Multi-field coupling based component simulation method and system

Abstract

The application relates to the technical field of electronic component simulation, and discloses a component simulation method and system based on multi-field coupling, wherein the method comprises the following steps: performing finite element grid discretization on a component calculation domain to generate a grid element set; independently solving electromagnetic fields, thermal fields and structural mechanical fields respectively to obtain initial field quantity values; calculating a cross-sensitivity matrix for each grid element and extracting a Frobenius norm thereof to generate a local coupling strength index value; performing partition marking on the grid element based on the local coupling strength index value; performing overall coupling solving on a strong coupling region, performing sequential iteration solving on a weak coupling region, and performing solving with boundary constraints on a transition region; and collecting field quantity results, judging convergence, and outputting a simulation result.

Description

Technical Field

[0001] This invention relates to the field of electronic component simulation technology, specifically to a component simulation method and system based on multi-field coupling. Background Technology

[0002] As power semiconductor devices, high-density packaged devices, and microelectronic devices continue to develop towards higher integration and higher power density, these components are typically subjected to the combined effects of multiple physical fields, including electromagnetic fields, thermal fields, and structural mechanical fields, during actual operation. Complex coupling relationships exist between these different physical fields. For example, electromagnetic losses generate Joule heating, temperature changes cause variations in the material's conductivity, permeability, and dielectric parameters, and thermal expansion leads to structural stress and deformation, further affecting the electrical performance and reliability of the components. Therefore, multiphysics coupling simulation has become an important technical means for the design optimization, lifetime prediction, and reliability analysis of electronic components.

[0003] Currently, multiphysics simulations typically employ two methods: global coupled solution or sequential coupled solution. Global coupled solution can simultaneously consider the interactions between different physics fields, offering high computational accuracy. However, it requires constructing a large set of coupled equations, resulting in high computational cost and long solution time. As the size of the component model increases, the overall solution efficiency significantly decreases. Sequential coupled solution calculates each physics field sequentially according to a pre-defined order, using the results of the previous physics field as input for the next. While this reduces computational complexity, it neglects some real-time feedback relationships, easily leading to large cumulative errors in strongly coupled multiphysics regions. This causes key simulation results, such as local hotspot temperatures, thermal stress, and electromagnetic responses, to deviate from reality.

[0004] Further analysis reveals that the degree of multiphysics coupling varies across different regions within electronic components. For example, the active region, solder joints, and bonding areas of a chip typically exhibit strong electro-thermal-mechanical coupling, while the inter-field coupling in areas such as the heat sink substrate and encapsulation filling layer is relatively weak. Existing technologies generally employ a uniform solution strategy for the entire computational domain, failing to adaptively select different solution methods based on the spatial differences in local coupling strength. This results in weakly coupled regions still employing computationally expensive overall coupling solutions, leading to a large amount of invalid computation; or the entire computational domain is solved using sequential coupling solutions, making it impossible to accurately reflect the real-time interactions between various physical fields in strongly coupled regions, ultimately making it difficult to balance simulation efficiency and computational accuracy.

[0005] Therefore, how to establish a method that can quantitatively evaluate the local multiphysics coupling strength of components, adaptively divide the computational region according to the coupling strength, adopt differentiated coupling solution strategies for different regions, and at the same time ensure the continuity of field quantities at the interface of different regions and the overall solution convergence, thereby balancing simulation accuracy and computational efficiency, has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] This invention provides a component simulation method and system based on multi-field coupling, which solves the technical problems in related technologies such as the lack of adaptive identification ability of physical field coupling strength in different regions of the component's computational domain, and the inability to select solution strategies according to regional differences, resulting in wasted computing resources or insufficient simulation accuracy.

