Electromagnetic field analogue simulation calculation method and device for frequency selective surface structure

Abstract

The invention provides an electromagnetic field analogue simulation calculation method and device for a frequency selective surface structure, and belongs to the technical field of periodic structure electromagnetic field analogue simulation. The method comprises the following steps: improving a split field time domain finite difference algorithm by using a narrow slit fitting technology to obtain a split field time domain finite difference algorithm based on narrow slit fitting; according to the electromagnetic field data of the frequency selective surface structure, performing electromagnetic field analogue simulation calculation on a non-narrow slit part in the frequency selective surface structure by using a split field time domain finite difference algorithm; and according to the electromagnetic field data of the frequency selective surface structure, carrying out electromagnetic field analogue simulation calculation on a narrow slit part in the frequency selective surface structure by utilizing a split field time domain finite difference algorithm based on narrow slit fitting. According to the method, the calculation efficiency can be improved while the electromagnetic field analogue simulation calculation accuracy of the frequency selective surface structure is improved.

Description

Technical Field

[0001] The invention relates to an electromagnetic field simulation calculation method and device for frequency selective surface structure, belonging to the technical field of periodic structure electromagnetic field simulation. Background Art

[0002] Periodic structures are now widely used in the military industry, such as frequency selective surfaces (FSS), antenna arrays, etc. Finite-Difference Time-Domain (FDTD) and Periodic Boundary Condition (PBC) are one of the most effective methods for analyzing oblique-incidence periodic structure problems.

[0003] Most FDTD algorithms on the market need to divide the narrow slits of periodic structures into very fine grids to improve calculation accuracy when calculating them. Since the time step speed in the calculation process of the FDTD algorithm is related to the spatial grid size, the smaller the spatial grid size, the slower the time step. Therefore, the FDTD algorithm consumes a lot of computing resources to calculate conductor narrow slits, and the calculation efficiency is low.

[0004] In order to solve this problem, experts and scholars have proposed many thin-slot formalism (TSF) technologies. These TSF technologies derive the electric field near the gap. ,magnetic field The approximate fitting of is performed, and the differential equation is obtained by using the integral form of the Maxwell equations. The current TSF technology mainly includes two categories. One is to treat the gap as a parallel plate capacitor and modify the dielectric constant by and magnetic permeability To simulate the gap, such as the grid capacitance method (CTSF). Another method is to set the electric field near the gap. ,magnetic field According to a certain distribution law, it is substituted into the difference equation of the algorithm using the loop integration method, such as the loop integration subgrid technology (TSF), enhanced thin slit formula (ETSF), etc.

[0005] However, although the existing TSF technology has improved the computing efficiency to a certain extent, some technologies will lead to reduced computing accuracy and the improvement in computing efficiency is not large. When analyzing frequency selective surfaces, which contain structures such as multi-layer slot arrays and dielectric plates, due to the large computing space, it occupies more computing resources and has lower computing efficiency, which seriously affects the use effect. Summary of the invention

[0006] The purpose of the present invention is to provide an electromagnetic field simulation calculation method and device for frequency selective surface structures, which can simulate and calculate the electromagnetic field of the frequency selective surface structure based on the narrow slot coupling formula and the split-field finite difference time domain (Split-Field FDTD) algorithm, and can greatly improve the calculation efficiency of complex periodic structures while achieving high calculation accuracy and shorten the calculation time.

[0007] In order to achieve the above purpose / solve the above technical problems, the present invention is implemented by adopting the following technical solutions:

[0008] In a first aspect, the present invention provides an electromagnetic field simulation calculation method for a frequency selective surface structure, comprising the following steps:

[0009] The split-field FDTD algorithm is improved by using narrow slit fitting technology, and the split-field FDTD algorithm based on narrow slit fitting is obtained.

[0010] According to the electromagnetic field data of the frequency selective surface structure, the electromagnetic field simulation calculation of the non-narrow slit part of the frequency selective surface structure is carried out using the split-field finite-difference time-domain algorithm;

[0011] According to the electromagnetic field data of the frequency selective surface structure, the electromagnetic field simulation calculation of the narrow slot part in the frequency selective surface structure is carried out using the split-field time-domain finite difference algorithm based on narrow slot fitting.

[0012] In combination with the first aspect, further, the split-field finite-difference time-domain algorithm is improved by using the narrow slit fitting technology to obtain a split-field finite-difference time-domain algorithm based on narrow slit fitting, including:

[0013] According to the differential form of the split-field time-domain finite difference equation, the integral form of the split-field time-domain finite difference equation is derived;

[0014] According to the narrow slot coupling formula, the approximate fitting equation of the electromagnetic field component near the narrow slot in the frequency selective surface structure is derived, and the distribution law of the electromagnetic field component near the narrow slot along its corresponding loop is obtained;

[0015] According to the distribution law of the electromagnetic field components near the narrow slot along its corresponding loop, the distribution law of the auxiliary field and the splitting field near the narrow slot at the same position is obtained;

[0016] According to the distribution law of the auxiliary field and the splitting field at the same position near the narrow slit and the splitting field finite difference time-domain equation in integral form, the difference equation of the splitting field finite difference time-domain algorithm based on narrow slit fitting is obtained.

