Method and apparatus for predicting temperature change of electronic component based on pentahedron unit

Abstract

This invention provides a method and device for predicting temperature changes in electronic components based on pentahedral elements. The method includes: meshing the electronic component into pentahedral elements based on its structural parameters; determining the three-dimensional transient heat conduction governing equation and initial algebraic equation for the target region; determining correction terms based on the virtual node domain defined for the pentahedral elements, the Galerkin weight function, the three-dimensional transient heat conduction governing equation, and the initial algebraic equation; correcting the initial algebraic equation based on the correction terms to obtain the target algebraic equation; determining the final algebraic equation based on the target algebraic equation and a preset time interval; solving the final algebraic equation to obtain the transient heat conduction temperature simulation result; adjusting design parameters based on the transient heat conduction temperature simulation result; and implementing optimized design of the electronic component based on the adjusted design parameters.

Description

Technical Field

[0001] This disclosure relates to the field of equipment manufacturing technology, and in particular to a method and equipment for predicting temperature changes in electronic components based on pentahedral units. Background Technology

[0002] For heat generated by components such as CPUs, efficient heat dissipation is achieved through optimized design of component structure, shape, size, and material parameters. This controls temperature and thermal stress deformation within acceptable ranges to ensure operational safety and performance. With the miniaturization, weight reduction, high-speed operation, and multifunctionality of electronic devices, the optimized design of electronic components increasingly relies on high-precision temperature simulation and prediction.

[0003] The Galerkin finite element method is a primary method for solving transient heat conduction equations and predicting temperature changes in electronic components. However, problems such as its mesh generation mode dependence and increased numerical errors due to low element quality remain unresolved, affecting the accuracy of simulation results and the optimization of design parameters, and increasing the risk of damage to electronic components due to temperature changes and thermal stress deformation. Summary of the Invention

[0004] In view of the aforementioned problems, this disclosure provides a method and device for predicting the temperature change of electronic components based on pentahedral elements. The aim is to obtain the structural parameter information of the target object, determine the pentahedral elements and the three-dimensional transient heat conduction governing equation, determine the initial algebraic equation based on the Galerkin finite element method, and then determine the correction term by combining the virtual nodal domain to correct the initial algebraic equation, thereby obtaining a more accurate target algebraic equation. This provides high-precision simulation of the temperature change of electronic components under various anticipated operating conditions influenced by heat sources, heat conduction, and heat dissipation, thereby ensuring that the temperature change and thermal stress deformation of electronic components are within the allowable range, reducing or eliminating the risk of damage to electronic components due to temperature changes and thermal stress deformation.

[0005] As a first aspect of the present invention, an embodiment of the present invention provides a method for predicting the temperature change of electronic components based on pentahedral units, comprising:

[0006] The structural parameter information of the electronic components used as the target object is obtained to perform pentahedral mesh generation, and the three-dimensional transient heat conduction governing equation for the target region in the target object is determined.

[0007] Based on the Galerkin finite element method and the three-dimensional transient heat conduction governing equation, the initial algebraic equation for the discretization of the Galerkin finite element method for the target region is determined.

[0008] Based on the virtual node domain defined for the pentahedral element, the Galerkin weight function, the three-dimensional transient heat conduction governing equation, and the initial algebraic equation, the correction term is determined, wherein the virtual node domain is used to characterize the volume that satisfies the conservation law with second-order precision.

[0009] Based on the correction term, the initial algebraic equation is corrected to obtain the target algebraic equation for the target region. The final algebraic equation is determined based on the target algebraic equation and the preset time interval length. The final algebraic equation is solved to obtain the simulation results of the transient heat conduction temperature of the target region.

[0010] The design parameters are adjusted based on the transient heat conduction temperature simulation results, and the electronic components are optimized based on the adjusted design parameters to control the temperature and thermal stress deformation of the target area within the allowable range.

[0011] In a preferred embodiment, determining the correction term based on the virtual node domain defined for the pentahedral element, the Galerkin weight function, the three-dimensional transient heat conduction governing equation, and the initial algebraic equation includes:

[0012] The element temperature expression of the pentahedral element is determined based on the temperature of each node of the pentahedral element, the shape function of the pentahedral element, and the number of nodes in the pentahedral element.

[0013] Based on the element temperature expression of the pentahedral element, the left side of the initial algebraic equation is transformed to determine the first equation at the object node in the pentahedral element;

[0014] Based on the Euclidean distance between the object node and other nodes in the pentahedral element, and the target heat flux corresponding to the object node and the other nodes, the second equation at the object node in the pentahedral element is determined, wherein the target heat flux is the second-order precision heat flux at the midpoint of the connecting line segment between the two nodes and pointing from the object node to the other nodes.

[0015] According to the second equation, determine the virtual node domain of the object node in the pentahedral unit;

[0016] The correction term is determined based on the virtual node domain of the object node, the Galerkin weight function, the source term in the three-dimensional transient heat conduction governing equation, and the value of the partial derivative of temperature with respect to time at the geometric center of the element.

[0017] In a preferred embodiment, determining the element temperature expression of the pentahedral element based on the temperature of each node of the pentahedral element, the shape function of the pentahedral element, and the number of nodes in the pentahedral element includes:

[0018] The element temperature expression is determined based on the temperature of the nodes within the pentahedral element. Among them, N i Let be the shape function on the pentahedral element. The temperature of the i-th node is given, and the number 6 indicates that there are 6 nodes in the pentahedral element.

[0019] The step of transforming the left side of the initial algebraic equation based on the element temperature expression of the pentahedral element to determine the first equation at the object node in the pentahedral element includes:

[0020] The first equation can be represented by the following expression:

[0021]

[0022] Where λ represents the thermal conductivity coefficient, ▽ is the Nabla operator, · is the vector inner product, and P is the object node. Here, represents the Galerkin weight function, and the subscript 1 indicates the local node number of the element corresponding to the object node P. Let Galerkin weight function be the function corresponding to node 1. Let Σ be the integral over the pentahedral element e, and Σ be the mathematical summation symbol.