[0007] This invention discloses a component simulation method based on multi-field coupling, including: The finite element mesh is discretized to generate a set of mesh elements in the computational domain of the components, and the initial field values ​​on each mesh element node are obtained by solving each physical field independently. For each grid cell, a preset small perturbation is applied to each physical field quantity in sequence, and the response change caused by the perturbation on the other physical fields is calculated. The cross sensitivity matrix of the grid cell is assembled according to the field quantity dimension, and the Frobenius norm of the cross sensitivity matrix is ​​calculated as the local coupling strength index value of the grid cell. Let the components of the disturbed field be The response field components are The reference scales for the two are respectively and Then the elements of the cross-sensitivity matrix for: ; in For the disturbance quantity, For the changes in the responses of the remaining physical fields; and To prevent extremely small positive numbers with a reference scale of zero; The preset small perturbation amount is determined as follows: ; This serves as the baseline value for this component in the current iteration round. As the smallest reference scale for this type of field quantity, The preset perturbation ratio; The local coupling strength index value of each grid cell is compared with the strong coupling threshold and the weak coupling threshold respectively, and the grid cell is marked as a strong coupling region, a transition region or a weak coupling region, generating a set of computational domain partition labels; Perform multiphysics global coupled solution for strongly coupled regions, perform sequential iterative solution for weakly coupled regions, and perform solution with boundary constraints for transition regions; Summarize all field quantity results for all regions and calculate the flux continuity residuals at the interfaces of each region. If the residuals exceed the preset allowable value, recalculate the cross sensitivity matrix based on the updated field quantities and repeat the partition solution until the residuals converge and then output the simulation results.

[0008] Furthermore, the assembly of the cross-sensitivity matrix includes: assuming the electromagnetic field vector on a certain grid cell is... The thermal field vector is The structural mechanical field quantity vector is The number of components of the three are respectively , , The cross-sensitivity matrix The number of rows and columns are both ; for the electromagnetic field quantity vector of the first Each component is subjected to a perturbation. Keeping the other field quantities constant, the response changes of the thermal field and structural mechanical field are recalculated. The corresponding column elements of the cross-sensitivity matrix are: ; ; in The first change in thermal field response One portion, The first change in the structural mechanical field response Each component; after perturbing each component of the thermal field and the structural mechanical field, the cross-field response elements are filled into the corresponding columns in the same way.

[0009] Furthermore, the cross-sensitivity matrix In the cross sensitivity matrix, all elements in the index region of the corresponding field response row of each physical field perturbation column are set to zero, so that the cross sensitivity matrix contains only cross-field coupling response elements; all elements of the cross sensitivity matrix are dimensionless values, and the numerator and denominator of each element are the changes and perturbations of the same type of field quantity, which have the same physical dimensions.

[0010] Furthermore, the expression for calculating the local coupling strength index value is as follows: ; in For matrix The number of rows and columns, For matrix No. Line number The element values ​​of the column.

[0011] Furthermore, marking mesh cells as strongly coupled regions, transition regions, or weakly coupled regions includes: when the local coupling strength index value is greater than or equal to the strong coupling threshold. When the local coupling strength index value is less than or equal to the weak coupling threshold, the mesh cell is marked as a strongly coupled region; When the local coupling strength index value is greater than 1, the mesh cell is marked as a weakly coupled region; when the local coupling strength index value is greater than 1, the mesh cell is marked as a weakly coupled region. and less than When this occurs, the grid cell is marked as a transition region; where, Take the upper quartile of the local coupling strength index values ​​of all mesh elements. Take the lower quartile of the local coupling strength index values ​​of all mesh elements.

[0012] Furthermore, the process of performing a multi-physics field-based coupled solution for the strongly coupled region includes: assembling a set of coupled equations for the electromagnetic field, thermal field, and structural mechanical field for the mesh elements of the strongly coupled region. The material parameters of the electromagnetic field equation depend on the temperature value of the thermal field, the internal heat source term of the thermal field equation depends on the Joule heat distribution of the electromagnetic field, and the thermal load of the structural mechanical field equation depends on the temperature gradient of the thermal field. The equations of each field are solved synchronously through the above dependencies.

[0013] Furthermore, the sequential iterative solution for the weakly coupled region includes: first solving the electromagnetic field equation to obtain the electromagnetic field quantity distribution; then using the electromagnetic field quantity distribution as a known source term to input the thermal field equation to solve for the temperature distribution; and finally using the temperature distribution as a known load to input the structural mechanics field equation to solve for the displacement and stress distribution.