[0017] In combination with the first aspect, further, the integral form of the split-field time-domain finite difference equation is as follows:

[0018] ;

[0019] ;

[0020] in, is the relative dielectric constant, is the relative magnetic permeability, c is the speed of light, t is the time variable, and Represents the vector form of the auxiliary field components, and Represents the vector form of the splitting field components, is the closed loop integral, l is the lth closed loop in the electromagnetic field of the frequency selective surface structure, The value of is the integral differential element of the closed loop l, A is the area enclosed by the closed loop l, The value of is the integral differential of area A.

[0021] In combination with the first aspect, further, the distribution law of the auxiliary field and the splitting field near the narrow slit at the same position is obtained according to the distribution law of the electromagnetic field component near the narrow slit along its corresponding loop, including:

[0022] According to the relationship between the auxiliary field component and the electromagnetic field component in the time domain, the distribution law of the auxiliary field near the narrow slot is derived by using the distribution law of the electromagnetic field component near the narrow slot along its corresponding loop.

[0023] According to the relationship between the auxiliary field component and the splitting field component, the distribution law of the splitting field at the same position is deduced using the distribution law of the auxiliary field of the narrow slit attachment.

[0024] In combination with the first aspect, further, the auxiliary field component , and the electric field component , magnetic field component The relationship in the time domain is:

[0025] ;

[0026] ;

[0027] in, .

[0028] In combination with the first aspect, further, the relationship between the auxiliary field component and the splitting field component is:

[0029] ;

[0030] in, and is the auxiliary field variable in the r direction, and is the splitting field variable in the r direction, is the relative dielectric constant, is the relative magnetic permeability.

[0031] In combination with the first aspect, further, the auxiliary field and the splitting field near the narrow slit are The changing rules of the directions are substituted into the integral form of the split-field finite-difference time-domain equation, the integral loop is solved and the central difference approximation is performed on the differential term of time, and the difference equation of the split-field finite-difference time-domain algorithm based on narrow slit fitting is obtained, which is expressed as follows:

[0032] ;

[0033] ;

[0034] ;

[0035] in, , Indicates the grid point when the time step is n The splitting field variables along the r direction at , Indicates the grid point when the time step is n The auxiliary field variables along the r direction at , are the three directions in the three-dimensional coordinate system, i, j, k are the grid coordinates in the x, y, and z directions respectively, n is the time step, Respectively represents moving forward or backward half a grid in the x, y, and z directions. Respectively represents moving forward or backward one grid along the x, y, and z directions. indicates moving forward or backward by half a time step. Indicates moving forward or backward one time step. , , are the grid sizes in the x, y, and z directions respectively, and B is the coefficient. is the relative dielectric constant, is the relative magnetic permeability, c is the speed of light, is the time step for calculation, w is the slit width of the narrow slit in the frequency selective surface structure, is the ratio of pi.

[0036] In a second aspect, the present invention provides an electromagnetic field simulation computing device for a frequency selective surface structure, comprising:

[0037] An algorithm derivation module is used to improve the split-field finite-difference time-domain algorithm by using the narrow-slit fitting technology to obtain a split-field finite-difference time-domain algorithm based on narrow-slit fitting;

[0038] A non-narrow slit part calculation module is used to perform electromagnetic field simulation calculation on the non-narrow slit part of the frequency selective surface structure using a split-field finite-difference time-domain algorithm according to the electromagnetic field data of the frequency selective surface structure;

[0039] The narrow slot calculation module is used to perform electromagnetic field simulation calculation on the narrow slot part in the frequency selective surface structure according to the electromagnetic field data of the frequency selective surface structure by using a split-field time-domain finite difference algorithm based on narrow slot fitting.

[0040] In conjunction with the second aspect, further, the algorithm derivation module is specifically used to:

[0041] According to the differential form of the split-field time-domain finite difference equation, the integral form of the split-field time-domain finite difference equation is derived;

[0042] According to the narrow slot coupling formula, the approximate fitting equation of the electromagnetic field component near the narrow slot in the frequency selective surface structure is derived, and the distribution law of the electromagnetic field component near the narrow slot along its corresponding loop is obtained;

[0043] According to the distribution law of the electromagnetic field components near the narrow slot along its corresponding loop, the distribution law of the auxiliary field and the splitting field near the narrow slot at the same position is obtained;

[0044] According to the distribution law of the auxiliary field and the splitting field at the same position near the narrow slit and the splitting field finite difference time-domain equation in integral form, the difference equation of the splitting field finite difference time-domain algorithm based on narrow slit fitting is obtained.

[0045] In combination with the second aspect, further, the auxiliary field and the splitting field near the narrow slit are The changing rules of the directions are substituted into the integral form of the split-field finite-difference time-domain equation, the integral loop is solved and the central difference approximation is performed on the differential term of time, and the difference equation of the split-field finite-difference time-domain algorithm based on narrow slit fitting is obtained, which is expressed as follows:

[0046] ;

[0047] ;

[0048] ;

