Integrated circuit electrical characteristic simulation methods, devices, terminals, and storage media

Abstract

This application discloses a method, device, terminal, and storage medium for simulating the electrical characteristics of integrated circuits. The method includes acquiring a model of the integrated circuit to be simulated; meshing the model to obtain an integrated circuit mesh dataset composed of multiple mesh cells; constructing corresponding charge basis functions and current basis functions based on the mesh cells; using the charge basis functions as the fusion object, progressively merging and updating the charge basis functions; simultaneously, merging and updating the current basis functions through geometric mapping; after all fusion and updates are completed, acquiring the integrated circuit basis function dataset; and performing electrical characteristic simulation on the integrated circuit to be simulated based on the integrated circuit basis function dataset. This achieves rapid updating and low-order representation of complex coupling capacitance matrices, reducing the theoretical complexity from O(n^2) to O(n^2) of traditional back-end order reduction methods. 3 The time complexity is reduced to O(n), while the model accuracy and order reduction effect are maintained, and the efficiency of model order reduction is greatly improved.

Description

Technical Field

[0001] This application relates to the field of electronic design automation technology, and in particular to a method, apparatus, terminal and storage medium for simulating the electrical characteristics of integrated circuits. Background Technology

[0002] In integrated circuit simulation, boundary conditions are applied to the field integral equations using a matching program to construct the system equations. After solving these system equations, the resulting current and charge distributions are used to evaluate the integrated circuit system performance. However, with increasing operating frequency, larger integration scale, and increased device structural complexity, the order of the system equations grows exponentially. The enormous computational overhead of solving such high-order systems directly restricts the practical application of rapid optimization programs in electronic design automation (EDA).

[0003] Currently, model reduction techniques are commonly used to reduce the order of a system, that is, to represent the original system with an equivalent low-order system, thereby accelerating simulation. Among these techniques, the Partial Component Equivalent Circuit (PEEC) model reduction method has advantages over other techniques, as it can construct a compact equivalent macro-model and establish the relationship between physical design features and low-order equivalent circuit models under quasi-static or even full-wave descriptions. However, the computational complexity of this model reduction method is O(n³), which faces a severe computational efficiency challenge in the simulation and optimization scenarios of high-frequency large-scale integrated circuits.

[0004] Therefore, there is an urgent need for a method to reduce the model order and improve simulation efficiency in the process of simulating the electrical characteristics of integrated circuits. Summary of the Invention

[0005] In view of the shortcomings of the prior art described above, the purpose of this application is to provide a method, apparatus, storage medium and terminal for simulating the electrical characteristics of integrated circuits, in order to solve the problem that the constructed system equations have a high order in the current process of simulating the electrical characteristics of integrated circuits, resulting in high computational complexity and a serious challenge to computational efficiency.

[0006] The first aspect of this application proposes a method for simulating the electrical characteristics of an integrated circuit, including:

[0007] Obtain the integrated circuit model to be simulated, perform mesh partitioning on the integrated circuit model to obtain an integrated circuit mesh dataset composed of multiple mesh cells, and construct the corresponding charge basis function and current basis function based on the mesh cells;

[0008] Using the charge basis function as the fusion object, a target charge basis function and its adjacent charge basis functions are selected successively. The target charge basis function is discretized and fused into the adjacent charge basis functions to achieve the gradual fusion and update of the charge basis function. At the same time, the current basis function is fused and updated accordingly through geometric mapping.

[0009] After all fusion updates are completed, the integrated circuit basis function dataset is obtained, and the electrical characteristics simulation of the integrated circuit to be simulated is performed based on the integrated circuit basis function dataset.

[0010] In some embodiments of this application, selecting a target charge basis function and its adjacent charge basis functions, discretizing the target charge basis function, and fusing it into the adjacent charge basis functions to achieve the fusion update of the charge basis functions includes:

[0011] Determine a target charge basis function to be absorbed, and a plurality of adjacent charge basis functions that are geometrically adjacent to the target charge basis function;

[0012] The target charge basis function is discretized into X parts and evenly distributed to all the adjacent charge basis functions. Based on the original scalar potential corresponding to each adjacent charge basis function and the fused scalar potential represented by the discrete charge basis functions, the potential equation corresponding to each adjacent charge basis function is constructed.

[0013] By locally solving each of the potential equations, the basis functions of each adjacent charge are updated;

[0014] Wherein, the target charge basis function is any charge basis function to be absorbed in the integrated circuit grid dataset, and X is the number of all the adjacent charge basis functions.

[0015] In some embodiments of this application, the potential equations corresponding to the adjacent charge basis functions are constructed based on the original scalar potentials corresponding to the adjacent charge basis functions and the fused scalar potentials represented by the discrete charge basis functions, including:

[0016] Based on the discrete electric field integral equation, the original scalar potential corresponding to the basis functions of the adjacent charges is calculated;

[0017] Based on the discretized target charge basis function, the scalar potential of the adjacent charge basis functions is calculated, which is used as the fused scalar potential represented by the discrete charge basis function.

[0018] The potential equations corresponding to the adjacent charge basis functions are constructed by matching the original scalar potentials of the adjacent charge basis functions with the fused scalar potentials represented by the discrete charge basis functions using the Galerkin method.

[0019] In some embodiments of this application, updating the basis functions of adjacent charges by locally solving the potential equation includes:

[0020] The principal guiding coefficients of the potential equation are reduced in order through parameter transformation, and the unknown parameters in the basis function architecture are solved by combining the combined charge basis function architecture.

[0021] Substitute the unknown parameters obtained from the solution into the combined charge basis function architecture to obtain the updated adjacent charge basis functions;

[0022] The combined charge basis function is a charge basis function that combines the adjacent charge basis functions with the discrete target charge basis function.