[0014] Furthermore, the solution with boundary constraints applied to the transition region includes: extracting the field values ​​of the shared boundary nodes of adjacent strongly coupled and weakly coupled regions as the boundary constraint conditions of the transition region; and applying distance-based weighted interpolation constraints to the nodes inside the transition region, whereby the distance from a certain internal node to the boundary of the strongly coupled region is... The distance to the boundary of the weakly coupled region is Then the weight of the strongly coupled region side and the weight of the weakly coupled region They are respectively: ; ; in This is the distance from the internal node to the boundary of the strongly coupled region. The interpolation weight is the distance from the internal node to the boundary of the weakly coupled region, and is used as the initial estimate when constraining the solution of the transition region.

[0015] Furthermore, when recalculating the cross sensitivity matrix based on the updated field quantity and repeatedly solving the partition, the partition label of a grid cell is only updated when the change in the local coupling strength index value of a certain grid cell relative to the previous iteration exceeds a preset stability threshold; grid cells whose change does not exceed the preset stability threshold retain their original labels.

[0016] This invention discloses a component simulation system based on multi-field coupling, used to execute the aforementioned component simulation method based on multi-field coupling, comprising: a mesh discretization module for acquiring the geometric model data, material property parameters, and boundary conditions of the component, performing finite element mesh discretization on the computational domain, and generating a set of mesh elements; an initial field quantity solution module for independently solving the electromagnetic field, thermal field, and structural mechanical field, and obtaining the initial field quantity values ​​at each mesh element node; and a coupling strength evaluation module for calculating the cross-sensitivity matrix for each mesh element and extracting the Frobenius norm of the cross-sensitivity matrix to generate a local coupling strength index value. The partitioning and marking module is used to mark all mesh elements as strongly coupled regions, transition regions, or weakly coupled regions based on the comparison results of the local coupling strength index value with the strong coupling threshold and weak coupling threshold, and to generate a set of computational domain partitioning and marking modules. The partitioning and solving module is used to perform global coupling solution for strongly coupled regions, sequential iterative solution for weakly coupled regions, and boundary-constrained solution for transition regions to obtain the field quantity results for all regions. The convergence judgment module is used to calculate the flux continuity residuals at the interfaces of each region, trigger iterative updates when the residuals exceed the preset allowable value, and output the multi-field coupling simulation results of the components when the residuals converge.

[0017] This invention obtains a quantitative index reflecting the difference in multi-field coupling strength at various spatial locations within a component by calculating the cross-sensitivity matrix on each grid cell and extracting its Frobenius norm. This allows the computational domain to be divided into strongly coupled regions, transition regions, and weakly coupled regions.

[0018] For strongly coupled regions, a global coupling solution is performed, preserving the synchronous cross-influence between physical fields and avoiding the field quantity calculation deviations caused by neglecting cross-coupling effects in sequential solutions within strongly coupled regions. For weakly coupled regions, a sequential iterative solution is performed, eliminating the unnecessary computational overhead generated by global coupling in weakly coupled regions. In transition regions, boundary constraint interpolation achieves a smooth connection between different solution strategies. This combination of partitioned solution and iterative convergence ensures both simulation accuracy and computational efficiency, overcoming the limitation of a global uniform coupling strategy in matching the spatial coupling strength distribution. Attached Figure Description

[0019] Figure 1 This is a flowchart of a component simulation method based on multi-field coupling provided in an embodiment of the present invention. Detailed Implementation

[0020] See Figure 1 As shown, electronic components are simultaneously subjected to electromagnetic, thermal, and structural mechanical fields during operation, with cross-influences between these different physical fields. Existing simulation methods employ a uniform coupling solution strategy across the entire computational domain of the component, but the multi-field coupling strength varies significantly at different spatial locations within the component. The global coupling strategy generates substantial unnecessary computational overhead in weakly coupled regions; the global sequential coupling strategy ignores the synchronous cross-influence between field quantities in strongly coupled regions, leading to systematic deviations in the calculation results. These contradictions make it impossible to simultaneously satisfy simulation accuracy and computational efficiency.

[0021] A component simulation method based on multi-field coupling according to an embodiment of the present invention includes the following steps: Step 1: Perform finite element mesh discretization on the computational domain of the component to generate a set of mesh elements; The system acquires the geometric model data of the components, material property parameters of each region, and multiphysics boundary conditions. It then performs finite element mesh discretization on the computational domain of the components to generate a set of mesh elements.