[0049] in, , Indicates the grid point when the time step is n The splitting field variables along the r direction at , Indicates the grid point when the time step is n The auxiliary field variables along the r direction at , are the three directions in the three-dimensional coordinate system, i, j, k are the grid coordinates in the x, y, and z directions respectively, n is the time step, Respectively represents moving forward or backward half a grid in the x, y, and z directions. Respectively represents moving forward or backward one grid along the x, y, and z directions. indicates moving forward or backward by half a time step. Indicates moving forward or backward one time step. , , are the grid sizes in the x, y, and z directions respectively, and B is the coefficient. is the relative dielectric constant, is the relative magnetic permeability, c is the speed of light, is the time step for calculation, w is the slit width of the narrow slit in the frequency selective surface structure, is the ratio of pi.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] The present invention proposes an electromagnetic field simulation calculation method and device for frequency selective surface structures. The existing split-field finite difference time-domain algorithm is improved by using narrow slit fitting technology to obtain a split-field finite difference time-domain algorithm based on narrow slit fitting. Since the narrow slit fitting technology can simulate the electromagnetic field distribution near the narrow slit more accurately, even if the narrow slit grid is coarsely divided, the accuracy of the electromagnetic field simulation result can be guaranteed. On this basis, the electromagnetic field distribution law near the narrow slit is converted into the distribution law of the auxiliary field and the splitting field, and then the electromagnetic field components near the narrow slit are calculated by using the differential equation, which can ensure the accuracy of the calculation result. At the same time, since the calculation process does not need to over-subdivide the narrow slit, there is no need to reduce the time stepping speed of the calculation process, thereby greatly shortening the calculation time and improving the electromagnetic field simulation calculation efficiency of the frequency selective surface structure.

[0052] The present invention solves the problem in the prior art that narrow slits must be divided into very fine grids to improve calculation accuracy, resulting in low calculation efficiency, and can improve calculation efficiency while achieving high-precision calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 FIG. 1 is a schematic diagram of the steps of an electromagnetic field simulation calculation method for a frequency selective surface structure provided by an embodiment of the present invention;

[0054] Figure 2 Shown is a schematic diagram of a coplanar conductor plate on the z plane (domain) in an embodiment of the present invention;

[0055] Figure 3FIG. 1 is a schematic diagram of a flat plate capacitor on a w plane (domain) in an embodiment of the present invention;

[0056] Figure 4 FIG. 1 is a schematic diagram showing the distribution law of the differential grid and field components on the xoy plane near the narrow slit in an embodiment of the present invention;

[0057] Figure 5 It is a schematic diagram showing the distribution law of the differential grid and field components on the xoz surface near the narrow slit in an embodiment of the present invention;

[0058] Figure 6 FIG. 1 is a top view of a frequency selective surface structure according to an embodiment of the present invention;

[0059] Figure 7 Shown is a side view of a frequency selective surface structure in an embodiment of the present invention;

[0060] Figure 8 Schematic diagrams of time domain waveforms of scheme (1), scheme (2) and scheme (3) at observation points in an embodiment of the present invention are shown;

[0061] Fig. 9 Schematic diagram of time domain waveforms of scheme (1) and scheme (3) at observation points in an embodiment of the present invention is shown;

[0062] Fig.10 The figure shows a schematic diagram of the comparison results of the transmission coefficients of scheme (1) and scheme (3) at the observation point in the embodiment of the present invention. DETAILED DESCRIPTION

[0063] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. The embodiments of the present invention and the technical features in the embodiments may be combined with each other unless there is a conflict.

[0064] Example 1

[0065] This embodiment introduces an electromagnetic field simulation calculation method for a frequency selective surface structure. Figure 1 As shown, the specific steps include:

[0066] Step A: The electric field E and the magnetic field H are replaced by vectors P and Q respectively, and the split-field finite-difference time-domain algorithm is improved by using the narrow-slit fitting technology to obtain a split-field finite-difference time-domain algorithm based on narrow-slit fitting.

[0067] Step B: Based on the electromagnetic field data of the frequency selective surface structure, a split-field finite-difference time-domain algorithm is used to perform electromagnetic field simulation calculations on the non-narrow slit portion of the frequency selective surface structure.

[0068] Step C: according to the electromagnetic field data of the frequency selective surface structure, a split-field finite-difference time-domain algorithm based on narrow-slit fitting is used to perform electromagnetic field simulation calculation on the narrow-slit part of the frequency selective surface structure.

[0069] R. Xiong et al. derived the narrow slot coupling formula (NTSF) technology based on the equivalent principle and the concept of equivalent magnetic flow, and used the loop integration method to complete the simulation of the narrow slot. The calculation accuracy of this method is much higher than the existing TSF technology, and it is simple and easy to implement. In step A of the present invention, the narrow slot coupling formula is used to improve the existing split-field finite difference time domain algorithm to obtain a split-field finite difference time domain algorithm based on narrow slot fitting, abbreviated as NTSF Split-Field FDTD.

[0070] Step A specifically includes the following steps:

[0071] Step A01: Starting from the differential form of the split-field time-domain finite difference equation, derive the integral form of the split-field time-domain finite difference equation.

[0072] The differential form of the lossless split-field finite-difference time-domain equation is expressed as follows:

[0073] (1)

[0074] (2)

[0075] in, is the relative dielectric constant, is the relative magnetic permeability, c is the speed of light, t is the time variable, and is the auxiliary field variable in the r direction, and are the splitting field variables in the r direction, which are all intermediate process quantities. , are the three directions in the three-dimensional coordinate system.

