Fast multipole electromagnetic simulation method based on PMCHW equation

Abstract

The invention discloses a rapid multipole electromagnetic simulation method based on a PMCHW equation, and the method comprises the following steps: taking a filter as an ideal conductor under the excitation feed of a port voltage, processing the current and magnetic current of a medium surface in the filter and the current of a metal surface, describing the current of the metal surface through an EFIE equation, and calculating the current of the metal surface according to the EFIE equation. A PMCHW equation is adopted to describe current and magnetic current on the surface of a medium, the two equations are simultaneous to obtain an EFIE-PMCHW equation of the filter, and the EFIE-PMCHW equation is solved by selecting a moment method or a fast multipole method. According to the method, the electromagnetic problem of the complex metal medium model can be calculated more quickly and accurately, the model is divided into blocks, far and near fields are calculated through the distance between the blocks, the near field is calculated through a moment method, the far field is calculated through fast multipole approximation, and compared with other methods, matrix filling and matrix equation solving time is shortened, and the simulation speed is increased.

Description

Technical Field

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

[0002] Full-wave simulation of electromagnetic problems is one of the most challenging problems in modern computing technology. The moment method based on integral equations is widely used as an effective solution method. Fast and accurate calculation of electromagnetic problems of complex metal-medium hybrid models is the key to antenna design and RF integrated circuit simulation. Due to its global characteristics, the moment method can obtain the most accurate results, but the generated impedance matrix is ​​relatively dense and the calculation time is relatively long. If an iterative solution is used, the calculation complexity can be reduced and the matrix can be solved quickly, but the calculation speed cannot meet our needs.

[0003] In order to overcome this problem, people have proposed various fast algorithms based on the moment method, such as integral equation fast Fourier transform (IE-FFT), multi-layer fast multipole (MLFMA), and fast multipole (FMM) methods. These are some acceleration techniques to approximate the interaction of the far field. However, the calculation efficiency is not high for objects with complex shapes.

[0004] The PMCHW equation, the full name of which is the Poggio-Miller-Chang-Harrington-Wu equation, is a mathematical model used in electromagnetics to analyze the distribution of electromagnetic fields when electromagnetic waves interact with objects. It is suitable for dealing with scattering problems of homogeneous dielectric bodies and can provide high computational accuracy and efficiency. The PMCHW equation 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, thereby being able to handle larger-scale and more complex electromagnetic scattering problems. Summary of the invention

[0005] An object of the present invention is to provide a broadband electromagnetic simulation method with efficient adaptive frequency scanning in order to address the deficiencies of the existing technology.

[0006] The method of the present invention comprises the following steps: Step (1): The filter is regarded as an ideal conductor under the excitation of the port voltage. The conductor is located at an electromagnetic parameter of In the medium space, there is a block with electromagnetic parameters below it. The electric field in the outer area of ​​the conductor is , the magnetic field is , the electric field and magnetic field inside the conductor are both 0; , is the dielectric constant, , is the magnetic permeability; Step (2) processes the current and magnetic current on the surface of the medium in the filter and the current on the metal surface. If the metal and the medium are in contact, the boundary needs to be processed. Since the current is continuous, the basis functions on the boundary need to be merged or deleted. When the medium on both sides of the metal is the same, the currents on both sides are equal and one current is deleted. If the medium on both sides is different, the currents on both sides are retained.

[0007] Step (3), using the EFIE equation (Electric Field Integral Equation) to describe the current on the metal surface, and using the PMCHW equation to describe the current and magnetic current on the dielectric surface; combining the two equations to obtain the EFIE-PMCHW equation of the filter; In this step, the current on the metal surface is described by the EFIE equation. If the metal material is not pec, an impedance boundary condition needs to be added. For the current on the medium surface, the magnetic flow needs to be expressed by the PMCHW equation; by combining the two equations, the EFIE-PMCHW equation can be obtained to solve the problem.

[0008] Step (4): Use RWG basis functions to expand the current and magnetic flow on the surface. Each surface element of the metal has a current basis function, and each surface element of the medium has a current basis function and a magnetic flow basis function.