[0023] The step of determining the second equation at the object node in the pentahedral element based on the Euclidean distance between the object node and other nodes in the pentahedral element, and the target heat flux corresponding to the object node and the other nodes, includes:

[0024] The second equation can be expressed by the following expression:

[0025]

[0026] in, Let I be the midpoint of the line segment connecting nodes 1 and i. 1i At point i, the second-order accurate heat flux from node 1 to node i. Let I be the area of ​​the flow cross-section, which passes through the midpoint I. 1i The plane is perpendicular to the heat flux, and their product is used to evaluate the flow area with second-order accuracy. heat flux, x i y i and z iLet x1, y1, and z1 be the coordinates of node i, and let x1, y1, and z1 be the coordinates of node 1.

[0027] The step of determining the virtual node domain of the object node in the pentahedral unit according to the second equation includes:

[0028] With the flow cross section Let be the base, and node 1 be the vertex. The distance from the vertex to the base is... The virtual node domain elements are calculated. :

[0029]

[0030] Calculate the sum of the five virtual node domain elements of node 1 as a vertex to obtain the virtual node domain of node 1, i.e., object node P:

[0031]

[0032] When nodes 2, 3, 4, 5, and 6 of the pentahedral unit are taken as object nodes, the virtual node domains of each node are calculated using the same method, and then... , , , , This represents the virtual node fields of nodes 2, 3, 4, 5, and 6.

[0033] In a preferred embodiment, determining the correction term based on the virtual node domain of the object node, the Galerkin weight function, the source term in the three-dimensional transient heat conduction governing equation, and the value of the partial derivative of temperature with respect to time at the geometric center of the element includes:

[0034] The integral value of the function is obtained by performing unit integration based on the Galerkin weight function.

[0035] The first parametric expression is obtained based on the difference between the virtual node domain of the object node and the corresponding function integral value;

[0036] The second parameter is determined based on the source term and the value of the partial derivative of temperature with respect to time at the geometric center of the element in the three-dimensional transient heat conduction governing equation.

[0037] The correction term is determined based on the product between the first parametric expression and the second parametric expression.

[0038] In a preferred embodiment, the correction term Y is represented by the following expression:

[0039] Y= ;

[0040] The initial algebraic equation is expressed by the following expression:

[0041] ;

[0042] The objective algebraic equation is expressed by the following expression:

[0043] ;

[0044] in, Let λ be the temperature and λ be the thermal conductivity coefficient. For time, For source terms, Let be the partial derivative of temperature with respect to time, ▽ be the Nabla operator, and · be the vector inner product. Let be the Galerkin weight function, and let e be any pentahedral element surrounding the object node P. The integral is defined over the pentahedral element e, Σ is the mathematical summation symbol, and the subscript O is used to indicate the value at the geometric center of the pentahedral element. This is the virtual node field of the object node P.

[0045] In a preferred embodiment, the step of determining the final algebraic equation based on the target algebraic equation and a preset time interval length, solving the final algebraic equation, and obtaining the transient heat conduction temperature simulation results of the target region includes:

[0046] Based on the target algebraic equation and the time interval length, the final algebraic equation for transient heat conduction of the pentahedral element is obtained:

[0047] ,in, For time parameters, , and The instantaneous heat conduction temperature and time interval length at time n and (n-1) are respectively. , and The source terms at the geometric centers of the pentahedral elements at time n and (n-1) are... and The source terms at time n and time n-1 are respectively. and These are the instantaneous thermal conduction temperatures at the geometric center of the pentahedral unit at time n and time n-1, respectively.

[0048] Input initial conditions and set... n = 1, 2, 3, 4, ...;

[0049] By solving the final algebraic equation and progressively changing the value of n, the simulation results of the transient heat conduction temperature of the target region at each time step are obtained.

[0050] In a preferred embodiment, determining the initial algebraic equations for the Galerkin finite element method discretization of the target region based on the Galerkin finite element method and the three-dimensional transient heat conduction governing equations includes:

[0051] Based on the Galerkin finite element method and the three-dimensional transient heat conduction governing equation, the integral equation of the object node is determined; based on the integration by parts theorem and Gauss-Green's theorem, the derivative of the integral equation of the object node is reduced to determine the initial algebraic equation discretized by the Galerkin finite element method for the target region.

[0052] As a second aspect of the present invention, an embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in any one of the first aspects.

[0053] As a third aspect of the present invention, an embodiment of the present invention provides an electronic device, comprising:

[0054] A memory having a computer program stored thereon; a processor for executing the computer program in the memory to implement the steps of the method of any one of the first aspects.

[0055] Through the above technical solution, this disclosure can achieve at least the following effective effects:

[0056] By acquiring the structural parameters of the target object, the pentahedral element and the three-dimensional transient heat conduction governing equations are determined. After obtaining the initial algebraic equations based on the Galerkin finite element method, correction terms are determined according to the virtual nodal domain. This effectively solves the problems of inconsistency between the traditional Galerkin finite element method in evaluating heat inflow and outflow and considering heat change generation and dissipation, the inability to satisfy conservation laws with second-order accuracy, and the problem of the finite element equations not converging to differential equations. By correcting the initial algebraic equations with correction terms, the resulting target algebraic equations more accurately reflect the heat conduction process, thereby accurately determining the instantaneous heat conduction temperature that changes over time and obtaining reliable transient heat conduction temperature simulation results. Based on these results, design parameters are adjusted to keep temperature changes and thermal stress deformation within acceptable ranges, reducing or eliminating the risk of damage to electronic components due to temperature changes and thermal stress deformation.

[0057] Other features and advantages of this disclosure will be described in detail in the following detailed description section. Attached Figure Description

[0058] The accompanying drawings are provided to further illustrate the present disclosure and form part of the specification. They are used together with the following detailed description to explain the present disclosure, but do not constitute a limitation thereof. In the drawings:

[0059] Figure 1 This is a schematic diagram showing a right-angled triangular pyramidal unit and the flow area of ​​its nodes.

[0060] Figure 2 This is a schematic diagram showing a regular triangular pyramidal unit and the flow area of ​​its nodes.

[0061] Figure 3 This is a schematic diagram of a local mesh regarding convergence.

[0062] Figure 4 This is a schematic diagram of the execution flow of the method for predicting temperature changes of electronic components based on pentahedral units provided in an embodiment of the present invention.

[0063] Figure 5 This is a schematic diagram of the elements of a virtual node domain provided in an embodiment of the present invention.

