In explicit coupling, each physical field is solved in sequence, and the result of the previous physical field is directly used as the input of the next physical field; in implicit coupling, the balance of each physical field at the coupling interface is guaranteed by iterative solution. During the iteration process, the physical field information of each area is continuously updated until the convergence conditions are met, and the coupled response information of the electromagnetic-thermal-structural multi-physics field application is obtained, including electromagnetic field distribution, temperature distribution, structural deformation and stress distribution.

[0045] Based on the output electromagnetic field results, thermal field results, and structural mechanics field results, users write custom post-processing codes according to standard C++ syntax, such as performing specific data analysis, visualization, or exporting electromagnetic simulation results to data files in a specific format. The written .cpp file is provided to the system as input together with the corresponding grid file (.cgns) and configuration file (.yaml). The system detects the custom code file at runtime, starts the dynamic compilation mechanism, compiles the user-defined code into an executable module, and associates it with the core data structure in the framework. After the numerical calculation is completed, the system automatically executes the user-defined post-processing code to achieve personalized processing of the calculation results and meet the special needs of users in the analysis of specific electromagnetic problems.

[0046] In one embodiment, the PDE solving base also includes a command line parameter module; the command line parameter module is used to read the configuration file path input by the command line; the PDE solving base also includes a parallel communication and file IO module; the parallel communication and file IO module is used to read the configuration file through the configuration file path, and load the model grid file according to the path specified in the configuration file.

[0047] Specifically, the framework building and configuration process of the PDE solving base includes: first, building the core module (Base module) to realize its general functions, such as developing command line parameter parsing module, runtime parameter management module, parallel communication and file IO module, logging module, exception handling module, performance optimization tool module and plug-in management module. Ensure that these modules work together normally to provide a stable basic environment for the entire system. Then, design the plug-in interface specification, define a unified abstract interface according to the functional requirements of different types of plug-ins (solving algorithms, PDE discretization, linear systems, grid file processing, physical models, etc.), and provide standards for the development and integration of plug-ins. Establish a mapping relationship between the configuration file format (.yaml format) and the system to ensure that the system can correctly read the information in the configuration file and dynamically load and manage the plug-in module according to the configuration information.

[0048] In one embodiment, the physical model plug-in includes a physical model subclass and related components; the physical model subclass includes physical equations and boundary conditions; and the related components include a grid file processing sub-plug-in, a solution algorithm sub-plug-in, and a PDE discretization sub-plug-in.

[0049] In this embodiment, before integration, plug-in development is performed based on the actual multi-physics field coupling problem. Taking the electromagnetic model plug-in as an example, the electromagnetic model subclass is derived based on the physical model plug-in interface to implement the physical equations and boundary condition settings related to the electromagnetic model. For example, the numerical expression of the Maxwell equations and the boundary condition processing methods for different electromagnetic problems (such as electrostatic fields, static magnetic fields, time-varying electromagnetic fields, etc.) are implemented in the electromagnetic model subclass. According to needs, the grid file processing sub-plug-in related to the electromagnetic model (if it is necessary to expand the specific electromagnetic grid format), the solution algorithm sub-plug-in (such as the iterative solution algorithm optimized for electromagnetic problems) and the PDE discretization sub-plug-in (such as the application of finite element discretization method in electromagnetic problems) are developed. In the process of plug-in development, the template factory design pattern is followed to ensure the interface compatibility between the plug-in and the framework.

[0050] The developed electromagnetic model plug-in and its related sub-plug-ins are registered in the system through the plug-in registration mechanism provided by the framework. During the registration process, the system automatically adds electromagnetic model-related options to the configuration file so that users can easily select and configure the electromagnetic model plug-in when using it. When the system starts, it dynamically loads the electromagnetic model plug-in and its related components according to the settings in the configuration file, completes the integration of the plug-in and the core module, and realizes the modeling and solving functions of electromagnetic problems.

[0051] In a specific embodiment, taking Through Silicon Via (TSV) technology as an example, in the development process of TSV, there is a typical electromagnetic-thermal-structural coupling phenomenon. An electromagnetic-thermal-structural coupling model of TSV is established, and thermal and electromagnetic effects will affect the structure of TSV. According to the actual geometric dimensions, material properties and operating conditions of the TSV structure, the boundary conditions such as the current excitation and magnetic field boundary conditions of the electromagnetic area, the heat dissipation conditions and initial temperature distribution of the thermal area, the fixing method of the structural area, and the load conditions are determined.

[0052] S1. Discrete equation construction and solver configuration.

