A fast multi-pole electromagnetic simulation method based on PMCHW equation

Abstract

The application discloses a fast multipole electromagnetic simulation method based on a PMCHW equation, and comprises the following steps: regarding a filter as an ideal conductor under port voltage excitation feed, processing the current and magnetic current of a dielectric surface in the filter and the current of a metal surface, using an EFIE equation to describe the current of the metal surface, using a PMCHW equation to describe the current and magnetic current of the dielectric surface, and combining the two equations to obtain an EFIE-PMCHW equation of the filter, and selecting to solve the EFIE-PMCHW equation by using a moment method or a fast multipole method. The application can more quickly and accurately calculate electromagnetic problems of a complex metal dielectric model, divides the model into blocks, calculates the near field and the far field through the distance between the blocks, calculates the near field by using the moment method, and approximately calculates the far field by using the fast multipole, so that compared with other methods, the matrix filling and matrix equation solving time are reduced, and the simulation speed is accelerated.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic field numerical calculation, specifically a fast multipole electromagnetic simulation method based on the PMCHW equation. Background Technology

[0002] Full-wave simulation of electromagnetic problems is one of the most challenging problems in modern computing technology. The method of moments (MoM), based on integral equations, is widely used as an effective solution method. Fast and accurate calculation of electromagnetic problems involving complex metallic dielectric hybrid models is crucial for antenna design and RF integrated circuit simulation. While the MoM method, due to its global nature, yields the most accurate results, it generates a dense impedance matrix, resulting in a long computation time. Iterative methods can reduce computational complexity and quickly solve the matrix, but the computational speed still cannot meet our requirements.

[0003] To overcome this problem, various fast algorithms have been proposed based on the method of moments, such as the Integral Equation Fast Fourier Transform (IE-FFT), Multilevel Fast Multipole (MLFMA), and Fast Multipole (FMM) methods. These use acceleration techniques to approximate the far-field interactions. However, their computational efficiency is not high for objects with complex shapes.

[0004] The PMCHW equations, short for the Poggio-Miller-Chang-Harrington-Wu equations, are mathematical models in electromagnetism used to analyze the distribution of electromagnetic fields when electromagnetic waves interact with objects. They are suitable for handling scattering problems in homogeneous media, offering high computational accuracy and efficiency. The PMCHW equations can also be combined with other numerical techniques, such as the Fast Multipole Method (FMM) and the Adaptive Cross-Approximation (ACA), to further improve computational efficiency and reduce memory requirements, thus enabling the handling of larger-scale and more complex electromagnetic scattering problems. Summary of the Invention

[0005] One objective of this invention is to provide an efficient adaptive frequency scanning broadband electromagnetic simulation method to address the shortcomings of existing technologies.

[0006] The method of the present invention includes the following steps:

[0007] Step (1): Treat the filter as an ideal conductor under port voltage excitation feed, where the electromagnetic parameters are... In the medium space, below it is a block with electromagnetic parameters of A medium object of limited size; the electric field in the outer region of the conductor is The magnetic field is The electric and magnetic fields inside the conductor are both zero; , Where is the dielectric constant. , Permeability;

[0008] Step (2): Process the current, magnetic current, and metal surface current in the filter. If the metal and the dielectric are in contact, the boundary needs to be processed. Because the current is continuous, the basis functions on the boundary need to be merged or deleted. When the dielectrics on both sides of the metal are the same, the currents on both sides are equal, so delete one current. When the dielectrics on both sides are different, retain the currents on both sides.

[0009] Step (3): Use the EFIE equation (Electric Field Integral Equation) to describe the current on the metal surface, and use the PMCHW equation to describe the current and magnetic current on the dielectric surface; combine the two equations to obtain the EFIE-PMCHW equation of the filter.

[0010] In this step, the current on the metal surface is described using the EFIE equation. If the metal material is not PEC, an impedance boundary condition needs to be added. For the current on the dielectric surface, the magnetic current needs to be represented using the PMCHW equation. By combining the two equations, the EFIE-PMCHW equation can be obtained to solve the problem.

[0011] Step (4): Expand the surface current and magnetic current using RWG basis functions. Each surface element of a metal has a current basis function, and each surface element of a dielectric has a current basis function and a magnetic current basis function.

[0012] Step (5): Count the number of basis functions generated in the previous step. If the number of basis functions is less than or equal to 6500, choose to solve using the method of moments. If it is greater than 6500, use the fast multipole method to solve the EFIE-PMCHW equation. Alternatively, the user can choose the solution method. In the multilevel fast multipole method, the computational target is wrapped in a sufficiently large cube. Then, the cube is cut into layers and grouped. Each layer is divided into a maximum of 8 groups. Each of these 8 groups can be further divided into 8 subgroups. This process is repeated until the side length of the smallest cube group is close to half a wavelength, ultimately constructing an octree structure.

