An Adaptive Sampling Interpolation Sweeping Method for Transmission Scattering Parameters

Abstract

The present invention belongs to the field of computational electromagnetics and relates to a method for interpolating and sweeping frequencies of transmission scattering parameters with adaptive sampling. Based on rational function fitting and according to the results of the previous step, the present invention uses the difference between the integrals of two fitting functions within a sub-interval, which better reflects the degree of change of the transmission scattering parameters within the interval and reduces the number of fittings; effectively improves the selection efficiency of sampling points, reduces the insertion of redundant sampling points, and improves the fitting accuracy for severely changing sections. In severely changing sections where the number of sampling points is insufficient, the difference between the two fittings is large, and the adaptive method of the present invention will naturally tend to insert new sampling points into this section; conversely, in gently changing sections, the difference between the two fittings before and after is small, and there is no need to insert new sampling points; thus improving the efficiency and accuracy of interpolating and sweeping frequencies. The present invention effectively solves the problems of poor adaptive sampling effect and complexity in existing methods.

Description

Technical Field

[0001] The present invention belongs to the field of computational electromagnetics and relates to a method for interpolating and sweeping frequencies of transmission scattering parameters with adaptive sampling. Background Art

[0002] In the design of electromagnetic devices, such as filters, power dividers, connectors, antennas, etc., the transmission scattering parameters are very important. At the same time, in the design, we generally not only focus on the transmission scattering parameters at a single frequency point, but also care more about the performance of the transmission scattering parameters of the model within a certain frequency band. Therefore, it is very necessary to introduce a frequency scanning tool in electromagnetic assisted design to obtain the frequency response characteristics of the transmission scattering parameters.

[0003] Currently, in the finite element method of computational electromagnetics, the calculation of the frequency response of broadband electromagnetic parameters mainly uses three methods: discrete frequency sweeping, interpolated frequency sweeping, and fast frequency sweeping. Discrete frequency sweeping means using the matrix generated by the same set of meshes to calculate the solutions at different frequencies. Interpolated frequency sweeping means selecting some points within the frequency band, using discrete frequency sweeping to calculate the results, and then using interpolation techniques to obtain the response curve. Fast frequency sweeping reduces the number of unknowns through model order reduction, thereby improving the calculation efficiency.

[0004] In the implementation of the interpolated frequency sweeping method, we use fitting based on the partial fraction form, which has stronger numerical stability. During the interpolated frequency sweeping process, several sampling points need to be selected, and for each sampling point, a matrix integration and solution are required, which is often the most time-consuming step in the finite element solution. It can be seen that the efficiency of interpolated frequency sweeping depends to a large extent on the number of sampling points. When the number of sampling points is too small, the fitting effect may be very poor; when too many, it may cause waste of resources. Observing the frequency response within a frequency band, it may contain both sections with gentle changes and sections with rapid changes. For the gentle sections, fewer sampling points can be used; for the sections with rapid changes, more sampling points should be added. However, before solving the problem, we often do not know the change trend of its frequency response and it is difficult to preset appropriate sampling points.

[0005] The existing adaptive sampling techniques in interpolated frequency sweeping of transmission scattering parameters are mostly based on discrete point errors, that is, by comparing the errors of the fitting function at the sampling points to find new sampling points; they cannot well reflect the error changes in each sub-section. There are also some adaptive methods that need to repeatedly take different subsets from the current sampling point set, generate multiple fitting functions, and then find new sampling points by comparing the fitting functions with each other and with the sampling point errors, which is a bit too cumbersome. Summary of the Invention

[0006] In view of the above problems or deficiencies, to solve the problems of poor effect and complexity in the adaptive sampling of the existing transmission scattering parameter interpolation sweep frequency, the present invention provides a method for adaptive sampling of transmission scattering parameter interpolation sweep frequency, which rationally inserts new sampling points based on rational function fitting according to the results of the previous step, and is accurate and easy to implement.

[0007] A method for adaptive sampling of transmission scattering parameter interpolation sweep frequency includes the following steps:

[0008] Step 1: Perform three-dimensional modeling on the target waveguide, add materials, boundaries, and excitations, and then extract the corresponding calculation model to obtain the corresponding solution domain V.

[0009] Step 2: Use tetrahedral mesh division for the solution domain V obtained in Step 1 to obtain the corresponding discrete domain.

[0010] Step 3: In this step, add new sampling points to the sampling point set K (j-1) , to obtain the sampling point set K (j) , and calculate the transmission scattering parameters of each port corresponding to the newly added sampling points. Where j represents the number of adaptive loops, and K (j) represents the sampling point set corresponding to the jth adaptive loop. It should be noted that special processing is required when j = 1.