[0064] Figure 6 This is a schematic diagram of exemplary hardware and software components of an electronic component temperature change prediction device based on pentahedral units provided in an embodiment of the present invention. Detailed Implementation

[0065] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0066] The specific embodiments of this disclosure will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit this disclosure.

[0067] Before introducing the method for predicting the temperature change of electronic components based on pentahedral units provided in this disclosure, we will first introduce the technical problems existing in the relevant scenarios.

[0068] by Figure 1 Taking the right-angled triangular pyramid shape shown as an example, we examine the conservation properties. That is, we stretch it along the vertically upward z-axis with a right-angled triangle in the xy-plane as the base, by h. zTaking the formed unit as an example, this unit has six nodes. The right-angled vertex of the base right-angled triangle is numbered 1. The unit is moved parallel to the origin. The unit is rotated around the z-axis so that the two right-angled sides of the base coincide with the +x and +y axes respectively. The node on the +x axis is numbered 2, and the node on the +y axis is numbered 3. The distances from the two nodes to node 1 are represented by h. x and h y This indicates that the nodes located above nodes 1, 2, and 3 are respectively numbered 4, 5, and 6.

[0069] First, taking node 1 as the object node P, the element integral result on the left side of the initial algebraic equation discretized by the Galerkin finite element method is:

[0070] (1)

[0071] like Figure 1 As shown in a, using To represent nodes and The midpoint of the line, using To represent the distance between two nodes, , Let i and j be the temperatures of nodes i and j, respectively. Midpoint From the node Flow to node The second-order precision heat flux. Therefore, the first term on the right side of equation (1) can be considered as... The square brackets [] contain a dot. The second-order accurate heat flux from node 1 to node 2 at point 2 and point 2 The weighted average of the second-order accurate heat flux from node 4 to node 5 at point 5, with coefficients... This is the flow area; multiplying the flow area and the heat flux gives the outflowing heat flux. This flow surface is perpendicular to the heat flux and passes through the midpoint. .

[0072] Similarly, the second item on the right It is a point The second-order accurate heat flux from node 1 to node 3 at point 3 and point 4 The weighted average of the second-order accurate heat flux from node 4 to node 6 at the flow area is obtained by passing through the flow area. The outflowing heat flux. This flow surface is perpendicular to the heat flux and passes through the midpoint. .

[0073] Similarly, the third item on the right It is a point The second-order accurate heat flux from node 1 to node 4 at point 4 The second-order accurate heat flux from node 2 to node 5 at point 5 and point 5 The weighted average of the second-order accurate heat flux from node 3 to node 6 at the flow area is obtained by passing through the flow area. The outflowing heat flux. The flow surface is perpendicular to the heat flux and passes through the midpoint. .

[0074] Next, taking node 3 as the object node P for further examination, the element integral result on the left side of the initial algebraic equation discretized by the Galerkin finite element method is: (2)

[0075] Similar to the discussion about node 1, the physical meaning of each term in the previous formula (2) is the heat flux estimated by second-order precision heat flux. Details are as follows... Figure 1 As shown in b. Comparing the two equations above, it is confirmed that the first term on the right side of equation (1) does not exist in equation (2). That is, the flow area of ​​the heat flux flowing out of node 1 is greater than that of node 3. .

[0076] On the other hand, let V represent the element volume, and perform element integration on the right side of the initial algebraic equation discretized by the Galerkin finite element method. When the transient and source terms are constant within the element, the integration result is shown in equation (3). The load is evenly distributed to each node:

[0077] (3)

[0078] It is evident that the initial algebraic equations discretized by the Galerkin finite element method use a different system when evaluating heat inflow and outflow than when considering heat changes over time and its generation and dissipation. This results in a failure to satisfy conservation laws at the second-order accuracy level.

[0079] like Figure 2 As shown, only when the element shape is a regular triangular pyramid, the flow area of ​​each node is equal, and the enclosed volume is V / 6, satisfying the conservation law at the second-order accuracy level. The regular triangular pyramid element is generally considered to have the highest simulation accuracy, which also corroborates the rationality of examining the conservation of heat flux based on second-order accuracy.

[0080] Furthermore, using units composed of eight pentahedral units... Figure 3 Taking the local mesh shown in Figure a as an example, we examine its convergence. Each element is a right-angled triangular pyramid as described in the conservation examination. Four elements form a layer, with the surfaces of the right-angled triangular elements placed in the 1st, 2nd, 3rd, and 4th quadrants of the z=0 plane, and connected to form a rhombus. Two layers are stacked along the z-direction. Taking the center node of this local mesh as P, the integral result of the initial algebraic equation discretized by the Galerkin finite element method, after Taylor expansion and other simplifications, can be written as equation (4).

[0081] (4)

[0082] At this point, the transient term and the source term are assumed to be constants. Equation (4) converges only to the original differential equation (6) in the z-direction, but does not converge in other directions.

[0083] Again Figure 3 Let's take a local mesh consisting of sixteen pentahedral elements as an example, as shown in b. Each element is a right-angled triangular pyramid as described in the conservation case. Eight elements form a layer, and two right-angled triangular element surfaces are placed in each quadrant of the z=0 plane and joined together to form a rectangle. Two layers are stacked along the z direction. Taking the center node of this local mesh as P, the integral result of the algebraic equation discretized by the Galerkin finite element method can be written as equation (5) after Taylor expansion and other simplifications:

[0084] (5)

[0085] At this point, assuming the transient term and the source term are constants, equation (5) converges to the original differential equation only in the z direction, and does not have convergence in other directions.

[0086] Therefore, it is evident that the initial algebraic equations obtained by discretization using the Galerkin finite element method have problems with conservation and convergence, and the resulting numerical errors will reduce the accuracy of the thermal conduction simulation results of electronic components based on the Galerkin finite element method.

[0087] This invention provides a method for predicting temperature changes in electronic components based on pentahedral units. (See also...) Figure 4 As shown, the method includes:

[0088] In step S11, the structural parameter information of the electronic components that are the target object is obtained to perform pentahedral element meshing, and the three-dimensional transient heat conduction governing equation for the target region in the target object is determined.

