Modeling simulation method for infinite two-dimensional periodic array antenna

Abstract

The invention provides a modeling simulation method for an infinite two-dimensional periodic array antenna, and the method comprises the following steps: modeling an array unit of an electromagnetic band gap (EBG) patch antenna in computer-aided software, the unit being composed of a top EBG metal layer, a magnetoelectric dipole layer and a ground plane; simulation parameters such as material parameters, port excitation and frequency sweeping range are set in computer-aided software, x and y directions of the unit EBG patch antenna are set as Bloch period boundaries, z direction is set as a first-order absorption boundary, and performance of the array unit antenna is simulated and analyzed when a plane wave incidence angle # imgabs0 # is 0 degree, 30 degrees and 60 degrees respectively; the finite element fast algorithm for the infinite two-dimensional periodic array antenna is provided, the algorithm is accurate in calculation and analysis of the electromagnetic problem of the infinite two-dimensional periodic array antenna, efficiency is high, memory consumption is low, and a theoretical analysis and fast simulation method is provided for engineering application of a periodic structure.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic field modeling and simulation, and specifically relates to a modeling and simulation method for an infinite two-dimensional periodic array antenna. Background Art

[0002] The EBG (Electromagnetic Band-Gap) structure is a periodic structure that can achieve the electromagnetic bandgap effect and has become a hot topic in microwave and millimeter wave technology research. EBG structure devices have the characteristics of low loss and good heat dissipation. These characteristics make the EBG structure have great application potential and value in the field of microwave engineering, especially antenna technology.

[0003] Periodic structures have important engineering applications and academic research value in many fields such as antennas and radar detection. From phased array antennas to frequency selective surfaces to electromagnetic metamaterials that have emerged in recent years, their basic forms are all in the form of periodic or quasi-periodic structures. In the electromagnetic field simulation process after the design of these structures is completed, electromagnetic numerical calculations will be performed on their models. Efficient and accurate simulation and analysis of large-scale periodic arrays has always been one of the important and difficult problems in the field of electromagnetic computing.

[0004] Traditional electromagnetic simulation methods will generate very large unknowns when calculating large-scale periodic structures, which will put a heavy burden on computing resources. As the array scale continues to expand and the antenna structure complexity continues to increase, the number of grids after the test model is discretized is getting larger and larger, and the traditional finite element method (FEM) is becoming increasingly difficult to cope with.

[0005] In view of this, it is very meaningful to propose a modeling and simulation method for infinite two-dimensional periodic array antennas. Summary of the invention

[0006] In order to solve the problem that the traditional electromagnetic simulation method will generate very large unknowns when calculating large-scale periodic structures, which will bring a great burden to computing resources. With the further expansion of the array scale and the further increase of the complexity of the antenna structure, the number of grids after the discretization of the test model is getting larger and larger, and the traditional finite element method (FEM) is becoming more and more difficult to cope with. The present invention provides a modeling and simulation method for infinite two-dimensional periodic array antennas to solve the above problems.

[0007] In a first aspect, the present invention proposes a modeling and simulation method for an infinite two-dimensional periodic array antenna, the method comprising the following steps:

[0008] Design and build a unit EBG patch antenna structure in COMSOL, which consists of a top EBG metal layer, a magneto-electric dipole layer, and a ground plane;

[0009] In COMSOL, set the simulation parameters of this unit EBG patch antenna, such as material parameters, port excitation, and frequency sweep range, set the x and y directions to Bloch periodic boundaries, and the z direction to the first-order absorption boundary, and simulate and analyze the performance of the array unit antenna when the plane wave incident angles θ are 0°, 30°, and 60° respectively;

[0010] The mesh data file of the COMSOL discrete array unit antenna model is read, and the hybrid finite element fast algorithm is used to simulate and analyze the model. The algorithm calculates and analyzes the electromagnetic problems of infinite two-dimensional periodic array antennas accurately, efficiently and with low memory consumption, providing theoretical analysis and fast simulation methods for the engineering application of periodic structures.

[0011] This method first designs and constructs a unit EBG patch antenna structure in COMSOL. The unit EBG patch antenna structure consists of a top EBG metal layer, a magneto-electric dipole layer, and a ground plane.