[0023] In some embodiments of this application, the combined charge basis function architecture is as follows:

[0024]

[0025] in Let be the combined charge basis function architecture corresponding to the i-th adjacent charge basis function after fusion and update. This represents the equivalent area corresponding to the i-th adjacent charge basis function before the fusion update. Let i be the charge basis function corresponding to the i-th adjacent charge basis function before the fusion update. This represents the equivalent area corresponding to the target charge basis function before fusion and update. Let be the charge basis function corresponding to the target charge basis function before the fusion update. The unknown parameters of the basis function of the i-th adjacent charge after fusion update.

[0026] In some embodiments of this application, the fusion update of the current basis function through geometric mapping includes:

[0027] A local radial subnetwork structure is selected in the target network structure. The local radial subnetwork structure includes a central node to be absorbed and all geometrically adjacent nodes to the central node. The local radial subnetwork structure is then equivalently mapped to a ring subnetwork structure with the same number of geometric paths as the local radial subnetwork structure. The ring subnetwork structure includes all the adjacent nodes of the central node. Based on the linear additivity of the current basis functions in the function space of the local radial subnetwork structure, the current basis functions in the ring subnetwork structure are constructed, making the port impedances before and after the mapping transformation equivalent.

[0028] In some embodiments of this application, the expression for the current basis function in the ring sub-network structure is:

[0029]

[0030] in This is to integrate the current basis functions corresponding to the path from the i-th adjacent node to the center node m in the previously described local radial subnetwork structure. To integrate the updated current basis functions of the path from the i-th adjacent node to the (i+1)-th adjacent node in the ring subnetwork structure, To integrate the current basis function corresponding to the path from the (i+1)th adjacent node to the central node m in the local radial sub-network structure before the update, the charge basis function and the node have a one-to-one correspondence.

[0031] A second aspect of this application provides an integrated circuit electrical characteristic simulation device, including a mesh generation and basis function acquisition module, a basis function update module, and a simulation module;

[0032] The mesh partitioning and basis function acquisition module is used to acquire the integrated circuit model to be simulated, perform mesh partitioning on the integrated circuit model to be simulated to obtain an integrated circuit mesh dataset composed of multiple mesh cells, and construct corresponding charge basis functions and current basis functions based on the mesh cells;

[0033] The basis function update module is used to select a target charge basis function and its adjacent charge basis functions one by one, using the charge basis function as the fusion object, to discretize the target charge basis function and fuse it into the adjacent charge basis functions, so as to realize the gradual fusion update of the charge basis function. At the same time, the current basis function is fused and updated accordingly through geometric mapping.

[0034] The simulation module is used to obtain the integrated circuit basis function dataset after all fusion updates are completed, and to perform electrical characteristic simulation on the integrated circuit to be simulated based on the integrated circuit basis function dataset.

[0035] A third aspect of this application provides a terminal comprising: at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor, wherein the processor executes the computer program to implement the method described above.

[0036] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0037] Compared with the prior art, one or more embodiments of the above solutions may have the following advantages or beneficial effects:

[0038] The integrated circuit electrical characteristic simulation method provided in this invention, based on the integrated circuit model mesh partitioning and original basis function acquisition, updates the charge basis functions in the integrated circuit mesh dataset by discretizing the charge basis functions into multiple parts and distributing them evenly to adjacent charge basis functions, and by using a local potential field minimum error solution strategy. Combined with a geometric mapping method, the current basis functions are fused and updated, further achieving rapid updating and low-order representation of complex coupling capacitance matrices. Compared to traditional back-end order reduction methods, the theoretical complexity is reduced from O(n^2) / 2. 3 The time complexity is reduced to O(n), while the model accuracy and order reduction effect are maintained, and the efficiency of model order reduction is greatly improved.

[0039] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the description, claims, and drawings. Attached Figure Description

[0040] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with the embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0041] Figure 1 The diagram shown is a flowchart illustrating the integrated circuit electrical characteristic simulation method described in this application embodiment.

[0042] Figure 2 The diagram shown is a schematic diagram of a radial mesh structure in the integrated circuit electrical characteristic simulation method described in this application embodiment.

[0043] Figure 3 Displayed as Figure 2 The diagram shows the structure of the annular grid structure corresponding to the radial grid structure shown.

[0044] Figure 4 The diagram shown is an example of a mesh structure in the integrated circuit electrical characteristic simulation method described in this application embodiment.

[0045] Figure 5 The diagram shown is a structural schematic of the integrated circuit electrical characteristic simulation device described in this application embodiment.

[0046] Figure 6 The diagram shown is a structural schematic of the terminal described in an embodiment of this application.

[0047] Detailed explanation of element symbols:

[0048] 10 is the mesh generation and basis function acquisition module, 11 is the basis function update module, 12 is the simulation module, 20 is the terminal, 21 is the processor, 22 is the memory, and 221 is the computer program. Detailed Implementation

[0049] To make the technical problems, technical solutions, and beneficial effects to be solved by this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of this application.

[0050] It should be noted that when a component is referred to as being "set on" another component, it can be directly on or indirectly on that other component. When a component is referred to as being "connected to" another component, it can be directly connected to or indirectly connected to that other component.

[0051] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0052] In traditional integrated circuit electrical characteristic analysis and simulation, the step of reducing the computational complexity of the circuit model occurs after the extraction of the equivalent circuit model. Model reduction techniques are used to reduce the system's order, that is, to represent the original system through an equivalent low-order system, thereby accelerating the simulation. Among these techniques, the traditional back-end component equivalent circuit (PEEC) model reduction method has advantages over other methods. Specifically, back-end component equivalent circuit compression originates from node absorption based on circuit transformation. Assuming that node q in the capacitor grid of the integrated circuit mesh dataset is an insignificant node that can be absorbed, its capacitance to ground can be evenly distributed among the N capacitor grids originally adjacent to node q. According to the grid arrangement, the transformed circuit and its corresponding grids are rearranged; through this transformation circuit, the essence of the circuit is preserved. After node q is absorbed, the branches generated during the circuit transformation process combine with the remaining part of the original circuit to re-form the PEEC form of the circuit. The insignificant node absorption process is repeated until all insignificant nodes are absorbed, resulting in a concise circuit model. Finally, the hybrid coupling between capacitors and inductors introduced during the model reduction process is internalized through surrounding conventional inductors. However, the computational complexity of the reduction method for the back-end component equivalent circuit (PEEC) model is O(n³), which poses a severe challenge to computational efficiency in the simulation and optimization of high-frequency large-scale integrated circuits.