[0009] 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, the moment method is selected for solution. If it is greater than 6500, the fast multipole method is used to solve the EFIE-PMCHW equation. The user can also select the solution method. In the multi-layer fast multipole method, the calculation target is wrapped with a sufficiently large cubic box, and then the cubic box is cut and layered. Each layer is divided into a maximum of 8 groups. Each of the eight groups can be divided into 8 sub-groups. Repeat until the side length of the smallest cubic group is close to half a wavelength, and finally an octree structure can be constructed.

[0010] After constructing the above tree structure, matrix-vector multiplication is implemented using bottom-up and top-down methods. For strong interactions between cube groups that are close to each other, direct calculation methods are required; for interactions between cube groups that are far away, fast multipole methods can be used to solve them.

[0011] Another object of the present invention is to provide an electronic device, comprising a processor and a memory, wherein the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the above-mentioned fast multipole electromagnetic simulation method based on the PMCHW equation.

[0012] Another object of the present invention is to provide a machine-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the above-mentioned fast multipole electromagnetic simulation method based on the PMCHW equation.

[0013] The beneficial effects of the present invention are: This method combines the PMCHW equation with the fast multipole method, which can calculate the electromagnetic problems of complex metal medium models more quickly and accurately compared with traditional methods.

[0014] The method proposed in the present invention divides the model into groups and blocks, calculates the near and far fields by the distance between blocks, calculates the near field by the method of moments, and calculates the far field approximately by multipole expansion. Compared with other fast methods, the calculation efficiency can be significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of the fast multipole electromagnetic simulation method based on PMCHW equation implemented by the present invention; Figure 2 It is a schematic diagram of the object segmentation; Figure 3 It is the low-pass filter model used for testing in the present invention.

[0016] Figure 4 It is the result of the test of the present invention. DETAILED DESCRIPTION

[0017] The present invention is described in detail below in conjunction with the accompanying drawings.

[0018] like Figure 1 As shown, the present invention provides a fast multipole electromagnetic simulation method based on the PMCHW equation, which uses a multipole approximation to calculate the far-field effect in the PMCHW equation to accurately simulate the electromagnetic field.

[0019] The method of the present invention comprises the following steps: Step (1): The filter is regarded as an ideal conductor under the excitation of the port voltage. The conductor is located at an electromagnetic parameter of In the medium space; under the conductor there is a block with electromagnetic parameters The electric field and magnetic field in the outer area of ​​the conductor are , the electric field and magnetic field inside the conductor are both 0; is the dielectric constant, is the magnetic permeability; Step (2) processes the current on the surface of the medium, the magnetic current, and the current on the metal surface. If the metal and the medium are in contact, the boundary needs to be processed. Since the current is continuous, the basis functions on the boundary need to be merged or deleted. When the medium on both sides of the metal is the same, the currents on both sides are equal, and one current is deleted. If the medium on both sides is different, the currents on both sides are retained.

[0020] Step (3): The current on the metal surface is described by the EFIE equation. If the metal material is not pec, an impedance boundary condition needs to be added. The current and magnetic flow on the dielectric surface need to be expressed by the PMCHW equation. By combining the two equations, the EFIE-PMCHW equation can be obtained to solve the problem.

[0021] Formula (1) Formula (2) Where n represents the normal vector of the electric and magnetic current elements, It represents the dielectric constant of electric and magnetic current elements, J represents the current density, and M represents the magnetic current density; In the above formula, the definitions of L operator and K operator are as follows: Formula (3) Formula (4) Formula (5) Where j represents the imaginary unit, represents the wave number in the medium environment, represents the vector differential operator; Step (4): Use RWG basis functions to expand the current and magnetic current on the surface. 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.

[0022] Step (5), counting the number of basis functions generated in the previous step, and choosing to use the method of moments or the fast multipole method for solution according to the number. If the number of basis functions is less than or equal to the threshold, the method of moments is chosen for solution. If it is greater than the threshold, the fast multipole method is used to solve the EFIE-PMCHW equation. The user can also choose the solution method. In this embodiment, the threshold is 6500. In the fast multipole method, the calculation target (the filter in the present invention) is wrapped with a sufficiently large cubic box, and then the cubic box is cut and layered and grouped. Each layer is divided into a maximum of 8 groups. Each of the eight groups can be divided into 8 sub-groups, and the process is repeated continuously. It should be noted that the minimum cubic group needs to satisfy the requirement that its side length is close to half a wavelength. Finally, an octet tree structure can be constructed.