[0053] Electromagnetic area: Use finite element software (such as COMSOL Multiphysics) to construct discrete equations in the electromagnetic area and transform the electromagnetic problem of TSV into a set of algebraic equations. Based on Maxwell's equations, consider factors such as the structural distribution of TSV, determine appropriate electromagnetic solver parameters, such as iterative algorithms, convergence criteria, etc., to accurately solve the electromagnetic field distribution.

[0054] Thermal region: The discrete equations of the thermal region are developed using the finite volume method to discretize the processes of heat conduction and convection heat transfer inside the TSV structure. According to the heat dissipation method of the motor (such as natural convection, forced air cooling, etc.) and the thermal physical properties of the material, the boundary conditions and calculation parameters of the thermal solver are set, such as thermal conductivity, specific heat capacity, and convection heat transfer coefficient.

[0055] Structural area: The discrete equations of the structural area are constructed by finite element analysis software (such as ABAQUS), and the stress-strain relationship of the TSV structure under thermal expansion and electromagnetic force is described based on the principles of elastic mechanics. Considering the complexity of the TSV structure, the type and parameters of the structural solver, such as unit type, contact algorithm, etc., are determined.

[0056] S2, physical parameter conversion and spatial alignment operation.

[0057] Physical parameter conversion: Determine the physical parameters involved in the TSV structure, such as electrical conductivity (used to calculate Joule heat), thermal conductivity (affects heat transfer), elastic modulus (determines structural deformation), etc. Perform parameter conversion based on the different definitions and requirements of these parameters for the electromagnetic, thermal, and structural solution algorithms. For example, convert the electrical conductivity obtained in the electromagnetic calculation into the heat generation rate parameter generated by Joule heat in the thermal calculation, and convert the thermal expansion coefficient into the thermal load parameter in the structural calculation to ensure the consistency of parameters in the coupled calculation.

[0058] Spatial alignment: Align the discrete spaces of different physical fields at the electromagnetic-thermal and thermal-structural coupling interfaces. Use interpolation algorithms to map physical quantities such as magnetic field intensity and current density in electromagnetic calculations from the grid nodes of the electromagnetic region to the corresponding positions of the thermal region. At the same time, map the temperature distribution calculated in the thermal region to the grid nodes of the structural region to ensure accurate data transfer between different physical fields.

[0059] S3, real-time data transmission and iterative equation solving.

[0060] Real-time data transmission: During the TSV simulation process, the Joule heat generated by the electromagnetic equation solver is transferred to the thermal area in real time through the adapter in each time step as the heat source term in the thermal equation solver. The thermal expansion displacement caused by the temperature distribution calculated by the thermal equation solver is transferred to the structural area in real time as the load of the structural equation solver. At the same time, the deformation of the structural area is fed back to the electromagnetic area, affecting the magnetic field distribution and inductance parameters of the electromagnetic area.

[0061] Iterative solution of equations: According to the characteristics of the TSV structure and the requirements of simulation accuracy, multiple coupling methods are selected from the coupling solution package provided by the coupling library. For example, for fast transient changes, explicit coupling can be used; for accurate calculations during steady-state operation, implicit coupling is selected. In the iterative solution process, the physical field information of the electromagnetic, thermal, and structural areas is continuously updated, and the convergence conditions (such as the residual is less than the set threshold, the change in physical quantity is less than the allowable error, etc.) are judged until convergence is reached, and sub-iteration within a time step is achieved to obtain the electromagnetic field distribution, temperature distribution, structural deformation, stress distribution and other coupling response information of the TSV structure under the electromagnetic-thermal-structural multi-physical field coupling, which provides strong support for the optimization design, performance evaluation and fault diagnosis of TSV.

[0062] In one embodiment, Figure 8 As shown, a multi-physics coupling analysis method for solving the base based on a general PDE is provided, including the following steps:

[0063] Step 802, respectively load the electromagnetic model plug-in, thermal model plug-in and structural mechanics model plug-in according to the acquired configuration file information, complete the integration of the plug-in and the core module through the standardized interface, and construct the corresponding electromagnetic field solution module, thermal solution module and structural solution module.

[0064] Step 804, according to the configuration information in the electromagnetic field solution module, the thermal solution module and the structural solution module, select the corresponding operator from the discrete operator library, discretize the physical model to obtain the corresponding linear equation group, solve each linear equation group, and obtain the electromagnetic field results, thermal field results and structural mechanics field results.

[0065] Step 806, during the electromagnetic-thermal-structural multi-physics field coupling analysis, the electromagnetic field results, thermal field results and structural mechanics field results of the coupling area are obtained in each iteration step, and parameter conversion and spatial alignment are performed to obtain the coupling response results. The physical model parameters in each physical field solution module are updated based on the coupling response results until the iteration stop condition is met, and the current electromagnetic field results, thermal field results and structural mechanics field results are output.