[0012] Secondly, the infinite two-dimensional periodic array antenna model is established in COMSOL and the performance of this antenna is analyzed, mainly in:

[0013] In COMSOL, set the material parameters, port excitation and other information of this EBG patch antenna. The simulation range of this model is 1-40GHz. Set the x and y directions as Bloch periodic boundaries, and the z direction as the first-order absorption boundary.

[0014] The antenna performance of the array unit antenna model is simulated and analyzed when the plane wave incident angle θ is 0°, 30° and 60° respectively.

[0015] Thirdly, the hybrid finite element fast algorithm is used to simulate and analyze this model, mainly in the following aspects:

[0016] Read the mesh data file of the COMSOL discrete array unit antenna model, and use hybrid finite element fast algorithm simulation to perform electromagnetic calculation analysis on this model;

[0017] The hybrid finite element fast algorithm based on Bloch periodic boundary is suitable for fast modeling and simulation of infinite two-dimensional periodic array antennas. The hybrid finite element fast algorithm based on Bloch periodic boundary includes:

[0018] According to the Bloch periodic theorem, the electromagnetic radiation analysis of an infinite periodic array can be limited to one array unit, and the array unit adopts the Bloch periodic boundary. This patent considers an infinite periodic array along the x and y directions. Since all the units in the array are the same, the hybrid finite element fast algorithm is used for analysis on only one unit, where the Bloch periodic boundary is used in the x and y directions and the first-order absorbing boundary condition is used in the z direction. The electric field wave equation satisfied on the unit is as follows:

[0019]

[0020] in, is the Hamiltonian operator, μ is the magnetic permeability, E is the electric field intensity, ∈ is the dielectric constant, σ e represents the conductivity, J i is the current source density, s represents the complex frequency, that is, s = jω, where j refers to the imaginary unit and ω is the angular frequency. For general radiation problems, the array elements may contain non-uniform materials with complex dielectric constants and complex magnetic constants.

[0021] In the array unit, the electric field in the x and y directions satisfies the following Bloch periodic boundary conditions:

[0022]

[0023] k x and k y is the wave number in the x and y directions, and the expression is: in Represents the direction of wave propagation; T x and T y are the periodic intervals in the x and y directions, respectively. Further, according to Floquet's theorem, the electric field E is transformed into the field E p It is expressed as:

[0024] E(r)=E P (r)e -jkr

[0025] Where E P (r) is a periodic function, k is the wave vector in the background, and r is the position vector;

[0026] In the hybrid finite element fast algorithm, the electric field in the wave equation is transformed into the field E p Represented by using tree-cotree decomposition technology, E p By defining the edge basis function Φ on the cotree edge c and the node basis functions defined at the free nodes The gradient expansion is expressed as follows:

[0027]

[0028] Among them, N c is the number of cotree edges in the grid, N n is the number of free nodes in the grid, refers to the i-th edge basis function defined on the cotree edge, It refers to the gradient of the jth node basis function defined at the free node, and e represents the corresponding unknown coefficient.

[0029] Preferably, the conductor loss of the infinite two-dimensional periodic array antenna is analyzed and modeled using impedance boundary conditions (IBC), and the expression is as follows:

[0030] n×H=jωY s (n×(E p ×n))

[0031] Where n is the normal vector outside the boundary, H is the magnetic field vector, and Y s is the surface admittance of the metal conductor, expressed as The IBC boundary accurately describes the relationship between the tangential electric field and the tangential magnetic field on the metal surface. The use of the IBC boundary avoids solving the problem inside the metal.

[0032] For the open area, the first-order absorbing boundary condition is used for modeling, and its expression is:

[0033]

[0034] Where k is the wave number in the background, ∈ rb and μ rb is the relative permittivity and relative permeability of the background;

[0035] use and As a test function, the weak solution form of the wave equation is obtained by the Galerkin method, and the IBC boundary and the first-order absorbing boundary are brought into the weak solution form. The final system matrix expression is as follows:

[0036]

[0037] Where b is the input matrix of the entire calculation area, M is the mass matrix, C is the damping matrix, K is the stiffness matrix, and Z is the boundary term matrix; let s = s0 (1 + δ), where s0 is the reference complex frequency, generally the complex center frequency. The expression of the matrix equation to be solved after expansion is:

