A circuit simulation method based on non-overlapping domain decomposition of rotational basis functions

Abstract

This invention discloses a circuit simulation method based on non-overlapping region decomposition using rotating basis functions. The method includes: dividing an ideal conductor in an integrated circuit device system model into non-overlapping sub-regions; constructing a virtual surface at the interface between any two sub-regions; subdividing the surface of each sub-region into a conformal mesh at the interface; discretizing the current in each sub-region using rotating basis functions to construct the method of moments equations; setting boundary conditions on the virtual surface to ensure current continuity; and solving the current in each sub-region using steady-state iteration to complete the circuit simulation. This invention partitions the complex model, reducing the computational scale through a divide-and-conquer approach. Simultaneously, it uses rotating basis functions to discretize the model, enabling the solution of large-scale problems even with limited memory. Compared to global matrix solving, it significantly reduces memory usage and achieves rapid convergence in low-frequency simulations.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic simulation application technology, and in particular to a circuit simulation method based on non-overlapping region decomposition using rotating basis functions. Background Technology

[0002] In the field of electromagnetic simulation applications, the most effective method to obtain accurate electromagnetic scattering results for arbitrary three-dimensional complex structural targets is to perform full-wave numerical analysis using Maxwell's integral equations. This method is based on Maxwell's equations, combined with electromagnetic field boundary conditions, and describes the scattering current through mesh generation and the establishment of basis functions. A discrete linear system is then constructed using the Galerkin test. The method of moments (MoM) is a discretized numerical solution method for continuous integral equations, commonly used in chip-level circuit simulation.

[0003] However, when integrated circuit device structures are extremely complex, precise mesh generation is often required to ensure simulation accuracy. The number of unknowns associated with precise meshes is enormous, placing extremely high demands on computational efficiency and memory. While stacking hardware can address memory issues to some extent, it is ultimately not a fundamental solution.

[0004] Therefore, how to reduce the computing scale and memory usage is a technical problem that urgently needs to be solved. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a circuit simulation method based on non-overlapping region decomposition using rotating basis functions. This method partitions complex models, reduces computational scale through a divide-and-conquer approach, and discretizes the model using rotating basis functions. This enables the solution of large-scale problems even with limited memory, significantly reducing memory usage compared to global matrix solving, and achieving rapid convergence in low-frequency simulations.

[0006] This invention provides the following solutions:

[0007] This invention provides a circuit simulation method based on non-overlapping region decomposition using rotational basis functions, the method comprising:

[0008] S1. Divide the ideal conductor in the integrated circuit device system model into non-intersecting sub-regions, and construct a virtual surface at the interface between any two sub-regions;

[0009] S2. The surface of each sub-region is subdivided, and the surface of each sub-region includes the outer surface of each sub-region and the virtual surface at the boundary. The interface is subdivided into a conformal mesh.

[0010] S3. Discretize the current in each sub-region by rotating basis functions and construct the method of moments equations;

[0011] S4. Set boundary conditions on the virtual surface to ensure current continuity;

[0012] S5. Iteratively solve the equations using the method of moments to obtain the current coefficients of the loop basis functions and the tree basis functions for each sub-region, and complete the circuit simulation.

[0013] Furthermore, step S2 includes the following process: dividing the outer surface and virtual surface of each sub-region into triangular and / or quadrilateral meshes, wherein the mesh node positions are the same at the interface of any two adjacent sub-regions.

[0014] Furthermore, the equation for the method of moments described in step S3 is: ,in:

[0015] ,

[0016] ,

[0017] ,

[0018] ,

[0019] ,

[0020] ,

[0021] ,

[0022] in, and Let be the current coefficients of the loop basis function and the tree basis function of the m-th sub-region to be solved, respectively; j is the imaginary unit; ω is the operating angular frequency of the integrated circuit device system; μ is the permeability of the dielectric; ε is the dielectric constant of the dielectric; and r and These are the field point coordinates and the source point coordinates, respectively. Let m be the loop basis function at the field point in the m-th sub-region. Let m be the loop basis function at the source point of the m-th sub-region. Let be the tree basis function at the field point in the m-th sub-region. Let be the tree basis function at the source point of the m-th subregion. For Green's function, Let be the incident electric field intensity at the m-th sub-region field point. Let be the scattered electric field intensity from the nth subregion to the mth subregion.

[0023] Furthermore, the boundary conditions described in step S4 are: , where j mn(r) represents the current at the interface between the m-th sub-region and the n-th sub-region, j nm (r) represents the current at the interface between the nth subregion and the mth subregion.