[0076] Auxiliary field component , and the electric field component , magnetic field component The relationship in the frequency domain is defined as follows:

[0077] (3)

[0078] (4)

[0079] in, are the field point coordinates, is the angular frequency of the electromagnetic wave, Auxiliary field variables and The frequency domain expression of is the real electromagnetic component and magnetic field components Frequency domain expression of; e is a natural constant, is the imaginary number symbol; and is the wave vector exist and Projection of direction, wave vector The size is , is the speed of light, and its direction is the direction of electromagnetic wave propagation. , ; is the wave vector and The angle of the axis, is the wave vector Horizontal projection and The angle of the axis; is the vacuum wave impedance, , is the vacuum permeability, is the dielectric constant of vacuum.

[0080] According to the time-frequency domain conversion relationship, formula (3) and formula (4) can be converted to:

[0081] (5)

[0082] (6)

[0083] in, .

[0084] Split field components and is defined by the following implicit equation:

[0085] (7)

[0086] The present invention writes the auxiliary field component and the splitting field component into vector form, and obtains:

[0087] (8)

[0088] (9)

[0089] in, Represents the vector form of the auxiliary field components, Represent the unit vectors in the x, y, and z directions respectively, Represents the vector form of the splitting field components.

[0090] Applying formula (8) and formula (9) to formula (1) and formula (2), we can get:

[0091] (10)

[0092] (11)

[0093] in, .

[0094] Applying Stokes' theorem, the integral form of the split-field time-domain finite difference equation can be obtained from formula (10) and formula (11):

[0095] (12)

[0096] (13)

[0097] in, is the closed loop integral, l is an arbitrary closed loop, The value is the integral differential element of loop l, the direction is the tangent direction of the loop, A is the area enclosed by the closed loop l, The value is the integral differential element of area A, and the direction is the normal of the area differential element.

[0098] Step A02: derive an approximate fitting equation of the electromagnetic field component near the narrow slot according to the narrow slot coupling formula, and obtain the distribution law of the electromagnetic field component near the narrow slot along its corresponding loop.

[0099] The present invention improves the Split-Field FDTD algorithm based on the narrow slit coupling formula to obtain the NTSF Split-Field FDTD algorithm. The derivation process of the narrow slit coupling formula is as follows:

[0100] Assume that Figure 2 The coplanar conductor plates shown in the figure have a slit width of 2S, and the two conductor plates are infinitely extended along the ±x direction and infinitely long along the y direction. Assume that the potential of the left conductor plate is -1 and the potential of the right conductor plate is +1. The spatial distribution law of the field quantity near the gap is actually a two-dimensional electrostatic field problem. Potential Satisfies the two-dimensional Laplace equation and can be obtained by using the conformal transformation method , that is, using complex transformation Figure 2 The z-plane is transformed to Figure 3 w plane, that is, Figure 2 The conductor plate is transformed into Figure 3 The transformation function of the plate capacitor is:

[0101] (14)

[0102] in, The new variables introduced.

[0103] (15)

[0104] If the real part u of w is taken as the potential function, then in the capacitor Potential ; Department ;exist arrive between Then according to hour Available , so:

[0105] (16)

[0106] Re in formula (16) is the real part.

[0107] Substituting formula (15) into formula (16) yields:

[0108] (17)

[0109] like Figure 2 If the potential on the conductor is an arbitrary constant, then formula (17) can be written as:

[0110] (18)

[0111] in, is the initial potential.

[0112] According to the vector electric field The relationship between and potential gradient is:

[0113] (19)

[0114] From formula (18) and formula (19), we can get:

[0115] (20)

[0116] (twenty one)

[0117] Figure 2 It can be considered as a transmission line formed by two conductors, transmitting TEM waves (transverse electromagnetic waves). The electric field and magnetic field of the transverse electromagnetic wave are orthogonal to each other, and the ratio of the two is numerically equal to the wave impedance, that is:

[0118] (twenty two)

[0119] (twenty three)

[0120] in, .

[0121] The change pattern of the corresponding magnetic field near the narrow gap is the same as that of the electric field.

[0122] In an embodiment of the present invention, Figure 4 , Figure 5 The differential grid and the distribution of field components near the narrow slit are given. For the three-dimensional structure, the loops related to the field components at the narrow slit include C 1 , C 2 , C 3 The distribution law of the field components at the narrow slit along the three loops is the core of the NTSF technology.

[0123] Integration Path C 1 yes , A surrounding rectangular path, Located in the normal direction of the loop plane, that is, the loop plane is perpendicular to the x direction. The plane is exactly located at the center of the seam in the x direction, and the distance to the upper and lower edges of the seam is exactly Now discuss , and In C 1 The change law of the center of the loop for , on the left for , on the right for Among them, i, j, and k are the grid coordinates in the x, y, and z directions respectively. Indicates moving forward or backward half a grid. It is parallel to the long side of the insulation and can be considered to change uniformly along the y direction without any special treatment.

[0124] During the difference calculation We need to do a surface integral, so we need to find The variation law along the y and z directions. Assume It is constant along the y direction, so in the integration plane It can be obtained by formula (20). Since the grid plane is located at the center of the seam, it is equivalent to Figure 2 In . correspond , so from formula (20) we can get:

[0125] (twenty four)

[0126] in, is the grid size in the z direction, and w is the slit width of the narrow slit in the frequency selective surface structure.

[0127] when hour, , from formula (24) we can get .