[0038] A0e+δA1e+δ 2 A2e=-s0(1+δ)b

[0039] In the above equation, The approximate equivalent is 1+0.5δ, where

[0040] Further preferably, the matrix equation to be solved in the above formula is subjected to model reduction. A low-dimensional Krylov subspace Q of the above equation can be obtained by using a modal reduction technique based on a second-order Arnoldi algorithm. The algorithm for constructing the low-dimensional subspace specifically includes:

[0041] S31, Q0=orth(Q0)=[q1,...,q M ], where M represents the number of columns of the right-hand side. P0 is a zero matrix with the same dimension as Q0, and orth represents orthogonalization of the matrix in the brackets;

[0042] S32, perform cyclic assignment,

[0043] S321, define the value of variable j from 1 to m;

[0044] S322, let r=A1q j +A2p j , t=q j ,in I represents the identity matrix, and 0 represents the zero matrix;

[0045] S33, define the value of variable i from 1 to j+M-1;

[0046] S331, order in sequence r=rq i h i,j , t = tp i h i,j ;

[0047] S332, when h j+l,j =norm(r), norm() means calculating the 2-norm of r, q j+l =r / h j+l,j , p j+l =t / h j+l,j When the loop ends;

[0048] S34. The loop ends.

[0049] Expand the unknown vector e using the orthogonal basis Q, that is,

[0050]

[0051] Where w=[w0,w1,…,w m-1] is the coefficient vector. Substitute the above formula into the matrix equation to be solved, and multiply both sides of the matrix equation to be solved by the transpose Q T , and the reduced matrix equation is obtained:

[0052]

[0053] Reduced Matrix and The expressions are By solving the reduced-order matrix equation at each frequency to obtain the coefficient vector w, the electric field E at each frequency can be obtained. p .

[0054] Compared with the prior art, the beneficial results of the present invention are: a high-frequency array unit antenna with good performance when the plane wave incident angle is 0°, 30° and 60° is designed in the computational auxiliary software, and a hybrid finite element fast algorithm based on Bloch periodic boundary is proposed in order to quickly calculate the antenna scattering parameters under different plane wave incident angles. The simulation results show that the S parameter simulation results of the algorithm are consistent with the COMSOL simulation results, and it has the characteristics of high efficiency and low memory consumption, which reflects the advantages of the hybrid finite element fast algorithm in calculating infinite two-dimensional periodic array antennas. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated into and constitute a part of this specification. The accompanying drawings illustrate the embodiments and are used together with the description to explain the principles of the present invention. It will be easy to recognize other embodiments and many expected advantages of the embodiments because they become better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale with each other. The same reference numerals refer to corresponding similar parts.

[0056] Figure 1 A schematic flow chart of a modeling and simulation method for an infinite two-dimensional periodic array antenna according to an embodiment of the present invention;

[0057] Figure 2 A schematic diagram of the structure of a unit EBG patch antenna in a modeling and simulation method of an infinite two-dimensional periodic array antenna according to an embodiment of the present invention;

[0058] Figure 3 A schematic diagram of a model structure in a modeling and simulation method of an infinite two-dimensional periodic array antenna according to an embodiment of the present invention;

[0059] Figure 4A comparison diagram of S parameters obtained by using a hybrid finite element fast algorithm based on Bloch periodic boundary and commercial software COMSOL for an infinite two-dimensional periodic array antenna model in an embodiment of the present invention in a frequency range of 1 GHz to 40 GHz when the plane incident wave angle θ=0°;

[0060] Figure 5 This is a comparison diagram of S parameters obtained by using a hybrid finite element fast algorithm based on Bloch periodic boundary and commercial software COMSOL in the infinite two-dimensional periodic array antenna model in the embodiment of the present invention in the frequency range of 1 GHz to 40 GHz and when the plane incident wave angle θ=30°;

[0061] Figure 6 This is a comparison diagram of S parameters obtained by using a hybrid finite element fast algorithm based on Bloch periodic boundary and commercial software COMSOL in the infinite two-dimensional periodic array antenna model in the embodiment of the present invention in the frequency range of 1 GHz to 40 GHz when the plane incident wave angle θ=60°; DETAILED DESCRIPTION

[0062] In the following detailed description, reference is made to the accompanying drawings, which form a part of the detailed description and are shown by illustrative specific embodiments in which the present invention can be put into practice. To this end, directional terms, such as "top", "bottom", "left", "right", "up", "down", etc., are used with reference to the orientation of the figures described. Because the parts of the embodiments can be positioned in several different orientations, directional terms are used for the purpose of illustration and are by no means limiting. It should be understood that other embodiments may be utilized or logical changes may be made without departing from the scope of the present invention. Therefore, the following detailed description should not be adopted in a limiting sense, and the scope of the present invention is defined by the appended claims.