[0022] Each mesh element in the mesh set has corresponding node coordinates, element type, material properties, and region identifier. Boundary conditions include electromagnetic field excitation source distribution, thermal field temperature or heat flux constraints, and structural mechanical field displacement or load constraints.

[0023] Step 2: Solve the initial field quantity distribution of each physical field independently to obtain the initial field quantity values ​​at each grid cell node; The electromagnetic field, thermal field, and structural mechanical field are solved independently to obtain the initial field quantities of each physical field at each grid cell node. The initial field quantities of the electromagnetic field include electric field strength and magnetic flux density, the initial field quantities of the thermal field include temperature distribution, and the initial field quantities of the structural mechanical field include displacement and stress components.

[0024] The independent solutions for each physical field use the boundary conditions and material property parameters obtained in step 1 as input. The cross-influence between field quantities is not considered in this stage, and the material parameters for each field equation are taken as fixed values.

[0025] Step 3: Calculate the cross sensitivity matrix for each grid cell; For each grid cell, a preset small perturbation is applied to each physical field quantity in sequence, and the response change caused by the perturbation on the other physical fields is calculated. The cross sensitivity matrix of the grid cell is then assembled according to the field quantity dimension.

[0026] Specifically, for the case of three-field coupling including electromagnetic field, thermal field and structural mechanical field, let the electromagnetic field vector on a certain grid cell be... The thermal field vector is The structural mechanical field quantity vector is The number of components of the three are respectively , , ,in The number of components in the electromagnetic field quantity vector. Let be the number of components of the thermal field vector. This represents the number of components in the structural mechanical field vector. Cross-sensitivity matrix. The number of rows and columns are both ,in represents the dimension of the cross-sensitivity matrix, with row indices corresponding to the response components of each field and column indices corresponding to the perturbation components of each field.

[0027] right The Each component is subjected to a perturbation. Keeping the other field quantities constant, recalculate the response changes of the thermal field quantities. and the response change of structural mechanical field quantities Then the cross-sensitivity matrix The elements in the corresponding column are: ; ; in, The change in thermal field quantity response The One portion, The change in the field quantity response of the structural mechanics field The One portion, The electromagnetic field vector is the first... The disturbance of each component Component index of thermal field quantity ( ), Component indexes for structural mechanical field quantities ( ), Component indexes of electromagnetic field quantities ( Cross-sensitivity matrix Only the effects of cross-field coupling are recorded; the row index in the electromagnetic field disturbance column is used. to All elements are set to zero, and only row indices are filled in. to and to Cross-field responsive elements.

[0028] For the hot field Each component is perturbed ( Keeping the other field quantities constant, recalculate the response changes of the electromagnetic field quantities. and the response change of structural mechanical field quantities Fill in the cross-sensitivity matrix The List: ; ; in, The change in electromagnetic field quantity response The One portion, Index of response components of electromagnetic field quantities ( ), The thermal field vector is the first... The disturbance of each component This is the index of the perturbation components of the thermal field. Row index in this column. to The corresponding thermal field response component is set to zero.

[0029] For the structural mechanical field Each component is perturbed ( Keeping the other field quantities constant, recalculate the response changes of the electromagnetic field quantities. and the response change of the thermal field quantity Fill in the cross-sensitivity matrix The List: ; ; in, The change in thermal field quantity response The One portion, The change in electromagnetic field quantity response The One portion, The structural mechanics field vector is the first... The disturbance of each component This is the index for the perturbation components of the structural mechanical field quantities. Row index in this column. to The corresponding structural mechanical field response components are set to zero. After traversing all disturbance components in the above manner, a complete cross-sensitivity matrix is ​​formed. Cross-sensitivity matrix The number of rows and columns are both .

[0030] It should be noted that the numerators and denominators of the above matrix elements represent the changes and disturbances of the same type of field quantity within the same physical field, respectively. Since they have the same physical dimensions, the ratios are dimensionless. Cross-sensitivity matrix All elements are dimensionless values ​​and can be directly used in subsequent Frobenius norm calculations.

[0031] It should be noted that the above-mentioned preset small disturbance is a fixed scaling value of the reference values ​​of each field quantity. The selection of the preset small disturbance must meet the premise that the response change and the disturbance quantity have an approximately linear relationship.