[0053] Based on this, this application improves the simulation method for the electrical characteristics of integrated circuits in related technologies.

[0054] refer to Figure 1 As shown, the integrated circuit electrical characteristic simulation method of this application embodiment includes the following steps.

[0055] Step S101: Obtain the integrated circuit model to be simulated, perform mesh partitioning on the integrated circuit model to obtain an integrated circuit mesh dataset composed of multiple mesh cells, and construct the corresponding charge basis function and current basis function based on the mesh cells.

[0056] The high-frequency integrated circuit to be simulated is determined, and its physical model, i.e., the integrated circuit model to be simulated, is obtained. Then, the integrated circuit model to be simulated is meshed to obtain the integrated circuit mesh dataset. At the same time, based on the electric field integral equation with discrete current and charge distribution, the charge basis function and current basis function corresponding to the mesh element are constructed.

[0057] Step S102: Taking the charge basis function as the fusion object, a target charge basis function and its adjacent charge basis functions are selected one by one. The target charge basis function is discretized and fused into the adjacent charge basis functions to realize the gradual fusion and update of the charge basis function. At the same time, the current basis function is fused and updated accordingly through geometric mapping.

[0058] Using charge basis functions as the fusion object, a target charge basis function and its adjacent charge basis functions are selected. The target charge basis function is then discretized and evenly fused into all its adjacent charge basis functions to achieve the fusion update of all adjacent charge basis functions. Simultaneously, current basis functions on the same mesh are fused and updated through geometric mapping to achieve single-mesh ablation. Then, a new target charge basis function and its adjacent charge basis functions are selected, and the above fusion update process for charge and current basis functions is repeated until all absorbable charge basis functions are absorbed and all updatable current basis functions are fused and updated, thus obtaining a concise integrated circuit basis function dataset.

[0059] It should be noted that the absorbable charge basis function can be determined based on the actual situation of the integrated circuit and the determination method of absorbable nodes in the existing equivalent circuit method of partial elements. For example, the absorbable basis function can be set to satisfy "equipotential" and "no independent source / external excitation", and the absorption should not change the external electrical characteristics and electromagnetic response accuracy of the integrated circuit. At the same time, once the absorbable charge basis function is determined, the current basis function of the corresponding grid can be updated.

[0060] Step S103: After all fusion updates are completed, obtain the integrated circuit basis function dataset, and perform electrical characteristic simulation on the integrated circuit to be simulated based on the integrated circuit basis function dataset.

[0061] Once the integrated circuit basis function dataset is obtained, the integrated circuit to be simulated can be simulated using existing simulation methods, and its electrical characteristics can be analyzed.

[0062] This embodiment, based on the mesh partitioning of the integrated circuit model and the acquisition of the original basis functions, updates the charge basis functions in the integrated circuit mesh dataset by discretizing the charge basis functions into multiple parts and distributing them evenly to adjacent charge basis functions, combined with a local potential field minimum error solution strategy. Simultaneously, it achieves the fusion update of the current basis functions through geometric mapping, ultimately realizing rapid updating and low-order representation of complex coupled capacitance matrices. Compared to traditional back-end order reduction methods, this scheme reduces the theoretical complexity from O(n^3) to O(n), significantly improving the model order reduction efficiency while ensuring model accuracy and order reduction effect.

[0063] The steps S101 to S103 of the integrated circuit electrical characteristic simulation method of this embodiment will be described in detail below.

[0064] Step S101: Obtain the integrated circuit model to be simulated, perform mesh partitioning on the integrated circuit model to obtain an integrated circuit mesh dataset composed of multiple mesh cells, and construct the corresponding charge basis function and current basis function based on the mesh cells.

[0065] Specifically, after determining the integrated circuit model to be simulated, a mesh generation method is used to partition the integrated circuit model to obtain an integrated circuit mesh dataset. Mesh generation (also called mesh creation) separates geometric surfaces and cubes into multiple units. Two-dimensional surfaces are mainly represented by triangles, quadrilaterals, or other reasonable shapes, while three-dimensional structures are typically divided into tetrahedral, pyramidal, and hexahedral structural units. Mesh generation allows the computer to solve the governing equations on the mesh units, and the mesh density is determined by the highest solution frequency. Numerical computation methods based on integral equations have a wide variety of mesh generation methods. The mesh generation method used in this embodiment can be determined based on the actual situation of the integrated circuit to be simulated, and this embodiment does not impose any fixed restrictions on it.

[0066] After acquiring the integrated circuit mesh dataset, the charge basis function and current basis function for each mesh cell are determined based on the Electric Field Integral Equation (EFIE) with discrete current and charge distributions. Specifically, the Electric Field Integral Equation (EFIE) can be expressed as:

[0067] (1)

[0068] in, Represents electric vector potential, Represents scalar potential. Let represent the magnetic permeability. And the scalar potential expression is:

[0069] (2)

[0070] Equivalent source discretization is a crucial step in transforming electromagnetic field problems into discrete equations, especially when dealing with boundary value problems and scattering problems, providing a foundation for establishing numerical models and solving the equations. This embodiment performs equivalent source discretization on the electric field integral equation (EFIE) to obtain expressions for the current and charge with unknowns:

[0071] (3)

[0072] (4)

[0073] in, Denotes the nth current basis function. Indicates the unknown current amplitude. Let m be the basis function of the m-th charge. For the unknown charge density amplitude, This represents the position vector. The further expressions for the charge basis function and current basis function are as follows:

[0074] (5)

[0075] (6)

[0076] in, This represents the m-th charge basis function in the integrated circuit mesh dataset. This represents the grid area corresponding to the charge basis function. This represents the supporting region of the charge basis function. This represents the nth current basis function in the integrated circuit mesh dataset. This represents the length of the common edge between the h-th node and the k-th node. This represents the triangular mesh corresponding to the h-th node. express area, This represents the triangular mesh corresponding to the k-th node. express area, This indicates the triangle mesh corresponding to the h-th node that shares a common edge with the other nodes. Relative vertex position vectors This indicates the triangle mesh corresponding to the k-th node that shares a common edge with the other nodes. The relative vertex position vector.