[0063] Figure 1 It is shown that the embodiment of the present invention discloses a modeling and simulation method of an infinite two-dimensional periodic array antenna, such as Figure 1 As shown, the method comprises the following steps:

[0064] S1. Design and construct a unit EBG patch antenna structure in COMSOL. The unit EBG patch antenna structure consists of a top EBG metal layer, a magneto-electric dipole layer, and a ground plane.

[0065] The top EBG structure is made of copper with a thickness of 0.02 mm. The space between the top EBG structure and the magnetic dipole is filled with Neltec NX9240 material with a relative dielectric constant of 2.4 and a thickness of 1.08 mm. The magnetic dipole made of copper is embedded in the Isola MT77-1078 dielectric with a relative dielectric constant of 2.9 and a thickness of 1.3 mm.

[0066] S2. Set the material parameters, port excitation and other information of this EBG patch antenna in COMSOL, set the x and y directions of the unit EBG patch antenna as Bloch periodic boundaries, the z direction as the first-order absorption boundary, and the simulation range is 1-40GHz;

[0067] The performance of the infinite two-dimensional periodic array antenna is simulated and analyzed when the plane wave incident angle θ is 0°, 30° and 60° respectively. Figure 4-6 The simulation results show that this infinite two-dimensional periodic array antenna exhibits good antenna performance at the three different angles mentioned above;

[0068] S3. Read the mesh data of the discrete array unit antenna of COMSOL, and use the hybrid finite element fast algorithm (MFEM) based on Bloch periodic boundary to simulate and analyze this model. The scattering parameters obtained by MFEM simulation are in good agreement with the simulation results of COMSOL. Compared with COMSOL, this algorithm calculates and analyzes the electromagnetic problems of infinite two-dimensional periodic array antennas accurately, efficiently and with low memory consumption, providing theoretical analysis and fast simulation methods for the engineering application of periodic structures.

[0069] According to the Bloch periodic theorem, the electromagnetic radiation analysis of an infinite periodic array can be limited to one array unit, and the array unit adopts the Bloch periodic boundary. This patent considers an infinite periodic array along the x and y directions. Since all the units in the array are the same, the hybrid finite element fast algorithm is used for analysis on only one unit, where the Bloch periodic boundary is used in the x and y directions and the first-order absorbing boundary condition is used in the z direction. The electric field wave equation satisfied on the unit is as follows:

[0070]

[0071] in, is the Hamiltonian operator, μ is the magnetic permeability, E is the electric field intensity, ∈ is the dielectric constant, σ e represents the conductivity, J i is the current source density, s represents the complex frequency, that is, s = jω, where j refers to the imaginary unit and ω is the angular frequency. For general radiation problems, the array elements may contain non-uniform materials with complex dielectric constants and complex magnetic constants.

[0072] In the array unit, the electric field in the x and y directions satisfies the following Bloch periodic boundary conditions:

[0073]

[0074] k x and k y is the wave number in the x and y directions, and the expression is: in Represents the direction of wave propagation; T x and T y are the periodic intervals in the x and y directions, respectively. Further, according to Floquet's theorem, the electric field E is transformed into the field E p It is expressed as:

[0075] E(r)=E P (r)e -jk·r

[0076] Where E P (r) is a periodic function, k is the wave vector in the background, and r is the position vector.

[0077] In the hybrid finite element fast algorithm, the electric field in the wave equation is transformed into the field E p Represented by using tree-cotree decomposition technology, E p By defining the edge basis function Φ on the cotree edge c and the node basis functions defined at the free nodes The gradient expansion is expressed as follows:

[0078]

[0079] Among them, N c is the number of cotree edges in the grid, N n is the number of free nodes in the grid, refers to the i-th edge basis function defined on the cotree edge, It refers to the gradient of the jth node basis function defined at the free node, and e represents the corresponding unknown coefficient.