[0089] The structural parameters of electronic components refer to design parameters such as structural configuration, shape and size, and material parameters (e.g., thermal conductivity, specific heat capacity). A pentahedral element is a pentahedral element used in finite element analysis to discretize the target region, approximating a portion of the target object. Multiple such elements are combined to simulate the entire target object. The three-dimensional transient heat conduction governing equation is a mathematical equation describing the heat propagation within an object in three-dimensional space, considering temperature variations in three spatial dimensions and temperature changes over time.

[0090] In this embodiment of the disclosure, in finite element analysis, a continuous target region can be discretized into a finite number of elements. Pentahedral elements can approximate the complex geometry of the target region relatively well. The process of determining the shape of the pentahedral elements typically includes mesh generation.

[0091] First, a suitable meshing strategy is selected based on the electronic components of the target object, its heat dissipation environment, structural configuration, shape, size, and material parameters. For simple, regular shapes, a uniform mesh can be used, where each cell is roughly the same size and shape. For complex geometries, adaptive meshing is required, with meshes finer in areas of rapid temperature change or critical heat conduction to achieve a balance between accuracy and cost. These cells are interconnected, collectively covering the entire target area, transforming the continuous heat conduction problem into a problem of nodal temperature variations.

[0092] In this embodiment of the disclosure, the governing equation for the three-dimensional transient heat conduction problem is as follows:

[0093] (6)

[0094] in, λ represents temperature, and λ represents the thermal conductivity coefficient. Indicates time, It is the source item, It is the partial derivative of temperature with respect to time, called the transient term; ▽ is the Nabla operator; · represents the vector inner product; and we take a rectangular coordinate system (x, y, z).

[0095] In step S12, based on the Galerkin finite element method and the three-dimensional transient heat conduction governing equation, the initial algebraic equation for the discretization of the Galerkin finite element method for the target region is determined.

[0096] In this embodiment, the target region is first divided into multiple pentahedral elements. For each element, the three-dimensional transient heat conduction governing equation is discretized according to the selected Galerkin weight function and shape function. During discretization, the continuous temperature field is represented by an interpolation function of the nodal temperatures, and the partial derivative operations are transformed into algebraic operations between nodal temperatures. For example, the partial derivative of temperature with respect to spatial coordinates can be approximated by the partial derivative of the interpolation function. Then, the initial algebraic equations are obtained by integrating and summing the equations with respect to each surrounding element with the target node as the center. Treating each node as the target node, a simultaneous initial algebraic equation system is obtained. This equation system contains the temperature unknowns of all nodes within the target region.

[0097] In this embodiment of the disclosure, the Galerkin finite element method is applied to equation (6), and the integral equation of equation (7) is obtained for the object node P under consideration.

[0098] (7)

[0099] Here, Let be the Galerkin weight function, and let e represent any element surrounding the object node P. Let Σ denote the integral over the element and Σ denote the sum of the integrals of all surrounding elements. Applying the integration by parts theorem and Gauss-Green's theorem to the element integral on the left side of equation (7), we perform derivative reduction to obtain the initial algebraic equation (8) as the discretization of the Galerkin finite element method:

[0100] (8)

[0101] In step S13, correction terms are determined based on the virtual node domain defined for the pentahedral element, the Galerkin weighted function, the three-dimensional transient heat conduction governing equation, and the initial algebraic equation.

[0102] In finite element analysis, shape functions are used to describe the changes in physical quantities (such as temperature) at each point within an element as a function of nodal physical quantities. They reflect the distribution law of physical quantities within the element.

[0103] The virtual nodal domain reflects the heat flow in and out of the system enclosed by the surfaces when applying the conservation law with second-order accuracy. For example, the virtual nodal domain of the node at the right-angle vertex of a right-angled triangular pyramid element is 8V / 36, while the virtual nodal domain of other nodes is 5V / 36. To satisfy the conservation law at second-order accuracy, the integral volume of the load needs to be determined according to the size of the virtual nodal domain. The correction term is used to modify the initial algebraic equations based on the consistency between the two systems at second-order accuracy, making them more accurately describe the heat conduction process and improving the accuracy of the simulation.

[0104] In step S14, the initial algebraic equation is modified according to the modification term to obtain the target algebraic equation for the target region. The final algebraic equation is determined according to the target algebraic equation and the preset time interval length. The final algebraic equation is solved to obtain the simulation results of the transient heat conduction temperature of the target region.

[0105] In this embodiment, the determined correction terms are substituted into the initial algebraic equation to correct it. The correction process involves adjusting the loads at the nodes to ensure the equations satisfy the conservation laws with higher precision. After correction, a target algebraic equation for the target region is obtained. This target algebraic equation more accurately reflects the generation, changes, and conduction of heat within the target region than the initial algebraic equation, providing a more reliable foundation for subsequent high-precision temperature calculations.

[0106] Furthermore, based on the target algebraic equation, a preset time interval length is set. The selection of the time interval length needs to consider both computational accuracy and efficiency. A time interval that is too small will increase the computational load but will more accurately describe the temperature change over time; a time interval that is too large will reduce computational accuracy but will reduce computation time. For example, a time parameter can be used. The method discretizes the time partial derivatives in the objective algebraic equation to obtain the final algebraic equation. Solving the final algebraic equation yields the instantaneous thermal conduction temperature of the target region over time, ultimately forming the transient thermal conduction temperature simulation result for the target region. This result is a time-varying temperature curve or temperature field distribution, which can intuitively reflect the heating, conduction, and heat dissipation of electronic components in the target region. Using the time parameter... The method for discrete-time partial derivatives is a second-order precision numerical method that uses the mean value theorem.

[0107] In step S15, the design parameters are adjusted according to the transient heat conduction temperature simulation results, and the electronic components are optimized according to the adjusted design parameters to control the temperature and thermal stress deformation of the target area within the allowable range.

[0108] The tolerance ranges for temperature and thermal stress deformation vary depending on the specific characteristics of the target area. For example, the tolerance ranges for temperature and thermal stress deformation can differ between the chip core area, pin connection area, and package casing. For instance, the core area typically allows a maximum junction temperature of 100-125°C. Exceeding this range can lead to increased transistor leakage current, performance degradation, and even permanent damage.