[0032] Step 4: Calculate the local coupling strength index value for each mesh element; Calculate the cross-sensitivity matrix for each grid cell. The Frobenius norm is used as an index of the local coupling strength of the mesh element. The expression for calculating the Frobenius norm is: ; in, For matrix The number of rows and columns, For matrix No. Line number The element values ​​of the column, Row index of the matrix ( ), Column index of the matrix ( The larger the local coupling strength index value, the stronger the cross-influence between the physical fields at the location of that grid cell.

[0033] It should be noted that, due to the cross-sensitivity matrix The diagonal block region (i.e., elements responding to co-field perturbations) is set to zero, and the summation of the Frobenius norm is contributed only by cross-field coupling elements. Therefore... It directly reflects the intensity of cross-field influence between various physical fields, and is not affected by the amplitude of the field quantity of each field itself.

[0034] Step 5: Perform partitioning marking on the mesh cells based on the coupling strength index value to generate a set of computational domain partitioning markings; The local coupling strength index value of each grid cell is compared with a preset strong coupling threshold. and weak coupling threshold Compare them. When the local coupling strength index value is greater than or equal to... When the local coupling strength index value is less than or equal to a certain value, the mesh cell is marked as a strongly coupled region; When the local coupling strength index value is greater than 1, the mesh cell is marked as a weakly coupled region; when the local coupling strength index value is greater than 1, the mesh cell is marked as a weakly coupled region. and less than At this point, the grid cell is marked as a transition region. After all grid cells are marked, a set of computational domain partition labels is generated.

[0035] It should be noted that, and The value of is related to the type of component and the simulation accuracy requirements. In one embodiment, Take the upper quartile of the local coupling strength index values ​​of all mesh elements. Take the lower quartile of the local coupling strength index values ​​of all mesh elements.

[0036] Step 6: Perform a multiphysics global coupling solution on the strongly coupled region to obtain the coupling field quantity solutions of each physics field in the strongly coupled region; For grid cells marked as strongly coupled regions, an overall coupled equation set of electromagnetic, thermal, and structural mechanical fields is assembled. The governing equations and their coupling terms of each field are incorporated into the overall coupled equation set, and multi-field synchronous solution is performed to obtain the coupled field quantity solutions of each physical field in the strongly coupled region.

[0037] Strongly coupled regions use a global unknown vector. ; ; Represents the unknown quantity in the electromagnetic field. This represents the unknown quantity in the temperature field. Indicates the unknown quantity of structural displacement; The overall coupled residual equation is: ; Electromagnetic field residual The electrical conductivity, magnetic permeability, or dielectric parameters are updated based on the current temperature value; ; ; In the overall coupled equation set, the material parameters of the electromagnetic field equation depend on the temperature of the thermal field, the internal heat source term of the thermal field equation depends on the Joule heat distribution of the electromagnetic field, and the thermal load of the structural mechanics field equation depends on the temperature gradient of the thermal field. The various field equations are synchronously coupled through the above dependencies.

[0038] Step 7: Perform sequential iterative solution on the weakly coupled region to obtain approximate field quantity solutions for each physical field in the weakly coupled region; The sequential solution for the weakly coupled region includes single-round propagation and necessary local iterations. First, the electromagnetic field is solved to obtain the electric field strength E, magnetic flux density B, and Joule heat. Then The temperature T is solved as a thermal field source term; then the temperature field T and temperature gradient are input into the structural mechanics equations to solve for displacement u and equivalent stress. When the temperature change and equivalent stress change in two adjacent weakly coupled regions are both less than a preset threshold, the sequential iteration stops. For mesh elements marked as weakly coupled regions, the physical field equations are solved sequentially in an iterative manner. First, the electromagnetic field equations are solved to obtain the electromagnetic field distribution. Then, the electromagnetic field distribution is used as a known source term to input the thermal field equations to solve for the temperature distribution. Finally, the temperature distribution is used as a known load to input the structural mechanics field equations to solve for the displacement and stress distribution, thereby obtaining approximate field quantity solutions for each physical field in the weakly coupled region.

[0039] Step 8: Perform a solution with boundary constraints on the transition region to obtain the field quantity distribution of each physical field in the transition region; For the grid cells marked as transition regions, the field quantities of the boundary nodes of adjacent strongly coupled and weakly coupled regions are extracted. The coupled field quantity solutions of the shared boundary nodes of the strongly coupled regions and the approximate field quantity solutions of the shared boundary nodes of the weakly coupled regions are used as the boundary constraints of the transition regions. The governing equations of each physical field in the transition regions are solved to obtain the field quantity distribution of the nodes inside the transition regions.