[0080] To analyze the conductor loss of the array element antenna, the impedance boundary condition (IBC) is used for modeling. The expression is as follows:

[0081] n×H=jωY s (n×(E p ×n))

[0082] Where n is the normal vector outside the boundary, H is the magnetic field vector, and Y s is the surface admittance of the metal conductor, expressed as The IBC boundary accurately describes the relationship between the tangential electric field and the tangential magnetic field on the metal surface. The use of the IBC boundary avoids solving the problem inside the metal.

[0083] For the open area, the first-order absorbing boundary condition is used for modeling, and its expression is:

[0084]

[0085] Where k is the wave number in the background ∈rb and μ rb is the relative permittivity and relative permeability of the background;

[0086] use and As a test function, the weak solution form of the wave equation is obtained by the Galerkin method, and the IBC boundary and the first-order absorbing boundary are brought into the weak solution form. The final system matrix expression is as follows:

[0087]

[0088] Where b is the input matrix of the entire calculation area, M is the mass matrix, C is the damping matrix, K is the stiffness matrix, and Z is the boundary term matrix; let s = s0 (1 + δ), where s0 is the reference complex frequency, generally the complex center frequency. The expression of the matrix equation to be solved after expansion is:

[0089] A0e+δA1e+δ 2 A2e=-s0(1+δ)b

[0090] In the above equation, The approximate equivalent is 1+0.5δ, where

[0091] The matrix equation to be solved in the above formula is subjected to model reduction. The low-dimensional Krylov subspace Q of the above equation can be obtained by using the modal reduction technique based on the second-order Arnoldi algorithm. The algorithm for constructing the low-dimensional subspace specifically includes:

[0092] S31, Q0=orth(Q0)=[q1,...,q M ], where M represents the number of columns of the right-hand side. P0 is a zero matrix with the same dimension as Q0, and orth represents orthogonalization of the matrix in the brackets;

[0093] S32, perform cyclic assignment,

[0094] S321, define the value of variable j from 1 to m;

[0095] S322, let r=A1q j +A2p j , t=q j ,in I represents the identity matrix, and 0 represents the zero matrix;

[0096] S33, define the value of variable i from 1 to j+M-1;

[0097] S331, order in sequence r=rq i h i,j , t = tp i h i,j ;

[0098] S332, when h j+l,j =norm(r), norm() means calculating the 2-norm of r, q j+l =r / h j+l,j , p j+l =t / h j+l,j When the loop ends;

[0099] S34. The loop ends.

[0100] Expand the unknown vector e using the orthogonal basis Q, that is,

[0101]

[0102] Where w=[w0,w1,…,w m-1 ] is the coefficient vector. Substitute the above formula into the matrix equation to be solved, and multiply both sides of the matrix equation to be solved by the transpose Q T , and the reduced matrix equation is obtained:

[0103]

[0104] Reduced Matrix and The expressions are By solving the reduced-order matrix equation at each frequency to obtain the coefficient vector w, the electric field E of the array unit antenna at each frequency can be obtained: p .

[0105] In this embodiment, the three-dimensional structure of the unit EBG patch antenna is constructed in COMSOL, as shown in Figure 2 As shown; the x and y directions of the unit EBG patch antenna are set as Bloch periodic boundaries, and the z direction is the first-order absorption boundary, as shown Figure 3 shown.

[0106] In COMSOL, electromagnetic simulation is performed on the infinite two-dimensional periodic array antenna to obtain the S parameter simulation results of this antenna in the range of 1-40GHz, such as Figure 4-6As shown in the figure, this model shows good antenna performance when the plane wave incident angles are 0°, 30° and 60°, and the simulation results calculated by the hybrid finite element fast algorithm (MFEM) and COMSOL are in good agreement. As shown in Table 1, the specific parameters of the test show that the algorithm of the present invention is 1.12 times more efficient than COMSOL, and the memory usage is reduced by about 20GB compared to COMSOL, which proves that the hybrid finite element fast algorithm (MFEM) based on Bloch periodic boundary can maintain accuracy, high efficiency and low memory consumption in calculating infinite two-dimensional periodic array antennas. The specific test parameters are shown in Table 1:

[0107]