[0013] After constructing the tree structure described above, matrix-vector multiplication is implemented using both bottom-up and top-down methods. For strong interactions between closely spaced cube groups, a direct calculation method is required; while for interactions between far-away cube groups, the fast multipole method can be used to solve the problem.

[0014] Another object of the present invention is to provide an electronic device including a processor and a memory, the memory storing machine-executable instructions that can be executed by the processor, the processor executing the machine-executable instructions to implement the above-described fast multipole electromagnetic simulation method based on the PMCHW equation.

[0015] Another object of the present invention is to provide a machine-readable storage medium storing machine-executable instructions that, when called and executed by a processor, cause the processor to implement the aforementioned fast multipole electromagnetic simulation method based on the PMCHW equations.

[0016] The beneficial effects of this invention are:

[0017] This method combines the PMCHW equation with the fast multipole method, which can calculate electromagnetic problems of complex metallic dielectric models more quickly and accurately compared with traditional methods.

[0018] The method proposed in this invention divides the model into groups and blocks, calculates the near and far fields by the distance between the blocks, calculates the near field using the method of moments, and approximates the far field using multipole expansion. Compared with other fast methods, it can significantly improve computational efficiency. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the fast multipole electromagnetic simulation method based on the PMCHW equations of this invention.

[0020] Figure 2 This is a schematic diagram of the object being divided into blocks;

[0021] Figure 3 This is the low-pass filter model used for testing in this invention.

[0022] Figure 4 This is the result of the test conducted by this invention. Detailed Implementation

[0023] The present invention will now be described in detail with reference to the accompanying drawings.

[0024] like Figure 1 As shown, this invention provides a fast multipole electromagnetic simulation method based on the PMCHW equation. It uses a multipole approximation to calculate the far-field action in the PMCHW equation to accurately simulate the electromagnetic field.

[0025] The method of the present invention includes the following steps:

[0026] Step (1): Treat the filter as an ideal conductor under port voltage excitation feed, where the electromagnetic parameters are... In the medium space; below the conductor is a block with electromagnetic parameters of A medium object of limited size; the electric and magnetic fields of the outer region of the conductor are respectively The electric and magnetic fields inside the conductor are both zero; Where is the dielectric constant. Permeability;

[0027] Step (2): Process the current, magnetic current, and metal surface current. If the metal and the dielectric are in contact, the boundary needs to be processed. Because the current is continuous, the basis functions on the boundary need to be merged or deleted. When the dielectrics on both sides of the metal are the same, the currents on both sides are equal, so delete one current. When the dielectrics on both sides are different, retain the currents on both sides.

[0028] Step (3): The current on the metal surface is described using the EFIE equation. If the metal material is not PEC, an impedance boundary condition needs to be added. The current and magnetic current on the dielectric surface are represented by the PMCHW equation. By combining the two equations, the EFIE-PMCHW equation can be obtained to solve the problem.

[0029] Formula (1)

[0030] Formula (2)

[0031] Where n represents the normal vector of the electric or magnetic flux element, J represents the dielectric constant of the electric and magnetic flux elements, J represents the magnitude of the current density, and M represents the magnitude of the magnetic flux density.

[0032] In the above formula, the L operator and the K operator are defined as follows:

[0033] Formula (3)

[0034] Formula (4)

[0035] Formula (5)

[0036] Where j represents the imaginary unit, Represents the wave number in the medium environment. Represents the vector differential operator;

[0037] Step (4): Expand the surface current and magnetic current using RWG basis functions. Each surface element of the metal has a current basis function, and each surface element of the dielectric has a current basis function and a dielectric basis function.

[0038] Step (5): Count the number of basis functions generated in the previous step. Based on the number, choose to solve using the method of moments (MoM) or the fast multipole method (FMP). If the number of basis functions is less than or equal to the threshold, choose to solve using the MoM; if it is greater than the threshold, use the FMP to solve the EFIE-PMCHW equation. Alternatively, the user can choose the solution method. In this embodiment, the threshold is 6500. In the FMP, the computation target (the filter in this invention) is wrapped in a sufficiently large cube. The cube is then cut into layers and grouped. Each layer is divided into a maximum of 8 groups, and each of these 8 groups can be further divided into 8 subgroups. This process is repeated continuously. Note that the smallest cube group needs to have a side length close to half a wavelength. Finally, an octree structure can be constructed.

[0039] Figure 2 This is a schematic diagram of cutting, layering, and grouping objects.

[0040] During the hierarchical grouping process, it is necessary to determine whether each group has a basis function. The calculation only needs to compute the cube groups that have basis functions. After constructing the tree structure, matrix-vector multiplication is implemented using bottom-up and top-down methods. For strong interactions between closely spaced cube groups (where the source points are located in adjacent groups), a direct calculation method is required; while for interactions between distant cube groups (where the source points are located in non-adjacent groups), a multipole expansion method can be used for rapid calculation.