[0024] Furthermore, step S5 specifically includes the following processes:

[0025] S5.1 Solve the equations separately for each sub-region, assuming that the coupled scattered field in each sub-region is 0, i.e. Please solve:

[0026] ,

[0027] The current coefficients of the loop basis function for the initial iteration of each sub-region are thus calculated. and tree basis function current coefficient ;

[0028] S5.2. Using the current calculation results of all sub-regions in the previous step as the right-hand side term, perform right-hand side term correction, and calculate the current result of the k-th iteration for each region. The correction equation is:

[0029] ,

[0030] ,

[0031] ,

[0032] ,

[0033] ,

[0034] Where k is the number of iterations. and These are the current coefficients of the loop basis function and the tree basis function in the k-th iteration of the m-th sub-region, respectively. and These are the current coefficients of the loop basis function and the tree basis function in the (k-1)th iteration of the nth sub-region, respectively. Let n be the loop basis function at the source point of the nth subregion. Let be the tree basis function at the source point of the nth subregion. and These are the Hamiltonian operators acting on the field point coordinates and the source point coordinates, respectively;

[0035] S5.3, when The iteration ends when the calculation is complete, and the current iteration is complete. and The current coefficients of the loop basis function obtained by the solution and tree basis function current coefficient ,in Let δ denote the matrix norm, and δ be the minimum convergent residual; otherwise, return to step S5.2 to proceed to the next iteration.

[0036] The beneficial effects of this invention based on its technical solution are as follows:

[0037] This invention provides a circuit simulation method based on non-overlapping region decomposition using rotating basis functions. This method partitions complex models, reducing computational scale through a divide-and-conquer approach. Simultaneously, it discretizes the model using rotating basis functions, enabling the solution of large-scale problems even with limited memory. Compared to global matrix solving, it significantly reduces memory usage and achieves rapid convergence in low-frequency simulations. This invention is applicable to full-wave simulation analysis of large-scale complex electromagnetic structures and simulation of multi-scale, multi-physics domain electromagnetic problems, including but not limited to radar cross-section calculations for large-scale models such as aircraft and ships, chip-package-PCB collaborative electromagnetic simulation, and signal integrity analysis. Furthermore, it does not rely on specific fast algorithms, dedicated hardware accelerators, commercial electromagnetic simulation software platforms, or overlapping region decomposition methods. It can be used in conjunction with the aforementioned fast algorithms, parallel computing frameworks, mesh optimization tools, preprocessing techniques, and high-frequency approximation methods to further improve computational efficiency, expand problem scale, or enhance multi-band simulation capabilities. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a schematic flowchart of a circuit simulation method based on non-overlapping region decomposition using rotating basis functions, provided by the present invention.

[0040] Figure 2 This is a schematic diagram of the sub-region division.

[0041] Figure 3 This is a schematic diagram of the mesh.

[0042] Figure 4 This is a schematic diagram illustrating a calculation example for a 60mm microstrip line.

[0043] Figure 5 This is a schematic diagram of the decomposition and mesh generation of a 60mm microstrip line region. Detailed Implementation

[0044] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the protection scope of the embodiments of the present invention.

[0045] Reference Figure 1 A circuit simulation method based on non-overlapping region decomposition using rotational basis functions is provided, the method comprising:

[0046] S1. Divide the ideal conductor in the integrated circuit device system model into non-intersecting sub-regions, and construct a virtual surface at the interface between any two sub-regions. (Refer to...) Figure 2 The yellow and green areas are two non-overlapping sub-regions.

[0047] S2. The surface of each sub-region is subdivided, where each sub-region surface includes the outer surface of the sub-region and the virtual surface at the boundary. At the interface, it is subdivided into a conformal mesh. (Refer to...) Figure 3 The surface of each sub-region is divided into triangular and / or quadrilateral grids, resulting in two sub-regions. and and the outer surface of the corresponding sub-region and and virtual sub-interface Two of the sub-regions are on the virtual surface The nodes on the upper grid are in the same position, and the arrows point in the direction of the rotation basis functions.

[0048] Figures 4 to 5 The effect of meshing a 60mm microstrip line before and after is shown.

[0049] S3. Discretize the current in each sub-region using rotating basis functions to construct the method of moments equations: ;

[0050] in:

[0051] ,

[0052] ,

[0053] ,

[0054] ,

[0055] ,

[0056] ,

[0057] ,

[0058] in, and Let be the current coefficients of the loop basis function and the tree basis function of the m-th sub-region to be solved, respectively; j is the imaginary unit; ω is the operating angular frequency of the integrated circuit device system; μ is the permeability of the dielectric (in H / m); ε is the dielectric constant of the dielectric (in F / m); and r and These are the field point coordinates and the source point coordinates, respectively. Let m be the loop basis function at the field point in the m-th sub-region. Let m be the loop basis function at the source point of the m-th sub-region. Let be the tree basis function at the field point in the m-th sub-region. Let be the tree basis function at the source point of the m-th subregion. For Green's function, Let V be the incident electric field intensity at the m-th sub-region field point (unit: V / m). The scattered electric field intensity from the nth subregion to the mth subregion (unit: V / m).

[0059] S4. Since the current is cut off at the interface due to partitioning, the current continuity is ensured by setting boundary conditions on the virtual surface.

[0060] The boundary conditions are: , where j mn (r) represents the current at the interface between the m-th sub-region and the n-th sub-region, j nm (r) represents the current at the interface between the nth subregion and the mth subregion.