[0128] Therefore, formula (24) can be rewritten as:

[0129] (25)

[0130] According to the prior art, On one side of the incident wave, it contains two parts: the total field and the quasi-static field generated by the magnetic current; on the other side, it contains only a quasi-static field. The change along the z direction is asymmetric on both sides of the conductor plate; when the narrow slit is rotated When , The change along the z direction is asymmetric. This depends on whether the incident wave has a corresponding component: when scanning the E surface, There is asymmetry; when scanning the H surface, , There is asymmetry. Taking E-surface scanning as an example, formula (25) needs to be corrected to:

[0131] (26)

[0132] in, .

[0133] (27)

[0134] From formula (23), we can know that:

[0135] (28)

[0136] .

[0137] (29)

[0138] In the integration path C 1 In this equation, formulas (26) and (28) are the distribution laws of the electromagnetic field near the narrow slit along the z direction.

[0139] Integration Path C 2Located on the surface of the conductor, so the conductor part , , The integration is performed only over the seam, so we need to get , The variation pattern along the x direction, the positions of these field components correspond to Figure 2 In .

[0140] Formula (20) gives:

[0141] (30)

[0142] for Figure 4 The center point of the narrow slit for ,but correspond Figure 2 In , is the grid size in the x direction. Figure 4 Formula (30) can be written as:

[0143] E x ( x , j , k ) = − ϕ 0 ( w / 2 ) 2 − [ ( i + 1 / 2 ) Δ x − x ] 2 (31)

[0144] Depend on And formula (31) can be obtained:

[0145] (32)

[0146] Substituting formula (32) into formula (31) yields:

[0147] E x ( x , j , k ) = E x ( i + 1 2 , j , k ) w / 2 ( w / 2 ) 2 − [ ( i + 1 / 2 ) Δ x − x ] 2 (33)

[0148] From formula (23), we can know that:

[0149] (34)

[0150] In the integral path C 2 In this equation, formula (33) and formula (34) are the distribution laws of the electromagnetic field near the narrow slit along the x direction.

[0151] In the embodiment of the present invention, formulas (26), (28), (33) and (34) are the distribution laws of the electromagnetic field near the narrow slit along the x and z directions. Substituting the distribution laws described by formulas (26), (28), (33) and (34) into the corresponding integral loops, the FDTD algorithm based on NTSF can be obtained. The advantage of this algorithm is that when dealing with the narrow slit problem, it is not necessary to reduce the grid size according to the size of the narrow slit, and a relatively coarse grid can be used to obtain a more accurate result.

[0152] Step A03: Apply the approximate fitting equation of the electromagnetic field component near the narrow slit to the split-field finite-difference time-domain algorithm to perform auxiliary field and split field By calculation, the distribution law of the auxiliary field and the splitting field at the same position near the narrow slit is obtained.

[0153] According to the distribution law of the electric field E and the magnetic field H in the x and z directions near the narrow gap in step A02, combined with formula (3) to formula (6), the distribution law of the auxiliary field and the splitting field at the same position can be derived.

[0154] In the z direction, according to formula (5) and formula (26), it can be deduced that:

[0155] (35)

[0156] in, The time domain waveform of the auxiliary field component at Represents the relevant intermediate process quantity of the field point.

[0157] (36)

[0158] (37)

[0159] Actually and The distribution patterns of are not exactly the same: One more item The incident wave on the narrow slit side is still composed of two parts and remains unchanged; however, on the other side, since the FSS structure usually contains two or more slot arrays and dielectric plates, reflected waves will be generated at the interface of different dielectric plates, and the waves generated by the magnetic flow on the surface of the next slot array will also have a certain impact on this side. Therefore It represents the sum of the reflected wave, the wave generated by the magnetic flow on the surface of the next slot array, and the quasi-static field generated by its own magnetic flow.

[0160] Similarly, according to formula (6) and formula (28), we can deduce:

[0161] (38)

[0162] in, The time domain waveform of the auxiliary field component at Represents the relevant intermediate process quantity of the field point.

[0163] (39)

[0164] (40)

[0165] In the present invention, formula (35) to formula (40) are the distribution laws of the auxiliary field components near the narrow slit along the z direction. Substituting them into The same position splitting field can be obtained The distribution law of:

[0166] (41)

[0167] in, The time domain waveform of the split field component at , , Represents the relevant intermediate process quantity of the field point, and the definition is as follows:

[0168] (42)

[0169] (43)

[0170] Next, consider the distribution law of the auxiliary field and the splitting field near the narrow slit along the x direction: In fact, there is no influence of the incident wave, reflected wave and surface magnetic current in the x direction. However, due to the problem of time delay (for example, the existence of item), and , and The spatial distribution of is different in the x and y directions. In the following calculation process, both the E and H plane scans are taken , so , formula (5) and formula (6) can be modified as follows:

[0171] (44)

[0172] (45)

[0173] From formula (44) and formula (45), we can see that if the fixed constant, and , and The spatial distribution laws along the y and z directions are the same, provided that the slit is long enough or has reached a steady state. From the above two equations, it can be seen that the consistency along the y and z directions is significantly better than that in the x direction.

[0174] According to formula (5) and formula (33), we can get:

[0175] (46)

[0176] in, , , .

[0177] Due to the seam width Very small, according to t x The expression of , then formula (46) can be approximated as:

[0178] (47)

[0179] in, is with Irrelevant amount.

[0180] Substituting formula (5) and t x Substituting the expression into formula (47) yields:

[0181] (48)

[0182] Similarly, we can get:

[0183] (49)

[0184] in, .