[0066] It should be understood that although Figure 8 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 8At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0067] For the specific definition of the multi-physics coupling analysis system based on the general PDE solution base, please refer to the definition of the multi-physics coupling analysis method based on the general PDE solution base mentioned above, which will not be repeated here. Each module in the above-mentioned multi-physics coupling analysis system based on the general PDE solution base can be implemented in whole or in part through software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0068] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0069] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A multi-physics field coupling analysis system based on general PDE solution for the base, characterized in that: The system includes a general PDE solving base and an adapter; the PDE solving base includes a core module, a plug-in management module and a numerical calculation module; The core module is used to manage the collaborative work between modules and provide a standardized interface; The plug-in management module is used to load the electromagnetic model plug-in, the thermal model plug-in and the structural mechanics model plug-in respectively according to the acquired configuration file information, complete the integration of the plug-in and the core module through the standardized interface, and construct the corresponding electromagnetic field solution module, thermal solution module and structural solution module; The numerical calculation module includes a discrete operator library, a numerical discretizer and a linear system solver. The numerical discretizer selects corresponding operators from the discrete operator library according to the configuration information in the electromagnetic field solution module, the thermal solution module and the structural solution module, and discretizes the physical model to obtain the corresponding linear equations. The linear system solver is used to solve each linear equation to obtain electromagnetic field results, thermal field results and structural mechanics field results. When the system performs electromagnetic-thermal-structural multi-physics field coupling analysis, the adapter obtains the electromagnetic field results, thermal field results and structural mechanics field results of the coupling area in each iteration step and performs parameter conversion and spatial alignment to obtain coupling response results, and updates the physical model parameters in each physical field solution module based on the coupling response results until the iteration stop condition is met, and then outputs the current electromagnetic field results, thermal field results and structural mechanics field results.

2. The system according to claim 1, characterized in that The PDE solving base also includes a command line parameter module; the command line parameter module is used to read the configuration file path input by the command line.

3. The system according to claim 2, characterized in that The PDE solving base also includes a parallel communication and file IO module; the parallel communication and file IO module is used to read the configuration file through the configuration file path and load the model grid file according to the path specified in the configuration file.

4. The system according to claim 1, characterized in that The physical model plug-in includes a physical model subclass and related components; the physical model subclass includes physical equations and boundary conditions; the related components include a grid file processing sub-plug-in, a solution algorithm sub-plug-in and a PDE discretization sub-plug-in.

5. The system according to claim 1, characterized in that The discrete operator library includes a plurality of mathematical operators that have been discretized; the mathematical operators are used to discretize continuous partial differential equations.

6. The system according to claim 1, characterized in that The numerical discretizer includes the finite element method and the finite volume method.

7. The system according to claim 1, characterized in that In each iteration step, the electromagnetic field results, thermal field results and structural mechanics field results of the coupling area are obtained and parameter conversion and spatial alignment are performed to obtain the coupling response results including: In each iteration step, the electromagnetic field results, thermal field results and structural mechanics field results of the coupled region are obtained; According to the equivalent conditions of the physical parameters in the coupling area, the representation forms of the electromagnetic field results, thermal field results and structural mechanics field results are converted to obtain the electromagnetic field results, thermal field results and structural mechanics field results after parameter equivalence. Then, the discrete points of the electromagnetic-thermal coupling interface, the thermal-structural coupling interface and the structural-electromagnetic coupling interface are aligned to obtain the coupling response results.

8. The system according to claim 1, characterized in that The physical model parameters in each physical field solution module are updated based on the coupled response results, including: In each iteration step, real-time data transmission is performed on the parameters and physical field information of the coupling region to update the physical model parameters in each physical field solution module.

9. A multi-physics coupling analysis method based on a general PDE solution base implemented in the system according to any one of claims 1 to 8, characterized in that: The method comprises: Load the electromagnetic model plug-in, thermal model plug-in and structural mechanics model plug-in respectively according to the acquired configuration file information, complete the integration of the plug-in and the core module through the standardized interface, and build the corresponding electromagnetic field solution module, thermal solution module and structural solution module; According to the configuration information in the electromagnetic field solution module, the thermal solution module and the structural solution module, the corresponding operator is selected from the discrete operator library, the physical model is discretized to obtain the corresponding linear equation group, and each linear equation group is solved to obtain the electromagnetic field results, thermal field results and structural mechanics field results; In the electromagnetic-thermal-structural multi-physics field coupling analysis, the electromagnetic field results, thermal field results and structural mechanics field results of the coupling area are obtained in each iterative step, and parameter conversion and spatial alignment are performed to obtain the coupling response results. The physical model parameters in each physical field solution module are updated based on the coupling response results until the iteration stop condition is met, and the current electromagnetic field results, thermal field results and structural mechanics field results are output.

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