[0077] By substituting the location vector and grid area data of the integrated circuit grid dataset into the above formula, the charge basis function and current basis function of each grid cell can be obtained.

[0078] Step S102: Taking the charge basis function as the fusion object, a target charge basis function and its adjacent charge basis functions are selected one by one. The target charge basis function is discretized and fused into the adjacent charge basis functions to realize the gradual fusion and update of the charge basis function. At the same time, the current basis function is fused and updated accordingly through geometric mapping.

[0079] The charge basis functions to be absorbed in the integrated circuit mesh dataset are sequentially fused using a charge basis function discretization and fusion method, and the adjacent charge basis functions of each charge basis function to be absorbed are updated. Furthermore, during the fusion and update of the charge basis functions, the current basis functions are simultaneously fused and updated sequentially using a geometric mapping method.

[0080] Specifically, the process of fusing individual charge basis functions and updating adjacent charge basis functions through the discretization and fusion of charge basis functions includes:

[0081] Let a certain basis function to be absorbed be the target charge basis function, and the target charge basis function has X adjacent charge basis functions. The target charge basis function and all its adjacent charge basis functions are connected through current basis functions. Assume that the index of the target charge basis function is m, the index of the adjacent charge basis function is adj, and the index of other charge basis functions in the integrated circuit grid dataset other than the target charge basis function and its adjacent charge basis functions is oth. At this time, based on the scalar potential expression (2), the following relationship exists for each type of charge basis function.

[0082] The scalar potential of the target charge basis function can be expressed as:

[0083] (7)

[0084] The scalar potential of the i-th adjacent charge basis function (i.e., the original scalar potential of the i-th adjacent charge basis function) can be expressed as:

[0085] (8)

[0086] in, The scalar potential representing the basis function of the target charge. Let represent the scalar potential of the basis functions of the i-th adjacent charge. Indicates the dielectric constant of the medium. This represents the unit charge at the source point r′ at the observation point. The potential generated at that point This represents the unit charge at the source point r′ at the observation point. The potential generated at that point Describes the basis function of the target charge. This represents the surface charge coefficient corresponding to the target charge basis function. Let i represent the basis function of the i-th adjacent charge. This represents the surface charge coefficient corresponding to the i-th adjacent charge basis function. Denotes the basis function of the k-th other charge. It represents the surface charge coefficient corresponding to the kth other charge basis function.

[0087] Discretize the target charge basis function into X parts (the number of parts is the same as that of adjacent charge basis functions), and then distribute the discrete X parts to each of the adjacent charge basis functions (each charge basis function receives a part). At this point, the scalar potential of the target charge basis function can be represented by the discretized target charge basis function, i.e., the following exists:

[0088] (9)

[0089] in This represents the surface charge coefficient corresponding to each part after the objective basis function is discretized.

[0090] Substituting equation (9) into equation (7), we obtain the new scalar potential expression for the target charge basis function:

[0091] (10)

[0092] Based on the principle that the local boundary condition of the forced tangential electric field on the conductor surface is zero, the scalar potential of the basis function of the i-th adjacent charge also has the following relationship:

[0093] (11)

[0094] in, Represents vector potential (magnetic vector potential).

[0095] Substituting the new scalar potential expression (10) of the target charge basis function into the scalar potential (11) of the i-th adjacent charge basis function, we get:

[0096] (12)

[0097] The above process yields the scalar potential of the adjacent charge basis functions represented by the discrete target charge basis functions, which is then used as the scalar potential represented by the discrete charge basis functions.

[0098] At this point, by matching the original scalar potential of the adjacent charge basis functions (i.e., equation (8)) and the scalar potential represented by the cut charge basis functions (i.e., equation (12)) using the Galerkin method, the potential equations corresponding to the adjacent charge basis functions can be obtained:

[0099] (13)

[0100] If we define a and b as at least one of m, adj, and oth, then the potential coefficient can be defined as:

[0101] (14)

[0102] Then, for the coefficient submatrix of the first term (i.e., the dominant term coefficient) on the right-hand side of equation (13), we have:

[0103] Let X be an X×X diagonal matrix, and all of its non-zero diagonal elements are 0. ;

[0104] Let be an X×X full-rank matrix, and the elements in its i-th row are... ;

[0105] Let be an X×X full-rank matrix, and the elements in its i-th column are... ;

[0106] Let X×X be a full-rank matrix, and its elements be denoted by . Provided.

[0107] Then, for the coefficient submatrix in the second term on the right-hand side of equation (13), we have:

[0108] Let X be a complete matrix of size X×mX, where the element in the i-th column is equal to... ;

[0109] It is a complete matrix of size X×mX, whose elements are composed of... Provided.

[0110] For the third term on the right side of equation (13), considering that the contribution of current to potential can be approximated by the Galerkin method, the following holds:

[0111] (15)

[0112] The elements of L are given by the following formula:

[0113] (16).