[0185] because It is approximately zero near the narrow slit, so according to formula (5), Substituting formula (48) and formula (49) into formula and consider , can be obtained The variation law along the x direction:

[0186] (50)

[0187] In the embodiment of the present invention, formula (35) to formula (50) are based on Figure 4The derived distribution law of the auxiliary field and splitting field of the narrow slit in the x and z directions. Since the present invention uses the NTSF technology to improve the existing Split-Field FDTD algorithm, it is possible to simulate the electromagnetic field near the narrow slit more accurately, and high-precision calculation can be achieved without excessively subdividing the narrow slit during the calculation process, thereby greatly shortening the calculation time.

[0188] Step A04: bring the distribution laws of the auxiliary field and the splitting field near the narrow slit into their respective loops, and combine the splitting-field finite-difference time-domain equation in integral form to obtain the differential equation of the splitting-field finite-difference time-domain algorithm based on narrow slit fitting.

[0189] The auxiliary field and splitting field near the narrow slit derived in step A03 are , The distribution laws of the directions are brought into their respective loops, and the differential equations of the NTSF Split-Field FDTD algorithm are derived by the loop integration method, as follows:

[0190] like Figure 4 C 1 loop, which , along Therefore, by substituting formula (38) and formula (41) into formula (12), solving the integral loop and performing central difference approximation on the time differential term, we can obtain:

[0191] (51)

[0192] Among them, B is the coefficient, and the expression is as follows:

[0193] (52)

[0194] For C 2 loop, on the surface of an ideal conductor, , , , then from the last line of formula (7) we can get In C 2 The integral loop of has:

[0195] (53)

[0196] C 2 Loop and , along The law of change of direction is related to that of the change of direction. Substituting formula (48) and formula (50) into formula (13) and applying formula (53) yields:

[0197] (54)

[0198] For C 3 loop, which along The law of change in direction is related to that of the change in direction. Substituting formula (48) into formula (13) and applying formula (53), solving the integral loop and performing central difference approximation on the time differential term yields:

[0199] (55)

[0200] when When , we can get:

[0201] (56)

[0202] In the embodiment of the present invention, formulas (51), (54), (55) and (56) are the differential equations of the NTSF Split-Field FDTD algorithm.

[0203] In order to improve the calculation efficiency, in step B, the embodiment of the present invention uses the split-field time-domain finite difference equation shown in formulas (12) and (13) to perform electromagnetic field simulation calculation on the non-narrow slit part of the frequency selective surface structure to obtain the electromagnetic field components of the non-narrow slit part. In step C, the embodiment of the present invention uses the split-field time-domain finite difference equation based on narrow slit fitting shown in formulas (51), (54), (55) and (56) to perform electromagnetic field simulation calculation on the narrow slit part of the frequency selective surface structure to obtain the electromagnetic field components of the narrow slit part. The present invention can effectively improve the calculation efficiency and shorten the calculation time while ensuring high calculation accuracy, thereby meeting the calculation requirements of the frequency selective surface structure.

[0204] In order to verify the effect of the method of the present invention, the embodiment of the present invention analyzes the electromagnetic field of the complex FSS structure by using the traditional Split-Field FDTD algorithm and the method of the present invention respectively, and compares them. The specific operations are as follows:

[0205] The calculation model of the FSS structure selected by the present invention is a four-leg loaded radome structure with three layers of dielectric plates and two layers of slot arrays. Its specific structure and parameters are as follows: Figure 6 , Figure 7 As shown: , slit width w = 0.225 mm, the outer length of the double cross structure is 7.2 mm, and the inner width is 0.9 mm; the two-layer slit array structure is exactly the same; the relative dielectric constants of the three-layer dielectric plate are 1.3, 1.9, and 1.3 respectively; periodic boundary conditions are used in the x and y directions, and a 16-layer PML cutoff is used in the z direction; the positions of the reflection and transmission sampling surface, the total field / scattering field connection boundary, and the two-layer FSS array are as follows Figure 7 As shown in the figure, the sampling point is at the center of the transmission sampling surface. In order to reduce the amount of calculation, an expansion grid is used from both sides to the middle in the z direction: the expansion coefficient in dielectric plates 1 and 3 is 1.06, and the expansion coefficient in dielectric plate 2 is 1.065. The minimum is 0.126 mm and the maximum is 0.5408 mm; the rest uses a uniform grid.

[0206] The embodiment of the present invention adopts the following three calculation schemes, and compares their time domain waveforms (point P) and transmission coefficients at 60° oblique incidence under E-plane scanning, wherein the calculation of the transmission coefficient adopts the main mode extraction method.

[0207] (1) Set 6 fine grids at the narrow gap, and calculate the total space 204×204×156 (fine grid division). The grid size , the traditional Split-Field FDTD algorithm is used to simulate the electromagnetic field of a four-legged loaded radome structure with three layers of dielectric plates and two layers of slot arrays.

[0208] (2) Set up three grids at the narrow gap, with a grid size of , the total calculation space is 102×102×156, and the traditional Split-Field FDTD algorithm is used to simulate the electromagnetic field of the four-leg loaded radome structure with three layers of dielectric plates and two layers of slot arrays.

[0209] (3) Only one grid is set at the narrow gap, and the grid size , the total space 34×34×156 (coarse grid division) is calculated, and the electromagnetic field of the four-leg loaded radome structure with three layers of dielectric plates and two layers of slot arrays is simulated by using the NTSF Split-Field FDTD algorithm proposed by the method of the present invention and the traditional Split-Field FDTD algorithm.