[0108] Table 1

[0109] In the specific implementation, this patent designs and constructs a unit EBG patch antenna structure in COMSOL, which consists of a top EBG metal layer, a magnetoelectric dipole layer and a ground plane. In COMSOL, the material parameters, simulation range and port excitation information of this EBG patch antenna are set. The model simulates the x and y directions as Bloch periodic boundaries and the z direction as the first-order absorption boundary. The infinite two-dimensional periodic array antenna performance is simulated and analyzed when the plane wave incident angle θ is 0°, 30° and 60° respectively. From the simulation results, it can be seen that this infinite two-dimensional periodic array antenna exhibits good antenna performance at the above three different angles. The mesh data of the discrete array unit antenna of COMSOL is read, and the hybrid finite element fast algorithm (MFEM) based on the Bloch periodic boundary is used to simulate and analyze this model. The scattering parameters simulated by MFEM are consistent with the simulation results of COMSOL. Compared with COMSOL, this algorithm calculates and analyzes the electromagnetic problems of infinite two-dimensional periodic array antenna accurately, efficiently and with low memory consumption, providing theoretical analysis and fast simulation methods for the engineering application of periodic structures.

[0110] The present invention proposes a modeling and simulation method for an infinite two-dimensional periodic array antenna. An EBG patch antenna unit is designed and modeled in COMSOL, and the x and y directions of the unit antenna are set as Bloch periodic boundaries. COMSOL and a hybrid finite element fast algorithm (MFEM) are used to simulate and analyze the performance of the infinite two-dimensional periodic array antenna when the plane wave incident angles θ are 0°, 30° and 60° respectively. The scattering parameter results of the infinite two-dimensional periodic array antenna calculated by the two simulation methods are consistent with each other, and MFEM is more efficient than COMSOL and reduces the memory usage by about 20GB. The hybrid finite element fast algorithm can be used to efficiently and accurately perform electromagnetic simulation on large-scale periodic structures, and can significantly reduce the memory usage during the simulation process.

[0111] The above description is only a preferred embodiment of the present invention and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the present invention is not limited to the technical solution formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above inventive concept. For example, the above features are replaced with the technical features with similar functions disclosed in the present invention (but not limited to) to form a technical solution.

Claims

1. A modeling and simulation method for an infinite two-dimensional periodic array antenna, characterized in that: The method comprises the following steps: Design and build a unit EBG patch antenna structure in COMSOL, which consists of a top EBG metal layer, a magneto-electric dipole layer, and a ground plane; In COMSOL, set the material parameters, port excitation, and frequency sweep range simulation parameters of this unit EBG patch antenna, set the x and y directions to Bloch periodic boundaries, and the z direction to the first-order absorption boundary, and simulate and analyze the performance of the infinite two-dimensional periodic array antenna when the plane wave incident angles θ are 0°, 30°, and 60° respectively; The mesh data file of the COMSOL discrete array unit antenna model is read, and the unit EBG patch antenna is simulated and analyzed using a fast algorithm based on a hybrid finite element.

2. The modeling and simulation method of the infinite two-dimensional periodic array antenna according to claim 1, characterized in that: The top EBG structure material is copper with a thickness of 0.02mm; the space between the top EBG structure and the magnetic dipole is filled with Neltec NX9240 material with a relative dielectric constant of 2.4 and a thickness of 1.08mm; the magnetic dipole made of copper is embedded in the Isola MT77-1078 dielectric with a relative dielectric constant of 2.9 and a thickness of 1.3mm.

3. The modeling and simulation method of the infinite two-dimensional periodic array antenna according to claim 2, characterized in that: In COMSOL, the material parameters and port excitation information of this EBG patch antenna are set; the x and y directions of the unit EBG patch antenna are set to infinite periodic arrays, the z direction is the first-order absorption boundary, the simulation range is 1-40GHz, and the performance of the infinite two-dimensional periodic array antenna is analyzed when the incident angles are 0°, 30°, and 60°, respectively.

4. The modeling and simulation method of the infinite two-dimensional periodic array antenna according to claim 3 is characterized in that: The mesh data of the COMSOL discrete array unit antenna model is read, and the hybrid finite element fast algorithm is used to simulate and analyze the unit EBG patch antenna.