[0114] To solve for the coefficient submatrix in the first term of the above equation (13), this embodiment reduces the order of the principal guiding coefficients of the potential equation through parameter transformation. Specifically, the following settings are first made:

[0115] (16)

[0116] (17)

[0117] Then, by substituting equations (16) and (17) into equation (13), a new potential equation corresponding to the basis functions of adjacent charges is obtained. This new potential equation includes the combined charge (i.e., (as indicated)

[0118] (18)

[0119] in (19)

[0120] (20)

[0121] (twenty one)

[0122] At this point, we introduce a combined charge basis function architecture. The combined charge basis function is the combined basis function formed by each adjacent charge basis function and its assigned cutting layer when the target charge basis function is discretized into X parts and evenly distributed among all adjacent charge basis functions. The combined charge basis function architecture is now defined as follows:

[0123] (twenty two)

[0124] in Let be the combined charge basis function architecture corresponding to the i-th adjacent charge basis function after fusion and update. Let represent the equivalent area corresponding to the basis function of the i-th adjacent charge before fusion update. Let i be the charge basis function corresponding to the i-th adjacent charge basis function before the fusion update. This represents the equivalent area corresponding to the target charge basis function before fusion update. Let be the charge basis function corresponding to the target charge basis function before the fusion update. is the unknown parameter of the basis function of the i-th adjacent charge during the fusion update.

[0125] At this point, the potential coefficients for adjacent combined charges after the fusion update are:

[0126] (twenty three)

[0127] Substituting the basis functions of the combined charge into the potential coefficient (23) of the combined charge, we get:

[0128] (twenty four)

[0129] Regarding the above formula, since the value on the left side of formula (24) can be obtained based on formulas (19) and (16), and based on the determination of the target charge basis function and the adjacent charge basis function in the integrated circuit grid dataset, the value on the right side of the above formula (24) excluding the unknown parameter is obtained. All parameters can be obtained from the outside, therefore the unknown parameters can be obtained through formula (24). The specific value. Then the unknown parameter. The specific values ​​are substituted into the combined charge basis function architecture (22) to obtain the updated i-th adjacent charge basis function. i is set to be equal to 1 to x in sequence; and the above process is repeated to update all adjacent charge basis functions of the target charge basis function. In each fusion update process, the equivalent area and equivalent center node corresponding to the adjacent charge basis functions are updated.

[0130] It is worth noting that updating the matrix elements is equivalent to using fused basis functions. It should also be noted that the number of X values ​​is typically small, thus the computational cost of solving such local subsystems is minimal. To maintain charge conservation, the weights should be less than 1.

[0131] Furthermore, the above process is repeated each time a fusion update of the charge basis functions is required, until all charge basis functions to be absorbed are absorbed.

[0132] The fusion update of charge basis functions is often accompanied by the fusion update of related current basis functions.

[0133] Currently mainstream order reduction strategies may introduce numerical instability when dealing with large-scale mesh systems. The most prominent problem is that the resulting inductance matrix may be non-positive definite, meaning that the mutual inductance term may be greater than the corresponding self-inductance term. This phenomenon violates the physical principle that the inductance matrix should satisfy, easily leading to problems such as energy non-conservation and numerical divergence in subsequent time-domain simulations, severely limiting the engineering practicality of the model. To address this issue, this embodiment draws on the Y-Δ transform (star-delta transform) method from classical circuit theory. The Y-Δ transform is a method to equivalently convert a three-branch Y-type network into a triangular Δ-type network. The core idea is to absorb the information from the intermediate nodes and implicitly integrate it into the equivalent inductance expression between each pair of sides.

[0134] In the partial equivalent circuit method, traditional order reduction methods typically first obtain partial inductance and potential coefficients by solving integral equations before performing order reduction. However, these partial inductance and potential coefficient matrices need to be calculated at every frequency point, resulting in a huge computational burden. This embodiment avoids explicitly solving for inductor and capacitor parameters. Instead, it directly constructs a new set of basis functions that can be used for order reduction by linearly superimposing the current basis functions. This achieves mesh-level fusion and simplification, thereby efficiently obtaining new inductance parameters.

[0135] The specific process of fusing and updating the current basis functions includes: First, determining the local radial sub-network structure in the integrated circuit mesh dataset using existing methods. The local radial sub-network structure includes a central node to be absorbed and all geometrically adjacent nodes to the central node. The local radial sub-network structure is any radial network structure in the integrated circuit mesh dataset to be fused and updated. Then, the local radial sub-network structure is equivalently mapped to a ring sub-network structure with the same number of geometric paths as the local radial sub-network structure. The ring sub-network structure includes all the adjacent nodes of the central node. Based on the linear additivity of the current basis functions in the function space of the local radial sub-network structure, the current basis functions in the ring sub-network structure are constructed, making the port impedances before and after the mapping transformation equivalent.

[0136] Taking the example of local Y-Δ equivalent mapping, for a given triangular mesh in an integrated circuit mesh dataset, each mesh is associated with a current basis function (i.e., RWG basis function) to represent the current density of that region. Order reduction mainly targets the local Y-shaped structure in the mesh, converting it into an equivalent Δ-shaped structure to achieve the fusion of network nodes. This transformation can reconstruct the original Y-shaped mesh with a central node into an equivalent Δ-shaped mesh, removing the original central node and establishing new connections between the peripheral nodes.

[0137] During the local Y-Δ transformation, a mapping relationship for updating the current basis functions needs to be established, primarily based on equivalent circuit theory and Kirchhoff's laws to maintain network equivalence. This is mainly achieved by constructing new current paths and linearly combining the original RWG basis functions to derive a new set of equivalent basis functions, thus preserving local impedance characteristics and overall physical consistency. (Reference) Figure 2 The mapping relationships in the radial network structure shown are illustrated in Table 1. (Reference) Figure 3 The mapping relationships in the ring network structure shown are illustrated in Table 2.

[0138] Table 1

[0139]

[0140] Table 2

[0141]

[0142] Correspondingly, by linearly superimposing the original current basis functions, an equivalent set of basis functions consistent with the new path is constructed, making the network before and after the transformation equivalent in terms of port impedance.