[0109] The coefficient of thermal expansion (CTE) of the silicon-based chip in the core area is typically around 2.6 ppm / °C, which differs significantly from the CTE of the packaging material (e.g., organic substrates, CTE ≈ 15-20 ppm / °C). The maximum permissible thermal stress deformation must be controlled within the micrometer range (e.g., <5μm), otherwise it may lead to solder joint fatigue or interlayer delamination. Larger mechanical deformation (e.g., lead bending <0.1mm) is permissible at the package edge areas, but the reliability of the electrical connections must be ensured.

[0110] In this embodiment, design parameters are adjusted based on temperature simulation results. These design parameters include the structural configuration, shape, size, and material parameters of electronic components, as well as the power of the heat source, the environmental heat dissipation method, and the power of the heat dissipation equipment.

[0111] The aforementioned technical solution first determines the pentahedral element and the three-dimensional transient heat conduction governing equation by acquiring the structural parameter information of the target object. Secondly, after obtaining the initial algebraic equation based on the Galerkin finite element method, correction terms are determined according to the virtual nodal domain. This effectively solves the problems of inconsistency between the traditional Galerkin finite element method in evaluating heat inflow and outflow and considering the generation and dissipation of heat changes, the inability to satisfy conservation laws with second-order accuracy, and the problem of the finite element equation not converging to the differential equation. By correcting the initial algebraic equation using the correction terms, the resulting target algebraic equation more accurately reflects the heat conduction process, thereby accurately determining the instantaneous heat conduction temperature change over time and obtaining reliable transient heat conduction temperature simulation results. Adjusting the design parameters based on these results can greatly improve the accuracy of predicting the temperature and thermal stress deformation of electronic components under various operating conditions, thus ensuring that they remain within acceptable ranges and reducing or eliminating the risk of damage to electronic components due to temperature changes and thermal stress deformation.

[0112] In a preferred embodiment, step S13, determining the correction term based on the virtual node domain defined for the pentahedral element, the Galerkin weight function, the three-dimensional transient heat conduction governing equation, and the initial algebraic equation, includes:

[0113] In step S131, the element temperature expression of the pentahedral element is determined based on the temperature of each node of the pentahedral element, the shape function of the pentahedral element, and the number of nodes in the pentahedral element.

[0114] For pentahedral elements, shape functions are typically a set of polynomial functions that take a value of 1 at a certain node and a value of 0 at other nodes. Through linear combinations of these shape functions, the temperature at any point within the element can be continuously and approximately represented. The specific form of the shape functions can be derived from the element geometry and node coordinates. The properties of the shape functions also guarantee the continuity of temperature at the element boundaries.

[0115] In this embodiment of the disclosure, the temperature at any point, the average temperature of the unit, or other parameters representing the overall temperature characteristics of the unit can be obtained using the unit temperature expression.

[0116] In step S132, the left side of the initial algebraic equation is transformed according to the element temperature expression of the pentahedral element to determine the first equation at the object node in the pentahedral element.

[0117] The first equation is a transition to the second equation.

[0118] In step S133, based on the Euclidean distance between the object node and other nodes in the pentahedral unit, and the target heat flux corresponding to the object node and the other nodes, a second equation is determined at the object node in the pentahedral unit, wherein the target heat flux is the second-order precision heat flux at the midpoint of the connecting line segment between the two nodes and pointing from the object node to the other nodes.

[0119] Heat flux represents the amount of heat passing through a unit area per unit time, and it is an important physical quantity describing the intensity of heat conduction. Heat flux is calculated according to Fourier's law q = −k∇T (where q is the heat flux, k is the thermal conductivity, and ∇T is the temperature gradient). The heat flux at the midpoint of the line segment connecting two nodes is used here because, within a linear element, only at this point does it possess second-order accuracy.

[0120] Furthermore, based on the Euclidean distance between nodes and the target heat flux, a second equation can be established at the nodes of the pentahedral element. This equation lays the foundation for the definition of the virtual nodal domain based on conservation laws.

[0121] In step S134, the virtual node domain of the object node in the pentahedral unit is determined according to the second equation.

[0122] In step S135, a correction term is determined based on the virtual node domain of the object node, the Galerkin weight function, the source term in the three-dimensional transient heat conduction governing equation, and the value of the partial derivative of temperature with respect to time at the geometric center of the element.

[0123] In this embodiment, the loads generated by the source term and the partial derivative of temperature with respect to time in the Galerkin method are adjusted through a virtual nodal domain according to the conservation law. The correction term uses the values ​​of the partial derivatives of the source term and temperature with respect to time at the centroid of the element. This is because it is simple to calculate and the value at the centroid has a certain degree of element averaging, which can also be used when correcting the loads at other nodes of the element.

[0124] In a preferred embodiment, step S131, determining the element temperature expression of the pentahedral element based on the temperature of each node of the pentahedral element, the shape function of the pentahedral element, and the number of nodes in the pentahedral element, includes:

[0125] The element temperature expression is determined based on the temperature of the nodes within the pentahedral element. Among them, N i Let be the shape function on the pentahedral element. The temperature of the i-th node is given, and the number 6 indicates that there are 6 nodes in the pentahedral element.

[0126] In step S132, the transformation of the left side of the initial algebraic equation based on the element temperature expression of the pentahedral element to determine the first equation at the node in the pentahedral element includes:

[0127] The first equation can be represented by the following expression (9):

[0128] (9)

[0129] Where λ represents the thermal conductivity coefficient, ▽ is the Nabla operator, · is the vector inner product, and P is the object node. Here, represents the Galerkin weight function, and the subscript 1 indicates the local node number of the element corresponding to the object node P. Let Galerkin weight function be the function corresponding to node 1. Let Σ be the integral over the pentahedral element e, and Σ be the mathematical summation symbol.

[0130] In step S133, determining the second equation at the object node in the pentahedral unit based on the Euclidean distance between the object node and other nodes in the pentahedral unit, and the target heat flux corresponding to the object node and the other nodes, includes:

[0131] The second equation can be represented by the following expression (10):

[0132] (10)

[0133] The derivation of equation (10) utilizes the proven relation. .in, Let I be the midpoint of the line segment connecting nodes 1 and i. 1i At point i, the second-order accurate heat flux from node 1 to node i. Let I be the area of ​​the flow cross-section, which passes through the midpoint I. 1i The plane is perpendicular to the heat flux, and their product is used to evaluate the flow area with second-order accuracy. heat flux, x i y i and z i Let x1, y1, and z1 be the coordinates of node i, and let x1, y1, and z1 be the coordinates of node 1.