[0210] Figure 8 The time domain waveforms of schemes (1), (2) and (3) at the observation points are given. It can be seen that the method of the present invention is in good agreement with the result of scheme (1), while the result error of scheme (2) is more obvious. This shows that the traditional Split-Field FDTD algorithm can achieve very high calculation accuracy when the grid division is very fine (scheme (1)), but when the grid division is not so fine (scheme (2)), the calculation accuracy of the traditional Split-Field FDTD algorithm will drop significantly. Unlike the traditional Split-Field FDTD algorithm, the method of the present invention can achieve very high calculation accuracy even when the grid division is very coarse (scheme (3)), which is equivalent to the accuracy of the traditional Split-Field FDTD algorithm with 6 grids set at the narrow gap (i.e., scheme (1)).

[0211] Fig. 9 The time domain waveforms of scheme (1) and scheme (3) at the observation point are given. Fig.10 The comparison results of the transmission coefficients of scheme (1) and scheme (3) at the observation point are given. Fig. 9 , Fig.10 It can be seen that the time domain waveform of the method of the present invention is well matched with that of the traditional Split-Field FDTD algorithm (Scheme (1) fine grid division), and the transmission coefficient is almost not offset and the center frequency is maintained at about 10 GHz, which shows that the method of the present invention is effective and has high calculation accuracy. However, the calculation results of the traditional Split-Field FDTD under scheme (3) coarse grid division have large errors. Therefore, compared with the traditional Split-Field FDTD algorithm, the method of the present invention can better adapt to the calculation under coarse grid division.

[0212] The embodiment of the present invention also provides computer resources consumed by three computing solutions, as shown in Table 1:

[0213] Table 1

[0214] According to the data in Table 1, compared with the traditional Split-Field FDTD algorithm, the method of the present invention can save a lot of computing time and computing memory, effectively alleviate the contradiction that the local refinement of the periodic structure grid causes a sharp increase in the amount of calculation, and greatly improve the computing efficiency.

[0215] Example 2

[0216] Based on the same inventive concept as that of Embodiment 1, this embodiment introduces an electromagnetic field simulation computing device for a frequency selective surface structure, comprising:

[0217] The algorithm derivation module is used to improve the split-field finite-difference time-domain algorithm by using the narrow-slit fitting technology to obtain the split-field finite-difference time-domain algorithm based on narrow-slit fitting.

[0218] The non-narrow slit part calculation module is used to perform electromagnetic field simulation calculation on the non-narrow slit part of the frequency selective surface structure according to the electromagnetic field data of the frequency selective surface structure using a split-field time-domain finite difference algorithm.

[0219] The narrow slot calculation module is used to perform electromagnetic field simulation calculation on the narrow slot part in the frequency selective surface structure according to the electromagnetic field data of the frequency selective surface structure by using a split-field time-domain finite difference algorithm based on narrow slot fitting.

[0220] The specific functional implementation of each of the above modules can be found in the relevant contents of the method in Example 1 and will not be elaborated here.

[0221] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented 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.

[0222] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0223] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0224] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0225] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which all fall within the protection of the present invention.

Claims

1. An electromagnetic field simulation calculation method for a frequency selective surface structure, characterized in that: The steps include: The split-field FDTD algorithm is improved by using narrow slit fitting technology, and the split-field FDTD algorithm based on narrow slit fitting is obtained. According to the electromagnetic field data of the frequency selective surface structure, the electromagnetic field simulation calculation of the non-narrow slit part of the frequency selective surface structure is carried out using the split-field finite-difference time-domain algorithm; According to the electromagnetic field data of the frequency selective surface structure, the electromagnetic field simulation calculation of the narrow slot part in the frequency selective surface structure is carried out using the split-field time-domain finite difference algorithm based on narrow slot fitting.

2. The electromagnetic field simulation calculation method for a frequency selective surface structure according to claim 1, characterized in that: The split-field finite-difference time-domain algorithm is improved by using the narrow-slit fitting technology to obtain a split-field finite-difference time-domain algorithm based on narrow-slit fitting, including: According to the differential form of the split-field time-domain finite difference equation, the integral form of the split-field time-domain finite difference equation is derived; According to the narrow slot coupling formula, the approximate fitting equation of the electromagnetic field component near the narrow slot in the frequency selective surface structure is derived, and the distribution law of the electromagnetic field component near the narrow slot along its corresponding loop is obtained; According to the distribution law of the electromagnetic field components near the narrow slot along its corresponding loop, the distribution law of the auxiliary field and the splitting field near the narrow slot at the same position is obtained; According to the distribution law of the auxiliary field and the splitting field at the same position near the narrow slit and the splitting field finite difference time-domain equation in integral form, the difference equation of the splitting field finite difference time-domain algorithm based on narrow slit fitting is obtained.

3. The electromagnetic field simulation calculation method for a frequency selective surface structure according to claim 2, characterized in that: The integral form of the split-field finite-difference time-domain equation is as follows: ； ； in, is the relative dielectric constant, is the relative magnetic permeability, c is the speed of light, t is the time variable, and Represents the vector form of the auxiliary field components, and Represents the vector form of the splitting field components, is the closed loop integral, l is the lth closed loop in the electromagnetic field of the frequency selective surface structure, The value of is the integral differential element of the closed loop l, A is the area enclosed by the closed loop l, The value of is the integral differential of area A.