[0143] Since the current basis functions and their fusion are in a corresponding relationship, and the charge basis functions and nodes are in a one-to-one correspondence, the target charge basis function is represented by m when the charge basis functions are fused. At this time, the corresponding center node should also be represented by m. Therefore, based on the original current basis function (6), the expression of the target current basis function in the ring subnetwork structure is:

[0144]

[0145] in To integrate the current basis functions corresponding to the path from the i-th adjacent node to the center node m in the local radial subnetwork structure before the update. To integrate the current basis functions corresponding to the path from the i-th adjacent node to the (i+1)-th adjacent node in the updated ring subnet structure. This is to define the current basis function corresponding to the path from the (i+1)th adjacent node to the center node m in the local radial subnetwork structure before fusion and updating. This represents the length of the common edge between the i-th node and the m-th node. This represents the triangular mesh corresponding to the i-th node. express area, This represents the triangular mesh corresponding to the m-th node. express area, This indicates the triangle mesh corresponding to the i-th node that shares a common edge with the i-th node. Relative vertex position vectors This represents the triangle mesh corresponding to the m-th node that shares a common edge with the edge. The relative vertex position vector.

[0146] It should be noted that the radial mesh structure may not be a Y-shaped structure, but may be other types of radial structures. Similarly, the ring mesh structure may not be a Δ structure, but may be the corresponding ring structure. This embodiment does not impose any fixed restrictions on it.

[0147] By repeating the above process, the fusion update of all current basis functions in the integrated circuit mesh dataset can be achieved. Compared with traditional methods, the current basis function fusion update method in this embodiment can omit the cumbersome inductor and capacitance calculation steps while ensuring that the equivalent impedance remains unchanged, thus significantly improving the model order reduction efficiency.

[0148] Once all fusion updates in the integrated circuit mesh dataset are completed, the integrated circuit basis function dataset is obtained.

[0149] Step S103: After all fusion updates are completed, obtain the integrated circuit basis function dataset, and perform electrical characteristic simulation on the integrated circuit to be simulated based on the integrated circuit basis function dataset.

[0150] Once all fusion updates are complete, the integrated circuit basis function dataset can be obtained. The electrical characteristics of the integrated circuit to be simulated can then be simulated using simulation software to achieve analysis of the electrical characteristics of the integrated circuit to be simulated.

[0151] To describe the model order reduction effect in the integrated circuit electrical characteristic simulation method of this embodiment, this embodiment uses a mesh structure containing four triangles, which is an equilateral triangle as an example (see reference). Figure 4 As shown, the order of the circuit is reduced by using the existing back-end circuit node fusion method and the basis function fusion update method proposed in this embodiment, respectively.

[0152] Table 3 shows the above-mentioned grid structure ( Figure 4 The P-matrix values ​​to be fused are split into layers; Table 4 shows the P-matrix values ​​after fusion using back-end circuit nodes; Table 5 shows the P-matrix values ​​after fusion and updating using the basis function in the integrated circuit electrical characteristic simulation method.

[0153] Table 3

[0154]

[0155] Figure 4

[0156]

[0157] Figure 5

[0158]

[0159] As shown in the table above, traditional back-end fusion methods are based on established equivalent element circuits, achieving matrix simplification through circuit-level equivalence. In contrast, the order reduction method in this embodiment performs node merging and surface clustering during the geometric modeling and mesh generation stages, reducing the number of coupled units from the source. The numerical results above verify that the proposed basis can be used to calculate the combined potential coefficients.

[0160] The integrated circuit electrical characteristic simulation method provided in this invention, based on the mesh partitioning of the integrated circuit model and the acquisition of the original basis functions, updates the charge basis functions in the integrated circuit mesh dataset by discretizing the charge basis functions into multiple parts and distributing them evenly to adjacent charges, and by using a local potential field minimum error solution strategy. Combined with a geometric mapping method, it achieves the fusion update of the current basis functions, further realizing the rapid update and low-order representation of complex coupling capacitance matrices. Compared with traditional back-end order reduction methods, the theoretical complexity is reduced from O(n^2) / 2. 3 The time complexity is reduced to O(n), while the model accuracy and order reduction effect are maintained, and the efficiency of model order reduction is greatly improved.

[0161] like Figure 5 As shown in the figure, this application embodiment also provides an integrated circuit electrical characteristic simulation device, including a mesh partitioning and basis function acquisition module 10, a basis function update module 11, and a simulation module 12.

[0162] The mesh partitioning and basis function acquisition module 10 is used to acquire the integrated circuit model to be simulated, perform mesh partitioning on the integrated circuit model to be simulated to obtain the integrated circuit mesh dataset, and construct the charge basis function of each charge and the current basis function of each current in the integrated circuit mesh dataset;

[0163] The basis function update module 11 is used to achieve the fusion update of each charge basis function through charge basis function segmentation and the fusion update of each current basis function through geometric mapping. After all fusion updates are completed, the integrated circuit basis function dataset is obtained.

[0164] Simulation module 12 is used to perform electrical characteristic simulation of the integrated circuit to be simulated based on the integrated circuit basis function dataset.

[0165] Furthermore, the basis function update module 11 is specifically used for:

[0166] Selecting a target charge basis function and its neighboring charge basis functions, discretizing the target charge basis function, and fusing it into the neighboring charge basis functions to achieve the fusion update of the charge basis functions includes:

[0167] Determine a target charge basis function to be absorbed, and a plurality of adjacent charge basis functions that are geometrically adjacent to the target charge basis function;

[0168] The target charge basis function is discretized into X parts and evenly distributed to all the adjacent charge basis functions. Based on the original scalar potential corresponding to each adjacent charge basis function and the fused scalar potential represented by the discrete charge basis functions, the potential equation corresponding to each adjacent charge basis function is constructed.

[0169] By locally solving each of the potential equations, the basis functions of each adjacent charge are updated;

[0170] Wherein, the target charge basis function is any charge basis function to be absorbed in the integrated circuit grid dataset, and X is the number of all the adjacent charge basis functions.