[0041] If the method of moments is used to solve for the electromagnetic field inside an object, the specific steps are as follows:

[0042] RWG basis functions are defined as the surface electric and magnetic current distributions of objects of arbitrary shapes on two adjacent triangles that share a common edge.

[0043] The definition of RWG basis functions is:

[0044] Formula (7)

[0045] In the formula Indicates the first For the length of the common side of adjacent triangles, and and It is a triangle vertex pointing to point vector, It is a triangle vertex pointing to point ; Indicates the first in the field region One RWG basis function;

[0046] An unknown magnetic current on the surface of an object can be expanded using RWG basis functions in the following form:

[0047] Formula (8)

[0048] Formula (9)

[0049] In the formula This represents the unknown current expansion coefficient. Represents an unknown quantity;

[0050] Substituting formulas (7) and (8) into formulas (1) and (2), we get:

[0051] Formula (10)

[0052] Formula (11)

[0053] in Representing RWG basis functions The linear equation;

[0054] Using the RWG basis functions as test functions, the electric field integral equation can be tested to obtain:

[0055] Formula (12)

[0056] Formula (13)

[0057] in Indicates the first in the field region One RWG basis function;

[0058] because Since it is always along the tangent to the surface of the object, it can be rewritten as follows:

[0059] Formula (14)

[0060] Formula (15)

[0061] Further written in matrix form:

[0062] Formula (16)

[0063] in express The method of moments "impedance" matrix, and All The column vectors represent the "current" vector and the "voltage" vector in the method of moments, respectively.

[0064] To facilitate the calculation and differentiation of current and magnetic current, a matrix is ​​used. It is divided into four parts, and the first of the four parts is... OK The elements of the column are represented as follows:

[0065] Formula (17)

[0066] Formula (18)

[0067] Formula (19)

[0068] Formula (20)

[0069] Matrix V is divided into two parts

[0070] Formula (21)

[0071] Formula (22)

[0072] In the formula , , Indicates frequency; Indicates the field point. Indicates the source point, Represents the Green's function. (Uniform unbounded space) , representing the distance from the field point to the source point. Represents the gradient operator, Denotes the divergence operator, Represents the surface vector element of the field region. Represents the surface vector infinitesimal element of the source region; Indicates the first in the source region One RWG basis function;

[0073] Substituting formulas (17)-(20) into matrix equation (16), and solving the matrix equation, we obtain the current. Current under a fixed voltage Represented as Admittance parameters; The admittance parameters are obtained through parameter transformation. Parameters, i.e., theoretical values ​​of frequency response;

[0074] in, It is the first basis functions The triangle pair they belong to It is the first basis functions The triangle pair;

[0075] This example demonstrates... Figure 3 The frequency response of a low-pass filter is simulated and analyzed. The analysis needs to cover the 1-15 GHz frequency band, and traditional methods use the method of moments (MoM). The method proposed in this invention utilizes the fast multipole approximation to calculate the far field, reducing the overall computation time.

[0076] Figure 4 This embodiment is for Figure 3 Test results of the low-pass filter.

[0077] The above embodiments are not intended to limit the present invention, and the present invention is not limited to the above embodiments. Any embodiment that meets the requirements of the present invention is within the protection scope of the present invention.

Claims

1. A fast multipole electromagnetic simulation method based on the PMCHW equations, characterized in that, Includes the following steps: Step (1): Treat the filter as an ideal conductor under port voltage excitation feed, where the electromagnetic parameters are... In the medium space, below it is a block with electromagnetic parameters of A medium of finite size; the electric field in the outer region of the conductor is The magnetic field is The electric and magnetic fields inside the conductor are both zero; , Where is the dielectric constant. , Permeability; Step (2): Process the current, magnetic current on the dielectric surface and the current on the metal surface in the filter; Step (3): Use the EFIE equation to describe the current on the metal surface; use the PMCHW equation to describe the current and magnetic current on the dielectric surface; combine the EFIE equation and the PMCHW equation to obtain the EFIE-PMCHW equation of the filter. Official (1) Official (2) Where n represents the normal vector of the electric or magnetic flux element, J represents the dielectric constant of the electric and magnetic flux elements, J represents the magnitude of the current density, and M represents the magnitude of the magnetic flux density. In the above formula, the L operator and the K operator are defined as follows: Official (3) Official (4) Official (5) Where j represents the imaginary unit, Represents the wave number in the medium environment. Represents the vector differential operator; Step (4): Expand the current and magnetic current of the surface using RWG basis functions, where each surface element of the metal surface has a current basis function and each surface element of the dielectric surface has a current basis function and a magnetic current basis function. Step (5): Count the number of basis functions generated in step (4), and determine whether the number of basis functions is greater than the threshold. If so, use the fast multipole method to solve the EFIE-PMCHW equation. If not, use the method of moments to solve the EFIE-PMCHW equation. After solving, obtain the current corresponding to the basis function. Obtain the Y parameter by counting the current of the basis function near the port. Finally, convert the Y parameter to the S parameter and Z parameter through parameter transformation.