[0134] In step S134, determining the virtual node domain of the object node in the pentahedral unit according to the second equation includes:

[0135] With the flow cross section Let be the base, and node 1 be the vertex. The distance from the vertex to the base is... The virtual node domain elements are calculated as shown in expression (11). :

[0136] (11)

[0137] Calculate the sum of the five virtual node domain elements of node 1 as a vertex, and obtain node 1 as shown in expression (12), that is, the virtual node domain of object node P:

[0138] (12)

[0139] When nodes 2, 3, 4, 5, and 6 of the pentahedral unit are taken as object nodes, the virtual node domains of each node are calculated using the same method, and then respectively... , , , , This represents the virtual node fields of nodes 2, 3, 4, 5, and 6.

[0140] In a preferred embodiment, step S14, determining the correction term based on the virtual node domain of the object node, the Galerkin weighted function, the source term in the three-dimensional transient heat conduction governing equation, and the value of the partial derivative of temperature with respect to time at the geometric center of the element, includes:

[0141] In step S141, unit integration is performed according to the Galerkin weighted function to obtain the function integral value.

[0142] In step S142, the first parametric expression is obtained based on the difference between the virtual node domain of the object node and the corresponding function integral value.

[0143] The difference reflects the discrepancy between the volume enclosed by the heat flux inflow / outflow surfaces around the node, represented by the virtual node domain, and the volume obtained by the element surface integral after weighting using the Galerkin weighting function. Physically, the difference reflects the inconsistency between considering the volume enclosed by the heat flux inflow / outflow surfaces around the node and considering the volume generated and dissipated due to heat changes. This inconsistency violates conservation laws and is caused by the use of elements with shapes other than regular triangular prisms. For regular triangular prism elements, the difference is zero. Compared to pentahedral elements of other shapes, regular triangular prism elements offer the highest accuracy; however, for target regions with complex shapes, it is necessary to use elements with shapes other than regular triangular prisms extensively.

[0144] In step S143, the second parameter is determined based on the source term in the three-dimensional transient heat conduction governing equation and the value of the partial derivative of temperature with respect to time at the geometric center of the unit.

[0145] In this embodiment of the disclosure, the source term and the partial derivative of temperature with respect to time are summed because the sum represents the change and generation / decrease of heat in the conservation law.

[0146] In step S144, the correction term is determined based on the product between the first parametric expression and the second parametric expression.

[0147] In this embodiment, the initial algebraic equations suffer from conservation and convergence issues, and cannot accurately describe the actual heat conduction process when pentahedral elements other than regular triangular prisms are used. However, when the target region has a complex shape, or when pentahedral elements other than regular triangular prisms must be used at the boundaries, the shortcomings of the initial algebraic equations can be compensated for, improving the accuracy of the numerical simulation. For example, when right-angled triangular prism elements are used, the correction term for the node corresponding to the right-angle vertex is positive, increasing the load on that node to match its larger heat flow area.

[0148] The theoretical basis for load correction is explained below: For regular triangular pyramidal elements... The correction term is zero. This type of element itself does not have a conservation problem. For elements of a general shape, the first term... The resulting nodal loads can be considered to originate from the load on the element volume V. P The weighted transient and source terms. The correction term introduced for the Galerkin finite element method is obtained by subtracting from the virtual node domain. Then, multiplying by the transient and source terms at the geometric center, the loads distributed to each node vary with the element shape. Adding the first and second terms highlights both the contribution of the transient and source terms near the node to the nodal load and emphasizes the role of the virtual nodal domain in improving the conservation of the nodal hierarchy. Especially when the transient phase and source terms are constants in the element, the area within the brackets on the right-hand side of the objective algebraic equation is directly simplified to... This means that the system volume considering transient and source terms is equal to the volume of the system enclosed by the flow cross-section when considering heat inflow and outflow with second-order precision. Compared with the Galerkin method, it satisfies the conservation law with higher precision.

[0149] Based on the theoretical support for conservation at the element level, for elements of arbitrary shape, it has been theoretically proven that the sum of the virtual node domains of its six nodes equals the volume of the element, as shown in expression (13):

[0150] (13)

[0151] This indicates that although the introduction of the correction term alters the load distribution at the nodes, the sum of the load distributions at each node of the element remains unchanged, still equal to the sum of the changes and eliminations at that element. This means that the objective algebraic equation strictly satisfies the conservation law even at the element level.

[0152] Regarding the convergence of the differential equation, for simplicity, it is assumed that the transient term and the source term are constants in the local mesh around the object node P, then we have the expression shown in expression (14):

[0153] (14)

[0154] See Figure 3 As shown in figure a, the virtual node domain of the central node is formed by eight right-angled triangular pyramidal elements. The formula obtained after Taylor expansion and other simplifications is shown in expression (15):

[0155] (15)

[0156] The coefficient 16V / 9 originates from eight units. Similarly... Figure 3 As shown in b, the virtual node domain of the central node, which is enclosed by sixteen right-angled triangular pyramidal units, is... This can be rearranged to obtain expression (16):

[0157] (16)

[0158] As can be seen, the introduction of the correction term makes the differential equation converge to the mean in the x, y, and z directions, thus improving the convergence compared to the Galerkin method. The convergence test is performed with the element size approaching zero; therefore, assuming that the transient and source terms are constants does not affect the convergence conclusion.

[0159] In a preferred embodiment, the modification term Y is represented by the following expression (17):

[0160] Y= (17)

[0161] The initial algebraic equation is expressed by the following expression (18):

[0162] (18)

[0163] The target algebraic equation is expressed by the following expression (19):

[0164] (19)

[0165] in, Let λ be the temperature and λ be the thermal conductivity coefficient. For time, For source terms, Let be the partial derivative of temperature with respect to time, ▽ be the Nabla operator, and · be the vector inner product. Let be the Galerkin weight function, and let e be any pentahedral element surrounding the object node P. The integral is defined over the pentahedral element e, Σ is the mathematical summation symbol, and the subscript O is used to indicate the value at the geometric center of the pentahedral element. This is the virtual node field of the object node P.