5. The modeling and simulation method of the infinite two-dimensional periodic array antenna according to claim 4, characterized in that: According to the Bloch periodic theorem, the electromagnetic radiation analysis of an infinite periodic array is limited to one array unit, and the array unit is modeled using the Bloch periodic boundary. The Bloch periodic boundary is used in the x and y directions, and the first-order absorbing boundary condition is used in the z direction. The electric field wave equation satisfied on the unit is as follows: in, is the Hamiltonian operator, μ is the magnetic permeability, E is the electric field intensity, ∈ is the dielectric constant, σ e represents the conductivity, J i is the current source density, s represents the complex frequency, that is, s = jω, where j refers to the imaginary unit and ω is the angular frequency; for general radiation problems, the array unit contains non-uniform materials with complex dielectric constants and complex magnetic constants; In the array unit, the electric field in the x and y directions satisfies the following Bloch periodic boundary conditions: k x and k y is the wave number in the x and y directions, and the expression is: in Represents the direction of wave propagation; T x and T y are the periodic intervals in the x and y directions respectively. According to Floquet’s theorem, the electric field E is transformed into the field E p It is expressed as: E(r)=E P (r)e -jk·r Where E P (r) is a periodic function, k is the wave vector in the background, and r is the position vector; In the hybrid finite element fast algorithm, the electric field in the wave equation is transformed into the field E p Represented by using tree-cotree decomposition technology, E p By defining the edge basis function Φ on the cotree edge c and the node basis functions defined at the free nodes The gradient expansion is expressed as follows: Among them, N c is the number of cotree edges in the grid, N n is the number of free nodes in the grid, refers to the i-th edge basis function defined on the cotree edge, It refers to the gradient of the jth node basis function defined at the free node, and e represents the corresponding unknown coefficient.

6. The modeling and simulation method of the infinite two-dimensional periodic array antenna according to claim 5, characterized in that: The conductor loss of the array element antenna is modeled using the impedance boundary condition, and the expression is as follows: n×H=jωY s (n×(E p ×n)) Where n is the normal vector outside the boundary, H is the magnetic field vector, and Y s is the surface admittance of the metal conductor, expressed as The IBC boundary accurately describes the relationship between the tangential electric field and the tangential magnetic field on the metal surface. The IBC boundary avoids solving the problem inside the metal. For the open area, the first-order absorbing boundary condition is used for modeling, and its expression is: Where k is the wave number in the background, ∈ rb and μ rb is the relative permittivity and relative permeability of the background; use and As a test function, the weak solution form of the wave equation is obtained by the Galerkin method, and the IBC boundary and the first-order absorbing boundary are brought into the weak solution form. The final system matrix expression is as follows: Where b is the input matrix of the entire calculation area, M is the mass matrix, C is the damping matrix, K is the stiffness matrix, and Z is the boundary term matrix; let s = s0 (1 + δ), where s0 is the reference complex frequency, generally the complex center frequency, and the expanded matrix equation to be solved is: A0e+δA1e+δ 2 A2e=-s0(1+δ)b In the above equation, The approximate equivalent is 1+0.5δ, where 7. The modeling and simulation method of the infinite two-dimensional periodic array antenna according to claim 6, characterized in that: Treat the matrix equation to be solved A0e+δA1e+δ 2 A2e=-s0(1+δ)b By adopting model reduction processing and modal reduction technology based on the second-order Arnoldi algorithm, a low-dimensional Krylov subspace Q of the above equation can be obtained. The algorithm for constructing the low-dimensional subspace specifically includes: S31, Q0=orth(Q0)=[q1,...,q M ], where M represents the number of columns of the right-hand side, P0 is a zero matrix with the same dimension as Q0, and orth represents orthogonalization of the matrix in the brackets; S32, perform cyclic assignment, S321, define the value of variable j from 1 to m; S322, let r=A1q j +A2p j , G T r=0, t=q j ,in I represents the identity matrix, and 0 represents the zero matrix; S33, define the value of variable i from 1 to j+M-1; S331, order in sequence r=rq i h i,j , t = tp i h i,j ; S332, when h j+l,j =norm(r), norm() means calculating the 2-norm of r, q j+l =r / h j+l,j , p j+l =t / h j+l,j When the loop ends; S34, the cycle ends; Expand the unknown vector e using the orthogonal basis Q, that is, Where w=[w0,w1,…,w m-1 ] is the coefficient vector, substitute the above formula into the matrix equation to be solved, and multiply both sides of the matrix equation to be solved by the transpose Q T , and the reduced matrix equation is obtained: Reduced Matrix and The expressions are By solving the reduced-order matrix equation at each frequency to obtain the coefficient vector w, the electric field E at each frequency of the array element antenna can be obtained: p .

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