[0171] Furthermore, the basis function update module 11 is specifically used for:

[0172] Based on the original scalar potentials corresponding to the adjacent charge basis functions and the fused scalar potentials represented by the discrete charge basis functions, the potential equations corresponding to the adjacent charge basis functions are constructed as follows:

[0173] Based on the discrete electric field integral equation, the original scalar potential corresponding to the basis functions of the adjacent charges is calculated;

[0174] Based on the discretized target charge basis function, the scalar potential of the adjacent charge basis functions is calculated, which is used as the fused scalar potential represented by the discrete charge basis function.

[0175] The potential equations corresponding to the adjacent charge basis functions are constructed by matching the original scalar potentials of the adjacent charge basis functions with the fused scalar potentials represented by the discrete charge basis functions using the Galerkin method.

[0176] Furthermore, the basis function update module 11 is specifically used for:

[0177] The update of the basis functions of adjacent charges is achieved by locally solving the potential equation, including:

[0178] The principal guiding coefficients of the potential equation are reduced in order through parameter transformation, and the unknown parameters in the basis function architecture are solved by combining the combined charge basis function architecture.

[0179] Substitute the unknown parameters obtained from the solution into the combined charge basis function architecture to obtain the updated adjacent charge basis functions;

[0180] The combined charge basis function is a charge basis function that combines the adjacent charge basis functions with the discrete target charge basis function.

[0181] Furthermore, the basis function update module 11 is specifically used for:

[0182] The combined charge basis function architecture is as follows:

[0183]

[0184] in Let be the combined charge basis function architecture corresponding to the i-th adjacent charge basis function after fusion and update. This represents the equivalent area corresponding to the i-th adjacent charge basis function before the fusion update. Let i be the charge basis function corresponding to the i-th adjacent charge basis function before the fusion update. This represents the equivalent area corresponding to the target charge basis function before fusion and update. Let be the charge basis function corresponding to the target charge basis function before the fusion update. The unknown parameter is the basis function of the i-th adjacent charge during the fusion update.

[0185] Furthermore, the basis function update module 11 is specifically used for:

[0186] The fusion update of the current basis function through geometric mapping includes:

[0187] A local radial subnetwork structure is selected in the target network structure. The local radial subnetwork structure includes a central node to be absorbed and all geometrically adjacent nodes to the central node. The local radial subnetwork structure is then equivalently mapped to a ring subnetwork structure with the same number of geometric paths as the local radial subnetwork structure. The ring subnetwork structure includes all the adjacent nodes of the central node. Based on the linear additivity of the current basis functions in the function space of the local radial subnetwork structure, the current basis functions in the ring subnetwork structure are constructed, making the port impedances before and after the mapping transformation equivalent.

[0188] Furthermore, the basis function update module 11 is specifically used for:

[0189] The expression for the current basis function in the ring subnetwork structure is:

[0190]

[0191] in This is to integrate the current basis functions corresponding to the path from the i-th adjacent node to the center node m in the previously described local radial subnetwork structure. To integrate the updated current basis functions of the path from the i-th adjacent node to the (i+1)-th adjacent node in the ring subnetwork structure, To integrate the current basis function corresponding to the path from the (i+1)th adjacent node to the central node m in the local radial sub-network structure before the update, the charge basis function and the node have a one-to-one correspondence.

[0192] This application embodiment also provides a terminal 20, such as Figure 6As shown, the terminal 20 includes: at least one processor 21, a memory 22, and a computer program 221 stored in the memory 22 and executable on at least one processor 21. When the processor 21 executes the computer program 221, it implements the steps in any of the above method embodiments, or when the processor 21 executes the computer program 221, it implements the functions of each module / unit in the above device embodiments.

[0193] For example, computer program 221 may be divided into one or more modules / units, one or more of which are stored in memory 22 and executed by processor 21 to complete this application. One or more modules / units may be a series of computer program 221 instruction segments capable of performing a specific function, which describe the execution process of computer program 221 in terminal 20.

[0194] Those skilled in the art will understand that Figure 6 This is merely an example of terminal 20 and does not constitute a limitation on terminal 20. It may include more or fewer components than shown, or combine certain components, or different components. For example, terminal 20 may also include input / output devices, network access devices, buses, etc.

[0195] The processor 21 mentioned above can be a Central Processing Unit (CPU), or other general-purpose processors 21, digital signal processors 21 (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor 21 can be a microprocessor 21, or any conventional processor 21, etc.

[0196] The memory 22 can be an internal storage unit of the terminal 20, such as the hard disk or RAM of the terminal 20. The memory 22 can also be an external storage device of the terminal 20, such as a plug-in hard disk, SmartMedia Card (SMC), Secure Digital (SD) card, or Flash Card equipped on the terminal 20. Furthermore, the memory 22 can include both internal storage units and external storage devices of the terminal 20.

[0197] This application embodiment also provides a readable storage medium storing a computer program 221, which, when executed by a processor 21, implements the steps in the above-described method embodiments.

[0198] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of this application can be implemented by a computer program 221 instructing related hardware. The computer program 221 can be stored in a computer-readable storage medium. When executed by the processor 21, the computer program 221 can implement the steps of the various method embodiments described above. The computer program 221 includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. A computer-readable medium can include at least: any entity or device capable of carrying computer program code to a photographic device / terminal device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks. In some jurisdictions, according to legislation and patent practice, computer-readable media cannot be electrical carrier signals or telecommunication signals.