[0166] In a preferred embodiment, the step of determining the final algebraic equation based on the target algebraic equation and a preset time interval length, solving the final algebraic equation, and obtaining the transient heat conduction temperature simulation results of the target region includes:

[0167] Based on the target algebraic equation and the time interval, the final algebraic equation for the transient heat conduction of the pentahedral unit is obtained, as shown in expression (20):

[0168] (20)

[0169] in, For time parameters, , and The instantaneous heat conduction temperature and time interval length at time n and (n-1) are respectively. , and The source terms at the geometric centers of the pentahedral elements at time n and (n-1) are... and The source terms at time n and time n-1 are respectively. and These are the instantaneous thermal conduction temperatures at the geometric center of the pentahedral unit at time n and time n-1, respectively.

[0170] Input initial conditions and set... n = 1, 2, 3, 4, ... By solving the final algebraic equation and progressively changing the value of n, the simulation results of the transient heat conduction temperature of the target region at each time step are obtained.

[0171] In a preferred embodiment, step S12, determining the initial algebraic equations discretized by the Galerkin finite element method for the target region based on the Galerkin finite element method and the three-dimensional transient heat conduction governing equation, includes:

[0172] In step S121, based on the Galerkin finite element method and the three-dimensional transient heat conduction governing equation, the element integral of each surrounding pentahedral element is calculated for each object node in the target region.

[0173] In this embodiment of the disclosure, for an object node, the element integral of each surrounding pentahedral element is calculated. There may be multiple pentahedral elements surrounding the object node. When calculating the element integral, the three-dimensional transient heat conduction governing equation is first multiplied by the Galerkin weight function, and then integrated within the element to obtain the element integral.

[0174] In step S122, the integral equation for the target region is determined by summing the integrals of the units corresponding to the nodes.

[0175] In this embodiment of the disclosure, the Galerkin finite element method is applied, and the integral equation obtained for the considered object node P is shown in expression (21):

[0176] (twenty one)

[0177] In step S123, based on the integration by parts theorem and Gauss-Green's theorem, the derivative of the integral function is reduced in order to determine the initial algebraic equation for the discretization of the Galerkin finite element method for the target region.

[0178] In this embodiment of the disclosure, the temperature field is approximated.

[0179] By substituting the approximate expression for temperature and the Galerkin weight function into the integral equation, the integral equation is transformed into a linear algebraic equation about the nodal temperatures, i.e., the initial algebraic equation.

[0180] This invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of any of the methods described in the foregoing embodiments.

[0181] An embodiment of the present invention provides an electronic device, comprising:

[0182] A memory on which computer programs are stored;

[0183] A processor for executing the computer program in the memory to implement the steps of any of the methods described in the foregoing embodiments.

[0184] Figure 6The illustrated pentahedral cell-based electronic component temperature change prediction device 100 includes a processor 1001 and a memory 1003. The processor 1001 and memory 1003 are connected, for example, via a bus 1002. The pentahedral cell-based electronic component temperature change prediction device 100 may further include a communication component 1004, which can be used for data interaction between the device 100 and other devices, such as data transmission and / or data reception. It should be noted that in actual operation, the communication component 1004 is not limited to one. The structure of this pentahedral cell-based electronic component temperature change prediction device 100 does not constitute a limitation on the embodiments of this application.

[0185] Processor 1001 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. Processor 1001 may also be a combination that implements computing functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0186] Bus 1002 may include a pathway for transmitting information between the aforementioned components. Bus 1002 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Bus 1002 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 6 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0187] The memory 1003 may be ROM (Read Only Memory) or other types of static storage devices capable of storing static information and instructions, RAM (Random Access Memory) or other types of dynamic storage devices capable of storing information and instructions, or EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media, other magnetic storage devices, or any other medium capable of carrying or storing program code and capable of being read by a computer, without limitation herein.

[0188] The memory 1003 is used to store program code for executing embodiments of the present disclosure, and its execution is controlled by the processor 1001. The processor 1001 is used to execute the program code stored in the memory 1003 to implement the steps shown in the foregoing embodiments of the method for predicting temperature changes of electronic components based on pentahedral units.

[0189] The preferred embodiments of the present disclosure have been described in detail above with reference to the accompanying drawings. However, the present disclosure is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present disclosure, various changes, modifications, substitutions and variations can be made to these embodiments, and all such changes, modifications, substitutions and variations fall within the protection scope of the present disclosure.

[0190] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction, and such combinations should also be considered as part of this disclosure. To avoid unnecessary repetition, this disclosure will not further describe the various possible combinations. The technical scope of this application is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for predicting temperature changes in electronic components based on pentahedral units, characterized in that, include: The structural parameter information of the electronic components used as the target object is obtained to perform pentahedral mesh generation, and the three-dimensional transient heat conduction governing equation for the target region in the target object is determined. Based on the Galerkin finite element method and the three-dimensional transient heat conduction governing equation, the initial algebraic equation for the discretization of the Galerkin finite element method for the target region is determined. Based on the virtual node domain defined for the pentahedral element, the Galerkin weight function, the three-dimensional transient heat conduction governing equation, and the initial algebraic equation, the correction term is determined, wherein the virtual node domain is used to characterize the volume that satisfies the conservation law with second-order precision. Based on the correction term, the initial algebraic equation is corrected to obtain the target algebraic equation for the target region. The final algebraic equation is determined based on the target algebraic equation and the preset time interval length. The final algebraic equation is solved to obtain the simulation results of the transient heat conduction temperature of the target region. The design parameters are adjusted based on the transient heat conduction temperature simulation results, and the electronic components are optimized based on the adjusted design parameters to control the temperature and thermal stress deformation of the target area within the allowable range.