[0023] Figure 2 It is a schematic diagram of object cutting and layering.

[0024] In the hierarchical grouping process, it is necessary to determine whether there is a basis function in each group. Only the cube groups with basis functions need to be calculated. After constructing the above tree structure, matrix-vector multiplication is implemented from bottom to top and from top to bottom. For strong interactions between cube groups that are close to each other (the field source points are located in adjacent groups), a direct calculation method is required; for interactions between cube groups that are far away (the field source points are located in non-adjacent groups), the multipole expansion method can be used to quickly calculate.

[0025] If the moment method is used to solve the electromagnetic field inside an object, the specific steps include: The RWG basis function is defined on two adjacent triangles with common edges, which can simulate the surface electric and magnetic current distribution of objects of arbitrary shapes; The definition of the RWG basis function is: Formula (7) In the formula Indicates For the length of the common sides of adjacent triangles, and and It is a triangle The vertex points to the point The vector of It is a triangle The vertex points to the point vector of; Indicates the field area RWG basis functions; The unknown current and magnetic flux on the surface of the object can be expanded into the following form using the RWG basis function: Formula (8) Formula (9) In the formula represents the unknown current expansion coefficient, Represents an unknown quantity; Substituting formula (7) and formula (8) into formula (1) and formula (2), we obtain: Formula (10) Formula (11) in Represents the RWG basis function The linear equation of Using the RWG basis function as the test function, the electric field integral equation can be tested to obtain: Formula (12) Formula (13) in Indicates the field area RWG basis functions; because It is always tangential to the surface of the object, so it can be rewritten as follows: Formula (14) Formula (15) Further written in matrix form: Formula (16) in express The method of moments "impedance" matrix, and Both The column vectors of , which represent the “current” vector and “voltage” vector of the moment method respectively; In order to facilitate the calculation and distinction of current and magnetic flow, the matrix It is divided into four parts, of which OK The elements of a column are represented as follows: Formula (17) Formula (18) Formula (19) Formula (20) The matrix V is divided into two parts Formula (21) Formula (22) In the formula , , Indicates frequency; Indicates the field point, Indicates the source point, represents the Green's function, (uniform unbounded space), , represents the distance from the field point to the source point, represents the gradient operator, represents the divergence operator, Represents the field area surface vector infinitesimal element, Represents the source area surface vector microelement; Indicates the source region RWG basis functions; Substituting formulas (17)-(20) into the matrix equation (16), solving the matrix equation yields the current ; Current at a fixed voltage Expressed as Admittance parameter; The admittance parameters are obtained through parameter conversion Parameters, i.e. theoretical values ​​of frequency response; in, It is Basis Functions The triangle pair where It is Basis Functions The triangle pair where it is located; This example is about Figure 3 The low-pass filter is simulated and analyzed for its frequency response. The frequency band of 1-15 GHz needs to be analyzed. The traditional analysis method is to use the moment method to solve. The method proposed in the present invention is to use the fast multipole approximation to calculate the far field, thereby reducing the overall calculation time.

[0026] Figure 4 This embodiment is Figure 3 Test results of low-pass filter.

[0027] The above embodiments are not limitations of the present invention, and the present invention is not limited to the above embodiments. As long as the requirements of the present invention are met, they belong to the protection scope of the present invention.