[0040] In this embodiment, to ensure a smooth transition of the field distribution at the interface of the transition region and avoid non-physical jumps, distance-based weighted interpolation constraints are applied to the nodes within the transition region. Let the distance from a node within the transition region to the boundary of the strongly coupled region be... The distance to the boundary of the weakly coupled region is Then the interpolation weight of the internal node is: ; ; in, For the weights on the strongly coupled region side, For the weights on the weakly coupled region side, This is the distance from the internal node to the boundary of the strongly coupled region. This is the distance from the internal node to the boundary of the weakly coupled region. The interpolation weights are used to constrain the initial estimates when solving the transition region, ensuring that the iterative solution has reasonable initial conditions. Step 9: Summarize all field quantity results and determine convergence, then output the multi-field coupling simulation results of the components; Summarize the field quantity solutions for the strongly coupled, weakly coupled, and transition regions, and calculate the flux continuity residuals at the interfaces of each region. The flux continuity residuals are the root mean square values ​​of the differences between the normal components of the field quantity gradients at corresponding nodes on both sides of the interface.

[0041] If the flux continuity residual exceeds the preset allowable value, then step 3 is re-executed with the updated field quantity data. Based on the current field quantity distribution, the cross sensitivity matrix of each grid cell is recalculated, a new set of computational domain partition markers is generated, and the solution process of steps 6 to 8 is repeated until the global residual converges to within the preset allowable value. The simulation results of multi-field coupling of the components are then output.

[0042] The regional interface residuals include thermal field residuals, electromagnetic field residuals, and structural mechanics residuals. The thermal field residual is the normalized root mean square value of the difference in the normal components of heat flux on both sides of the interface; the structural mechanics residual is the normalized root mean square value of the difference in traction force on both sides of the interface; the electromagnetic field residual is the normalized root mean square value of the continuity error of the tangential electric field or magnetic field on both sides of the interface; the global residual is the maximum value or weighted sum of the three. When the global residual is less than the preset allowable value, the regional coupling solution is considered to have converged.

[0043] In this embodiment, to avoid frequent oscillations in the computational domain partition label set during iteration, which could lead to convergence difficulties, when step 5 is re-executed, the partition label of a grid cell is only updated if the change in the local coupling strength index value of a certain grid cell relative to the previous iteration exceeds a preset stability threshold; grid cells whose change does not exceed the preset stability threshold retain their original labels. This process gradually stabilizes the partition boundaries during iteration, reducing the additional computational overhead caused by repeated partition changes.

[0044] Technical effects of this embodiment; This implementation obtains a quantitative index reflecting the differences in multi-field coupling strength at various spatial locations within the component by calculating the cross-sensitivity matrix on each grid cell and extracting the Frobenius norm of the cross-sensitivity matrix. The local coupling strength index value directly corresponds to the objective physical difference between the electrothermal strong coupling region and the weak coupling region in the component. Therefore, the partitioning based on the local coupling strength index value can accurately divide spatial regions with different coupling strengths.

[0045] For strongly coupled regions, a global coupling solution is performed, preserving the synchronous cross-influence between various physical fields and avoiding the field quantity calculation deviations caused by neglecting cross-coupling effects in sequential solutions within strongly coupled regions. For weakly coupled regions, a sequential iterative solution is performed. Since the interaction between fields in weakly coupled regions is extremely weak, the approximation error introduced by sequential solutions is within an acceptable range. This also eliminates the unnecessary computational overhead of assembling and solving a large global coupling equation set in weakly coupled regions. In transition regions, boundary constraint interpolation achieves a smooth transition between different solution strategies. This combination of partitioned solution and iterative convergence specifically addresses the problem in component simulation where a global uniform coupling strategy cannot match the spatial coupling strength distribution, resulting in a tradeoff between accuracy and efficiency.

[0046] On the other hand, the present invention also proposes a component simulation system based on multi-field coupling, comprising: The mesh discretization module is used to acquire the geometric model data, material property parameters and boundary conditions of components, perform finite element mesh discretization on the computational domain, and generate a set of mesh elements.