2. The fast multipole electromagnetic simulation method based on the PMCHW equations as described in claim 1, characterized in that, The processing in step (2) is as follows: if the metal surface and the dielectric surface are in contact, the basis functions on the contact boundary are merged or deleted; when the dielectrics on both sides of the metal surface are the same, one of the current basis functions is deleted; when the dielectrics on both sides are different, the current basis functions on both sides are retained.

3. The fast multipole electromagnetic simulation method based on the PMCHW equations as described in claim 1, characterized in that, When choosing the fast multipole pair to solve the EFIE-PMCHW equation, the computational objective is first wrapped in a sufficiently large cube. Then, the cube is cut and divided into layers and groups. Each layer is divided into a maximum of 8 groups, and each of these 8 groups can be further divided into 8 subgroups. This process is repeated until an octree structure is finally constructed. During the hierarchical grouping process, it is necessary to determine whether each group has a basis function. In the calculation, only the cube groups with basis functions need to be calculated. After constructing the above octree structure, matrix-vector multiplication is implemented from bottom to top and from top to bottom. The solution is performed based on the distance between groups. If the field point and the source point are located in adjacent groups, the solution is performed directly using the method of moments. If they are not located in adjacent groups, the multi-layer fast multipole is used to accelerate the filling and solution.

4. The fast multipole electromagnetic simulation method based on the PMCHW equations as described in claim 3, characterized in that, During the hierarchical grouping process, the side length of the smallest subgroup is close to half a wavelength.

5. The fast multipole electromagnetic simulation method based on the PMCHW equations as described in claim 3, characterized in that, The method of moments (MoM) is used to solve the problem as follows: RWG basis functions are defined as the surface electric and magnetic current distributions of objects of arbitrary shapes on two adjacent triangles that share a common edge. The definition of RWG basis functions is: Official (7) In the formula Indicates the first For the length of the common side of adjacent triangles, and and It is a triangle vertex pointing to point vector, It is a triangle vertex pointing to point ; Indicates the first in the field region One RWG basis function; An unknown magnetic current on the surface of an object can be expanded using RWG basis functions in the following form: Official (8) Official (9) In the formula This represents the unknown current expansion coefficient. Represents an unknown quantity; Substituting formulas (8) and (9) into formulas (1) and (2), we get: Official (10) Official (11) in Representing RWG basis functions The linear equation; Using the RWG basis functions as test functions, the electric field integral equation can be tested to obtain: Official (12) Official (13) in Indicates the first in the field region One RWG basis function; because Since it is always along the tangent to the surface of the object, it can be rewritten as follows: Official (14) Official (15) Further written in matrix form: Official (16) in express The method of moments "impedance" matrix, and All The column vectors represent the "current" vector and the "voltage" vector in the method of moments, respectively. To facilitate the calculation and differentiation of current and magnetic current, a matrix is ​​used. It is divided into four parts, and the first of the four parts is... OK The elements of the column are represented as follows: Official (17) Official (18) Official (19) Official (20) Matrix V is divided into two parts Official (21) Official (22) In the formula , , Indicates frequency; Indicates the field point. Indicates the source point, Represents the Green's function. It is a uniform, unbounded space; , representing the distance from the field point to the source point. Represents the gradient operator, Denotes the divergence operator, Represents the surface vector element of the field region. Represents the surface vector infinitesimal element of the source region; Indicates the first in the source region One RWG basis function; Substituting formulas (17)-(20) into matrix equation (16), and solving the matrix equation, we obtain the current. Current under a fixed voltage Represented as Admittance parameters; The admittance parameters are obtained through parameter transformation. Parameters, i.e., theoretical values ​​of frequency response; in, It is the first basis functions The triangle pair they belong to It is the first basis functions The triangle they belong to.

6. An electronic device, characterized in that, It includes a processor and a memory, the memory storing machine-executable instructions that can be executed by the processor, the processor executing the machine-executable instructions to implement the fast multipole electromagnetic simulation method based on the PMCHW equations as described in any one of claims 1-5.

7. A machine-readable storage medium, characterized in that, The machine-readable storage medium stores machine-executable instructions that, when invoked and executed by a processor, cause the processor to implement the fast multipole electromagnetic simulation method based on the PMCHW equations as described in any one of claims 1-5.

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