[0199] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0200] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0201] In the embodiments provided in this application, it should be understood that the disclosed apparatus / device and method can be implemented in other ways. For example, the apparatus / device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0202] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0203] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for simulating the electrical characteristics of an integrated circuit, comprising: Obtain the integrated circuit model to be simulated, perform mesh partitioning on the integrated circuit model to obtain an integrated circuit mesh dataset composed of multiple mesh cells, and construct the corresponding charge basis function and current basis function based on the mesh cells; Using the charge basis function as the fusion object, a target charge basis function and its adjacent charge basis functions are selected successively. The target charge basis function is discretized and fused into the adjacent charge basis functions to achieve the gradual fusion and update of the charge basis function. At the same time, the current basis function is fused and updated accordingly through geometric mapping. After all fusion updates are completed, obtain the integrated circuit basis function dataset, and perform electrical characteristic simulation on the integrated circuit to be simulated based on the integrated circuit basis function dataset; The fusion update of the current basis function through geometric mapping includes: A local radial subnetwork structure is selected in the target network structure. The local radial subnetwork structure includes a central node to be absorbed and all geometrically adjacent nodes to the central node. The local radial subnetwork structure is then equivalently mapped to a ring subnetwork structure with the same number of geometric paths as the local radial subnetwork structure. The ring subnetwork structure includes all the adjacent nodes of the central node. Based on the linear additivity of the current basis functions in the function space of the local radial subnetwork structure, the current basis functions in the ring subnetwork structure are constructed, making the port impedances before and after the mapping transformation equivalent.

2. The integrated circuit electrical characteristic simulation method according to claim 1, characterized in that, Selecting a target charge basis function and its neighboring charge basis functions, discretizing the target charge basis function, and fusing it into the neighboring charge basis functions to achieve the fusion update of the charge basis functions includes: Determine a target charge basis function to be absorbed, and a plurality of adjacent charge basis functions that are geometrically adjacent to the target charge basis function; The target charge basis function is discretized into X parts and evenly distributed to all the adjacent charge basis functions. Based on the original scalar potential corresponding to each adjacent charge basis function and the fused scalar potential represented by the discrete charge basis functions, the potential equation corresponding to each adjacent charge basis function is constructed. By locally solving each of the potential equations, the basis functions of each adjacent charge are updated; Wherein, the target charge basis function is any charge basis function to be absorbed in the integrated circuit grid dataset, and X is the number of all the adjacent charge basis functions.

3. The integrated circuit electrical characteristic simulation method according to claim 2, characterized in that, Based on the original scalar potentials corresponding to the adjacent charge basis functions and the fused scalar potentials represented by the discrete charge basis functions, the potential equations corresponding to the adjacent charge basis functions are constructed as follows: Based on the discrete electric field integral equation, the original scalar potential corresponding to the basis functions of the adjacent charges is calculated; Based on the discretized target charge basis function, the scalar potential of the adjacent charge basis functions is calculated, which is used as the fused scalar potential represented by the discrete charge basis function. The potential equations corresponding to the adjacent charge basis functions are constructed by matching the original scalar potentials of the adjacent charge basis functions with the fused scalar potentials represented by the discrete charge basis functions using the Galerkin method.

4. The integrated circuit electrical characteristic simulation method according to claim 2, characterized in that, The update of the basis functions of adjacent charges is achieved by locally solving the potential equation, including: The principal guiding coefficients of the potential equation are reduced in order through parameter transformation, and the unknown parameters in the basis function architecture are solved by combining the combined charge basis function architecture. Substitute the unknown parameters obtained from the solution into the combined charge basis function architecture to obtain the updated adjacent charge basis functions; The combined charge basis function is a charge basis function that combines the adjacent charge basis functions with the discrete target charge basis function.

5. The integrated circuit electrical characteristic simulation method according to claim 4, characterized in that, The combined charge basis function architecture is as follows: in Let be the combined charge basis function architecture corresponding to the i-th adjacent charge basis function after fusion and update. This represents the equivalent area corresponding to the i-th adjacent charge basis function before the fusion update. Let i be the charge basis function corresponding to the i-th adjacent charge basis function before the fusion update. This represents the equivalent area corresponding to the target charge basis function before fusion and update. Let be the charge basis function corresponding to the target charge basis function before the fusion update. The unknown parameters of the basis function of the i-th adjacent charge after fusion update.

6. The integrated circuit electrical characteristic simulation method according to claim 1, characterized in that, The expression for the current basis function in the ring subnetwork structure is: in This is to integrate the current basis functions corresponding to the path from the i-th adjacent node to the center node m in the previously described local radial subnetwork structure. To integrate the updated current basis functions of the path from the i-th adjacent node to the (i+1)-th adjacent node in the ring sub-network structure. To integrate the current basis function corresponding to the path from the (i+1)th adjacent node to the central node m in the local radial sub-network structure before the update, the charge basis function and the node have a one-to-one correspondence.

7. An integrated circuit electrical characteristic simulation device, characterized in that, It includes a mesh generation and basis function acquisition module, a basis function update module, and a simulation module; The mesh partitioning and basis function acquisition module is used to acquire the integrated circuit model to be simulated, perform mesh partitioning on the integrated circuit model to be simulated to obtain an integrated circuit mesh dataset composed of multiple mesh cells, and construct corresponding charge basis functions and current basis functions based on the mesh cells; The basis function update module is used to select a target charge basis function and its adjacent charge basis functions one by one, using the charge basis function as the fusion object, to discretize the target charge basis function and fuse it into the adjacent charge basis functions, so as to realize the gradual fusion update of the charge basis function. At the same time, the current basis function is fused and updated accordingly through geometric mapping. The simulation module is used to obtain the integrated circuit basis function dataset after all fusion updates are completed, and to perform electrical characteristic simulation of the integrated circuit to be simulated based on the integrated circuit basis function dataset; The fusion update of the current basis function through geometric mapping includes: A local radial subnetwork structure is selected in the target network structure. The local radial subnetwork structure includes a central node to be absorbed and all geometrically adjacent nodes to the central node. The local radial subnetwork structure is then equivalently mapped to a ring subnetwork structure with the same number of geometric paths as the local radial subnetwork structure. The ring subnetwork structure includes all the adjacent nodes of the central node. Based on the linear additivity of the current basis functions in the function space of the local radial subnetwork structure, the current basis functions in the ring subnetwork structure are constructed, making the port impedances before and after the mapping transformation equivalent.

8. A terminal, characterized in that, include: At least one processor, a memory, and a computer program stored in the memory and executable on at least one processor, wherein the processor, when executing the computer program, implements the method as claimed in any one of claims 1 to 6.

9. A storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 6.

Images