[0047] The initial field quantity solution module is used to independently solve the electromagnetic field, thermal field and structural mechanical field, and obtain the initial field quantity values ​​at each grid element node.

[0048] The coupling strength evaluation module is used to calculate the cross sensitivity matrix for each grid cell and extract the Frobenius norm of the cross sensitivity matrix to generate a local coupling strength index value.

[0049] The partitioning and marking module is used to mark all grid cells as strongly coupled regions, transition regions, or weakly coupled regions based on the comparison results of the local coupling strength index value and the threshold, and generate a set of computational domain partitioning and marking modules.

[0050] The partitioned solution module is used to perform global coupled solution for strongly coupled regions, sequential iterative solution for weakly coupled regions, and solution with boundary constraints for transition regions, to obtain the field quantity results for all regions.

[0051] The convergence judgment module is used to calculate the flux continuity residual at the interface of each region, determine whether the convergence condition is met, trigger iterative update when convergence is not achieved, and output the multi-field coupling simulation results of the components when convergence is achieved.

[0052] By way of example, the system proposed in this invention may also include various features and combinations thereof in the method embodiments, which will not be elaborated here.

[0053] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A component simulation method based on multi-field coupling, characterized in that, include: The finite element mesh is discretized to generate a set of mesh elements in the computational domain of the components, and the initial field values ​​on each mesh element node are obtained by solving each physical field independently. For each grid cell, a preset small perturbation is applied to each physical field quantity in sequence, and the response change caused by the perturbation on the other physical fields is calculated. The cross sensitivity matrix of the grid cell is assembled according to the field quantity dimension, and the Frobenius norm of the cross sensitivity matrix is ​​calculated as the local coupling strength index value of the grid cell. Let the components of the disturbed field be The response field components are The reference scales for the two are respectively and Then the elements of the cross-sensitivity matrix for: ； in For the disturbance quantity, For the changes in the responses of the remaining physical fields; and To prevent extremely small positive numbers with a reference scale of zero; The preset small perturbation amount is determined as follows: ； This serves as the baseline value for this component in the current iteration round. As the smallest reference scale for this type of field quantity, The preset perturbation ratio; The local coupling strength index value of each grid cell is compared with the strong coupling threshold and the weak coupling threshold respectively, and the grid cell is marked as a strong coupling region, a transition region or a weak coupling region, generating a set of computational domain partition labels; Perform multiphysics global coupled solution for strongly coupled regions, perform sequential iterative solution for weakly coupled regions, and perform solution with boundary constraints for transition regions; Summarize all field quantity results for all regions and calculate the flux continuity residuals at the interfaces of each region. If the residuals exceed the preset allowable value, recalculate the cross sensitivity matrix based on the updated field quantities and repeat the partition solution until the residuals converge and then output the simulation results.

2. The component simulation method based on multi-field coupling according to claim 1, characterized in that, The assembly of the cross-sensitivity matrix includes: Let the electromagnetic field vector on a certain grid cell be... The thermal field vector is The structural mechanical field quantity vector is The number of components of the three are respectively , , The cross-sensitivity matrix The number of rows and columns are both ; For the electromagnetic field vector of the first Each component is subjected to a perturbation. Keeping the other field quantities constant, the response changes of the thermal field and structural mechanical field are recalculated. The corresponding column elements of the cross-sensitivity matrix are: ； ； in The first change in thermal field response One portion, The first change in the structural mechanical field response Each component; after perturbing each component of the thermal field and the structural mechanical field, the cross-field response elements are filled into the corresponding columns in the same way.

3. The component simulation method based on multi-field coupling according to claim 2, characterized in that, The cross-sensitivity matrix In the cross sensitivity matrix, all elements in the index region of the corresponding field response row of each physical field perturbation column are set to zero, so that the cross sensitivity matrix contains only cross-field coupling response elements; all elements of the cross sensitivity matrix are dimensionless values, and the numerator and denominator of each element are the changes and perturbations of the same type of field quantity, which have the same physical dimensions.

4. The component simulation method based on multi-field coupling according to claim 1, characterized in that, The expression for calculating the local coupling strength index is as follows: ； in For matrix The number of rows and columns, For matrix No. Line number The element values ​​of the column.