4. The electromagnetic field simulation calculation method for a frequency selective surface structure according to claim 2, characterized in that: The distribution law of the auxiliary field and the splitting field near the narrow slit at the same position is obtained according to the distribution law of the electromagnetic field component near the narrow slit along its corresponding loop, including: According to the relationship between the auxiliary field component and the electromagnetic field component in the time domain, the distribution law of the auxiliary field near the narrow slot is derived by using the distribution law of the electromagnetic field component near the narrow slot along its corresponding loop. According to the relationship between the auxiliary field component and the splitting field component, the distribution law of the splitting field at the same position is deduced using the distribution law of the auxiliary field of the narrow slit attachment.

5. The electromagnetic field simulation calculation method for a frequency selective surface structure according to claim 4, characterized in that: Auxiliary field component , and the electric field component , magnetic field component The relationship in the time domain is: ； ； 。 6. The electromagnetic field simulation calculation method for a frequency selective surface structure according to claim 5, characterized in that: The relationship between the auxiliary field component and the splitting field component is: ； in, and is the auxiliary field variable in the r direction, and is the splitting field variable in the r direction, is the relative dielectric constant, is the relative magnetic permeability.

7. The electromagnetic field simulation calculation method for a frequency selective surface structure according to claim 2, characterized in that: The auxiliary field and splitting field near the narrow slit are moved along x, y, The changing rules of the directions are substituted into the integral form of the split-field finite-difference time-domain equation, the integral loop is solved and the central difference approximation is performed on the differential term of time, and the difference equation of the split-field finite-difference time-domain algorithm based on narrow slit fitting is obtained, which is expressed as follows: ； ； ； in, , Indicates the grid point when the time step is n The splitting field variables along the r direction at , Indicates the grid point when the time step is n The auxiliary field variables along the r direction at , are the three directions in the three-dimensional coordinate system, i, j, k are the grid coordinates in the x, y, and z directions respectively, n is the time step, Respectively represents moving forward or backward half a grid in the x, y, and z directions. Respectively represents moving forward or backward one grid along the x, y, and z directions. indicates moving forward or backward by half a time step, Indicates moving forward or backward one time step. , , are the grid sizes in the x, y, and z directions respectively, and B is the coefficient. is the relative dielectric constant, is the relative magnetic permeability, c is the speed of light, is the time step for calculation, w is the slit width of the narrow slit in the frequency selective surface structure, is the ratio of pi.

8. An electromagnetic field simulation computing device for frequency selective surface structure, characterized in that: include: An algorithm derivation module is used to improve the split-field finite-difference time-domain algorithm by using the narrow-slit fitting technology to obtain a split-field finite-difference time-domain algorithm based on narrow-slit fitting; A non-narrow slit part calculation module is used to perform electromagnetic field simulation calculation on the non-narrow slit part of the frequency selective surface structure using a split-field finite-difference time-domain algorithm according to the electromagnetic field data of the frequency selective surface structure; The narrow slot calculation module is used to perform electromagnetic field simulation calculation on the narrow slot part in the frequency selective surface structure according to the electromagnetic field data of the frequency selective surface structure by using a split-field time-domain finite difference algorithm based on narrow slot fitting.

9. The electromagnetic field simulation computing device for frequency selective surface structure according to claim 8, characterized in that: The algorithm derivation module is specifically used for: According to the differential form of the split-field time-domain finite difference equation, the integral form of the split-field time-domain finite difference equation is derived; According to the narrow slot coupling formula, the approximate fitting equation of the electromagnetic field component near the narrow slot in the frequency selective surface structure is derived, and the distribution law of the electromagnetic field component near the narrow slot along its corresponding loop is obtained; According to the distribution law of the electromagnetic field components near the narrow slot along its corresponding loop, the distribution law of the auxiliary field and the splitting field near the narrow slot at the same position is obtained; According to the distribution law of the auxiliary field and the splitting field at the same position near the narrow slit and the splitting field finite difference time-domain equation in integral form, the difference equation of the splitting field finite difference time-domain algorithm based on narrow slit fitting is obtained.

10. The electromagnetic field simulation computing device for frequency selective surface structure according to claim 9, characterized in that: The auxiliary field and splitting field near the narrow slit are moved along x, y, The changing rules of the directions are substituted into the integral form of the split-field finite-difference time-domain equation, the integral loop is solved and the central difference approximation is performed on the differential term of time, and the difference equation of the split-field finite-difference time-domain algorithm based on narrow slit fitting is obtained, which is expressed as follows: ； ； ； in, , Indicates the grid point when the time step is n The splitting field variables along the r direction at , Indicates the grid point when the time step is n The auxiliary field variables along the r direction at , are the three directions in the three-dimensional coordinate system, i, j, k are the grid coordinates in the x, y, and z directions respectively, n is the time step, Respectively represents moving forward or backward half a grid in the x, y, and z directions. Respectively represents moving forward or backward one grid along the x, y, and z directions. indicates moving forward or backward by half a time step, Indicates moving forward or backward one time step. , , are the grid sizes in the x, y, and z directions respectively, and B is the coefficient. is the relative dielectric constant, is the relative magnetic permeability, c is the speed of light, is the time step for calculation, w is the slit width of the narrow slit in the frequency selective surface structure, is the ratio of pi.

Images