[0061] S5. Use the Gauss-Seidel iterative method to calculate the original problem, thereby solving the equations in each sub-region. Use the calculation results as excitation for other regions, and correct the current calculation results in each region through iterative calculation. The calculation stops when the calculation residuals meet the convergence condition, obtaining the current in each sub-region and completing the circuit simulation. This includes the following steps:

[0062] S5.1 Solve the equations separately for each sub-region, assuming that the coupled scattered field in each sub-region is 0, i.e. Please provide a solution:

[0063] ,

[0064] The current coefficients of the loop basis function for the initial iteration of each sub-region are thus calculated. and tree basis function current coefficient ;

[0065] S5.2. Using the current calculation results of all sub-regions in the previous step as the right-hand side term, perform right-hand side term correction, and calculate the current result of the k-th iteration for each region. The correction equation is:

[0066] ,

[0067] ,

[0068] ,

[0069] ,

[0070] ,

[0071] Where k is the number of iterations. and These are the current coefficients of the loop basis function and the tree basis function in the k-th iteration of the m-th sub-region, respectively. and These are the current coefficients of the loop basis function and the tree basis function in the (k-1)th iteration of the nth sub-region, respectively. Let n be the loop basis function at the source point of the nth subregion. Let be the tree basis function at the source point of the nth subregion. and These are the Hamiltonian operators acting on the field point coordinates and the source point coordinates, respectively.

[0072] S5.3, when The iteration ends when the calculation is complete, and the current iteration is complete. and The current coefficients of the loop basis function obtained by the solution and tree basis function current coefficient ,in Let δ denote the matrix norm, and δ be the minimum convergent residual; otherwise, return to step S5.2 to proceed to the next iteration.

[0073] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0074] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0075] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A circuit simulation method based on non-overlapping region decomposition using rotating basis functions, characterized in that, The method includes: S1. Divide the ideal conductor in the integrated circuit device system model into non-intersecting sub-regions, and construct a virtual surface at the interface between any two sub-regions; S2. The surface of each sub-region is subdivided, and the surface of each sub-region includes the outer surface of each sub-region and the virtual surface at the boundary. The interface is subdivided into a conformal mesh. S3. Discretize the current in each sub-region by rotating basis functions and construct the method of moments equations; S4. Set boundary conditions on the virtual surface to ensure current continuity; S5. Iteratively solve the equations using the method of moments to obtain the current coefficients of the loop basis functions and the tree basis functions for each sub-region, and complete the circuit simulation.

2. The circuit simulation method based on non-overlapping region decomposition using rotating basis functions according to claim 1, characterized in that: Step S2 includes the following process: dividing the outer surface and virtual surface of each sub-region into triangular and / or quadrilateral meshes, wherein the mesh node positions are the same at the interface of any two adjacent sub-regions.

3. The circuit simulation method based on non-overlapping region decomposition using rotating basis functions according to claim 1, characterized in that: The equation for the method of moments described in step S3 is: ,in: ， ， ， ， ， ， ， in, and Let be the current coefficients of the loop basis function and the tree basis function of the m-th sub-region to be solved, respectively; j is the imaginary unit; ω is the operating angular frequency of the integrated circuit device system; μ is the permeability of the dielectric; ε is the dielectric constant of the dielectric; and r and These are the field point coordinates and the source point coordinates, respectively. Let m be the loop basis function at the field point in the m-th sub-region. Let m be the loop basis function at the source point of the m-th sub-region. Let be the tree basis function at the field point in the m-th sub-region. Let be the tree basis function at the source point of the m-th subregion. For Green's function, Let be the incident electric field intensity at the m-th sub-region field point. Let be the scattered electric field intensity from the nth subregion to the mth subregion.

4. The circuit simulation method based on non-overlapping region decomposition using rotating basis functions according to claim 3, characterized in that: The boundary conditions described in step S4 are: , where j mn (r) represents the current at the interface between the m-th sub-region and the n-th sub-region, j nm (r) represents the current at the interface between the nth subregion and the mth subregion.

5. The circuit simulation method based on non-overlapping region decomposition using rotating basis functions according to claim 4, characterized in that: Step S5 details Includes the following processes: S5.1 Solve the equations separately for each sub-region, assuming that the coupled scattered field in each sub-region is 0, i.e. Please provide a solution: ， The current coefficients of the loop basis function for the initial iteration of each sub-region are thus calculated. and tree basis function current coefficient ; S5.

2. Using the current calculation results of all sub-regions in the previous step as the right-hand side term, perform right-hand side term correction, and calculate the current result of the k-th iteration for each region. The correction equation is: ， ， ， ， ， Where k is the number of iterations. and These are the current coefficients of the loop basis function and the tree basis function in the k-th iteration of the m-th sub-region, respectively. and These are the current coefficients of the loop basis function and the tree basis function in the (k-1)th iteration of the nth sub-region, respectively. Let n be the loop basis function at the source point of the nth subregion. Let be the tree basis function at the source point of the nth subregion. and These are the Hamiltonian operators acting on the field point coordinates and the source point coordinates, respectively; S5.3, when The iteration ends when the calculation is complete, and the current iteration is complete. and The current coefficients of the loop basis function obtained by the solution and tree basis function current coefficient ,in Let δ denote the matrix norm, and δ be the minimum convergent residual; otherwise, return to step S5.2 to proceed to the next iteration.

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