5. The component simulation method based on multi-field coupling according to claim 1, characterized in that, The step of marking mesh cells as strongly coupled regions, transition regions, or weakly coupled regions includes: When the local coupling strength index value is greater than or equal to the strong coupling threshold When the local coupling strength index value is less than or equal to the weak coupling threshold, the mesh cell is marked as a strongly coupled region; When the local coupling strength index value is greater than 1, the mesh cell is marked as a weakly coupled region; when the local coupling strength index value is greater than 1, the mesh cell is marked as a weakly coupled region. and less than When this occurs, the grid cell is marked as a transition region; in, Take the upper quartile of the local coupling strength index values ​​of all mesh elements. Take the lower quartile of the local coupling strength index values ​​of all mesh elements.

6. The component simulation method based on multi-field coupling according to claim 1, characterized in that, The process of performing a multiphysics global coupling solution on the strongly coupled region includes: For mesh elements in strongly coupled regions, an overall coupled set of equations for electromagnetic field, thermal field, and structural mechanical field is assembled. The material parameters of the electromagnetic field equation depend on the temperature value of the thermal field, the internal heat source term of the thermal field equation depends on the Joule heat distribution of the electromagnetic field, and the thermal load of the structural mechanical field equation depends on the temperature gradient of the thermal field. The equations of each field are solved simultaneously through the above dependencies.

7. The component simulation method based on multi-field coupling according to claim 1, characterized in that, The sequential iterative solution for the weakly coupled region includes: First, solve the electromagnetic field equations to obtain the electromagnetic field quantity distribution. Then, use the electromagnetic field quantity distribution as a known source term to input the thermal field equations to solve for the temperature distribution. Finally, use the temperature distribution as a known load to input the structural mechanics field equations to solve for the displacement and stress distribution.

8. The component simulation method based on multi-field coupling according to claim 1, characterized in that, The solution process involving boundary constraints on the transition region includes: The field values ​​shared by boundary nodes between adjacent strongly coupled and weakly coupled regions are extracted as boundary constraints for the transition region. Distance-based weighted interpolation constraints are applied to nodes within the transition region, where the distance from a certain internal node to the boundary of the strongly coupled region is denoted as . The distance to the boundary of the weakly coupled region is Then the weight of the strongly coupled region side and the weight of the weakly coupled region They are respectively: ； ； in This is the distance from the internal node to the boundary of the strongly coupled region. The interpolation weight is the distance from the internal node to the boundary of the weakly coupled region, and is used as the initial estimate when constraining the solution of the transition region.

9. The component simulation method based on multi-field coupling according to claim 1, characterized in that, When recalculating the cross sensitivity matrix based on the updated field quantity and repeatedly solving the partition, the partition label of a grid cell is only updated when the change in the local coupling strength index value of a certain grid cell relative to the previous iteration exceeds the preset stability threshold; grid cells whose change does not exceed the preset stability threshold retain their original labels.

10. A component simulation system based on multi-field coupling, used to execute the component simulation method based on multi-field coupling as described in any one of claims 1 to 9, characterized in that, include: The mesh discretization module is used to acquire the geometric model data, material property parameters and boundary conditions of components, perform finite element mesh discretization on the computational domain, and generate a set of mesh elements. The initial field quantity solution module is used to independently solve the electromagnetic field, thermal field and structural mechanical field, and obtain the initial field quantity values ​​at each grid element node; The coupling strength evaluation module is used to calculate the cross sensitivity matrix for each grid cell and extract the Frobenius norm of the cross sensitivity matrix to generate a local coupling strength index value. The partitioning and marking module is used to mark all grid cells as strongly coupled regions, transition regions, or weakly coupled regions based on the comparison results between the local coupling strength index value and the strong coupling threshold and weak coupling threshold, and to generate a set of computational domain partitioning and marking modules. The partitioned solution module is used to perform global coupled solution for strongly coupled regions, sequential iterative solution for weakly coupled regions, and solution with boundary constraints for transition regions, to obtain the field quantity results for all regions. The convergence judgment module is used to calculate the flux continuity residuals at the interfaces of each region. When the residuals exceed the preset allowable value, it triggers iterative updates and outputs the multi-field coupling simulation results of the components when the residuals converge.

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