2. The method for predicting temperature changes of electronic components based on pentahedral units according to claim 1, characterized in that, The step of determining correction terms based on the virtual node domain defined for the pentahedral element, the Galerkin weight function, the three-dimensional transient heat conduction governing equation, and the initial algebraic equation includes: The element temperature expression of the pentahedral element is determined based on the temperature of each node of the pentahedral element, the shape function of the pentahedral element, and the number of nodes in the pentahedral element. Based on the element temperature expression of the pentahedral element, the left side of the initial algebraic equation is transformed to determine the first equation at the object node in the pentahedral element; Based on the Euclidean distance between the object node and other nodes in the pentahedral element, and the target heat flux corresponding to the object node and the other nodes, the second equation at the object node in the pentahedral element is determined, wherein the target heat flux is the second-order precision heat flux at the midpoint of the connecting line segment between the two nodes and pointing from the object node to the other nodes. According to the second equation, determine the virtual node domain of the object node in the pentahedral unit; The correction term is determined based on the virtual node domain of the object node, the Galerkin weight function, the source term in the three-dimensional transient heat conduction governing equation, and the value of the partial derivative of temperature with respect to time at the geometric center of the element.

3. The method for predicting temperature changes of electronic components based on pentahedral units according to claim 2, characterized in that, The step of determining the element temperature expression of the pentahedral element based on the temperature of each node of the pentahedral element, the shape function of the pentahedral element, and the number of nodes in the pentahedral element includes: The element temperature expression is determined based on the temperature of the nodes within the pentahedral element. , where N i Let be the shape function on the pentahedral element. The temperature of the i-th node is given, and the number 6 indicates that there are 6 nodes in the pentahedral element. The step of transforming the left side of the initial algebraic equation based on the element temperature expression of the pentahedral element to determine the first equation at the object node in the pentahedral element includes: The first equation can be represented by the following expression: Where λ represents the thermal conductivity coefficient, ▽ is the Nabla operator, · is the vector inner product, and P is the object node. Here, represents the Galerkin weight function, and the subscript 1 indicates the local node number of the element corresponding to the object node P. Let Galerkin weight function be the function corresponding to node 1. Let Σ be the integral over the pentahedral element e, and Σ be the mathematical summation symbol. The step of determining the second equation at the object node in the pentahedral element based on the Euclidean distance between the object node and other nodes in the pentahedral element, and the target heat flux corresponding to the object node and the other nodes, includes: The second equation can be expressed by the following expression: in, Let I be the midpoint of the line segment connecting nodes 1 and i. 1i At point i, the second-order accurate heat flux from node 1 to node i. Let I be the area of ​​the flow cross-section, which passes through the midpoint I. 1i The plane is perpendicular to the heat flux, and their product is used to evaluate the flow area with second-order accuracy. heat flux, x i y i and z i Let x1, y1, and z1 be the coordinates of node i, and let x1, y1, and z1 be the coordinates of node 1. The step of determining the virtual node domain of the object node in the pentahedral unit according to the second equation includes: With the flow cross section Let be the base, and node 1 be the vertex. The distance from the vertex to the base is... The virtual node domain elements are calculated. : Calculate the sum of the five virtual node domain elements of node 1 as a vertex to obtain the virtual node domain of node 1, i.e., object node P: When nodes 2, 3, 4, 5, and 6 of the pentahedral unit are taken as object nodes, the virtual node domains of each node are calculated using the same method, and then... , , , , This represents the virtual node fields of nodes 2, 3, 4, 5, and 6.

4. The method for predicting temperature changes of electronic components based on pentahedral units according to claim 2, characterized in that, The step of determining the correction term based on the virtual node domain of the object node, the Galerkin weight function, the source term in the three-dimensional transient heat conduction governing equation, and the value of the partial derivative of temperature with respect to time at the geometric center of the element includes: The integral value of the function is obtained by performing unit integration based on the Galerkin weight function. The first parametric expression is obtained based on the difference between the virtual node domain of the object node and the corresponding function integral value; The second parameter is determined based on the source term and the value of the partial derivative of temperature with respect to time at the geometric center of the element in the three-dimensional transient heat conduction governing equation. The correction term is determined based on the product between the first parametric expression and the second parametric expression.

5. The method for predicting temperature changes of electronic components based on pentahedral units according to claim 4, characterized in that, The correction term Y is represented by the following expression: Y= ； The initial algebraic equation is expressed by the following expression: ； The objective algebraic equation is expressed by the following expression: ； in, Let λ be the temperature and λ be the thermal conductivity coefficient. For time, For source terms, Let be the partial derivative of temperature with respect to time, ▽ be the Nabla operator, and · be the vector inner product. Let be the Galerkin weight function, and let e be any pentahedral element surrounding the object node P. The integral is defined over the pentahedral element e, Σ is the mathematical summation symbol, and the subscript O is used to indicate the value at the geometric center of the pentahedral element. This is the virtual node field of the object node P.

6. The method for predicting temperature changes of electronic components based on pentahedral units according to claim 5, characterized in that, The process of determining the final algebraic equation based on the target algebraic equation and a preset time interval, solving the final algebraic equation, and obtaining the transient heat conduction temperature simulation results of the target region includes: Based on the target algebraic equation and the time interval length, the final algebraic equation for transient heat conduction of the pentahedral element is obtained: ,in, For time parameters, , and The instantaneous heat conduction temperature and time interval length at time n and (n-1) are respectively. , and The source terms at the geometric centers of the pentahedral elements at time n and (n-1) are... and The source terms at time n and time n-1 are respectively. and These are the instantaneous thermal conduction temperatures at the geometric center of the pentahedral unit at time n and time n-1, respectively. Input initial conditions and set... n = 1, 2, 3, 4, ...; By solving the final algebraic equation and progressively changing the value of n, the simulation results of the transient heat conduction temperature of the target region at each time step are obtained.

7. The method for predicting temperature changes of electronic components based on pentahedral units according to any one of claims 1-6, characterized in that, The initial algebraic equations for the discretization of the Galerkin finite element method for the target region, based on the Galerkin finite element method and the three-dimensional transient heat conduction governing equation, are determined, including: Based on the Galerkin finite element method and the three-dimensional transient heat conduction governing equation, the integral equation of the object node is determined. Based on the integral by parts theorem and Gauss-Green theorem, the derivative of the integral equation of the object node is reduced to determine the initial algebraic equation for the discretization of the Galerkin finite element method for the target region.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method described in any one of claims 1-7.

9. An electronic device, characterized in that, include: A memory on which computer programs are stored; A processor for executing the computer program in the memory to implement the steps of the method according to any one of claims 1-7.

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