Claims

1. A fast multipole electromagnetic simulation method based on PMCHW equation, characterized in that: The following steps are involved: Step (1): The filter is regarded as an ideal conductor under the excitation of the port voltage. The conductor is located at an electromagnetic parameter of In the medium space, there is a block with electromagnetic parameters below it. The electric field in the outer region of the conductor is , the magnetic field is , the electric field and magnetic field inside the conductor are both 0; , is the dielectric constant, , is the magnetic permeability; Step (2), processing the current and magnetic current on the dielectric surface and the current on the metal surface in the filter; Step (3), using the EFIE equation to describe the current on the metal surface; using the PMCHW equation to describe the current and magnetic current on the medium surface; combining the EFIE equation and the PMCHW equation to obtain the EFIE-PMCHW equation of the filter; Formula (1) Formula (2) Where n represents the normal vector of the electric and magnetic current elements, It represents the dielectric constant of electric and magnetic current elements, J represents the current density, and M represents the magnetic current density; In the above formula, the definitions of L operator and K operator are as follows: Formula (3) Formula (4) Formula (5) Where j represents the imaginary unit, represents the wave number in the medium environment, represents the vector differential operator; Step (4), using RWG basis functions to expand the current and magnetic flow on the surface, wherein each surface element on the metal surface has a current basis function, and each surface element on the dielectric surface has a current basis function and a magnetic flow basis function; Step (5), counting the number of basis functions generated in step (4), and determining whether the number of basis functions is greater than a threshold value. If so, the EFIE-PMCHW equation is solved by fast multipole, and if not, the EFIE-PMCHW equation is solved by the method of moments. After solving, the current corresponding to the basis function is obtained, and the Y parameter is obtained by counting the current of the basis function near the port, and finally the Y parameter is converted into the S parameter and the Z parameter by parameter conversion.

2. The fast multipole electromagnetic simulation method based on PMCHW equation according to 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 PMCHW equation as claimed in claim 1, characterized in that: When choosing fast multipole to solve the EFIE-PMCHW equation, first wrap the calculation target with a large enough cube box, then cut the cube box into layers and groups, each layer is divided into a maximum of 8 groups, each of these 8 groups can be divided into 8 sub-groups, and repeat this process to finally build an octree structure; In the process of hierarchical grouping, it is necessary to determine whether there is a basis function in each group. In the calculation, only the cube groups with basis functions need to be calculated. After constructing the above octet structure, matrix-vector multiplication is implemented from bottom to top and from top to bottom. The solution is performed according to the distance between groups. If the field point and the source point are located in adjacent groups, they are solved directly by the moment method. 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 PMCHW equation as claimed in claim 3 is characterized in that: During the hierarchical grouping process, the side length of the smallest sub-group is close to half a wavelength.

5. The fast multipole electromagnetic simulation method based on PMCHW equation as claimed in claim 3, characterized in that: The method of moments solution is as follows: The RWG basis function is defined on two adjacent triangles with common edges, which can simulate the surface electric and magnetic current distribution of objects of arbitrary shapes; The definition of the RWG basis function is: Formulas (7) In the formula Indicates For the length of the common sides of adjacent triangles, and and It is a triangle The vertex points to the point The vector of It is a triangle The vertex points to the point vector of; Indicates the field area RWG basis functions; The unknown current and magnetic flux on the surface of the object can be expanded into the following form using the RWG basis function: Formulas (8) Formulas (9) In the formula represents the unknown current expansion coefficient, Represents an unknown quantity; Substituting formula (7) and formula (8) into formula (1) and formula (2), we obtain: Formulas (10) Official(11) in Represents the RWG basis function The linear equation of Using the RWG basis function as the test function, the electric field integral equation can be tested to obtain: Formula(12) Official(13) in Indicates the field area RWG basis functions; because It is always tangential to the surface of the object, so it can be rewritten as follows: Official(14) Official(15) Further written in matrix form: Official(16) in express The moment method "impedance" matrix, and Both The column vectors of , which represent the "current" vector and "voltage" vector of the moment method respectively; In order to facilitate the calculation and distinction of current and magnetic flow, the matrix It is divided into four parts, of which OK The elements of a column are represented as follows: Official(17) Official(18) Official(19) Official(20) The 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, (uniform unbounded space), , represents the distance from the field point to the source point, represents the gradient operator, represents the divergence operator, Represents the field area surface vector infinitesimal element, Represents the source area surface vector microelement; Indicates the source region RWG basis functions; Substituting formulas (17)-(20) into the matrix equation (16), solving the matrix equation yields the current ; Current at a fixed voltage Expressed as Admittance parameter; The admittance parameters are obtained through parameter conversion Parameters, i.e. theoretical values ​​of frequency response; in, It is Basis Functions The triangle pair where It is Basis Functions The triangle pair.

6. An electronic device, characterized in that: It comprises a processor and a memory, wherein the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the fast multipole electromagnetic simulation method based on the PMCHW equation as described in any one of claims 1 to 5.

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

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