[0011] When j = 1 (i.e., the first adaptive loop), the sampling point set K min is generated from two sampling points f max and f (1) . In the formula, f min is the minimum frequency of the frequency band W to be solved, and f max is the maximum frequency of the frequency band W to be solved. Using the finite element method for the discrete domain obtained in Step 2, calculate its transmission scattering parameters H(s min ) and H(s max ). In the formula, s min and s max correspond to the values after the newly added sampling points f min and f max are transformed into the complex frequency domain.

[0012] When j ≠ 1, the newly added sampling point f new is added to the sampling point set K (j-1) to obtain the sampling point set K (j) , and using the finite element method for the discrete domain obtained in Step 2, calculate its transmission scattering parameter H(s new ), where s new is the value after the newly added sampling point f new is transformed into the complex frequency domain.

[0013] The specific process of calculating the transmission scattering parameters is as follows:

[0014] For the newly added sampling point f new (when j = 1, it is respectively for f min and f max calculate). First, for the discrete domain generated in step 2, the vector finite element method is adopted, and the finite element matrix is integrated according to the grid information to obtain the linear equation to be solved Ax = b; where, b corresponds to the source, and x is the coefficient of the basis function.

[0015] Solve this equation to obtain the coefficient x. Combining with the basis function of the tetrahedral element, the electromagnetic field at the corresponding frequency can be obtained.

[0016] Extract the electromagnetic field on the port, calculate and obtain the transmission scattering parameters of each port, that is, H(s new ); when j = 1, then H(s min ) and H(s max ) are obtained respectively.

[0017] Step 4: Use the sampling point set K of the current adaptive loop (j) and the calculated value H(s k ) of the transmission scattering parameter of the sampling point, where k is the number of the sampling point in the sampling point set K (j) , s k corresponds to the value of the k-th sampling point f k transformed to the complex frequency domain, and H(s k ) corresponds to the calculated value of the transmission scattering parameter of the sampling point f k , and perform rational function fitting to obtain the fitting function H fit,j (s); in the formula, the subscript fit indicates that this function is a fitting function, and the subscript j indicates that this fitting function corresponds to the j-th adaptive loop.

[0018] The fitting method is based on the complex frequency domain state space of the transmission scattering parameter under passivity:

[0019]

[0020] In the formula, x(s) is the state vector, y(s) is the output vector, u(s) is the input vector, A is the state matrix, B is the input matrix, C is the output matrix. D and D1 are the feedforward matrices, where D corresponds to the input vector itself, and D1 corresponds to the first derivative of the input vector in the time domain.

[0021] Fitting iteration format:

[0022] H fit (s) = σ(s)H(s) (1)

[0023] Among them, s represents the complex frequency domain variable, H(s) correspondingly represents the actual frequency response function (unknown), H fit(s) is the fitting function and σ(s) is the iteration factor. By substituting the sampling point set K (j) and the calculated values of the corresponding transmission scattering parameters H(s k ), a least squares problem of this fitting iteration format (1) is established.

[0024] The fitting iteration is divided into two nested loops:

[0025] Inner loop: At the q-th inner loop, substitute the sampling point set K (j) data, solve the least squares of the above fitting iteration format (1), and use the zeros of the iteration factor σ (q) (s) obtained in the q-th inner loop as the new poles to start the (q + 1)-th inner loop. And repeat the inner loop until the poles converge.

[0026] Outer loop: Starting from the order m = 1, if RMS ≤ RMS max or m ≥ m max , then end the fitting to obtain the fitting function H fit,j (s). Otherwise, let m = m + 1 and restart the inner loop. Among them, RMS is the root mean square error of the fitting function domain at the sampling points, RMS max is the error limit, m is the order of the fitting function; m max is the maximum allowed order, and it should satisfy 2n ≥ (2m max +3), where n represents the number of sampling points in the sampling point set K (j) .

[0027] Step 5. Use the frequency points in the sampling point set K (j) to divide the frequency band W. It should be noted that the case when j = 1 needs to be specially processed.

[0028] When j = 1, that is, corresponding to the first adaptive loop, at this time, there are only two sampling points f (1) and f min in the sampling point set K max . Therefore, at this time, let the new sampling point f new to be inserted = (f min + f max ) / 2, j = j + 1, and then jump to Step 3 to start the next round of adaptive loop.

[0029] When j ≠ 1, use the frequency points in the sampling point set K (j) to divide the frequency band W into a total of n - 1 intervals:

[0030] W1 = [f1, f2], W2 = [f2, f3], …, W n-1 = [f n-1 , f n ​

[0031] Step 6, traverse all intervals \(W_1, W_2, \ldots, W\) n-1 , for the fitting functions \(H\) fit,j (s) and \(H\) fit,j-1 (s), find the interval \(W\) with the largest error maxErr , and the corresponding error \(\varepsilon\) max .

[0032] For the interval \(W\) t , where \(t\) represents the \(t\)-th frequency band (\(t = 1, 2, \ldots, n - 1\)). Perform Gaussian integration to obtain the integral \(F\) of \(H\) fit,j (s) over this interval, and the integral \(F\) of \(H\) j,t (s) over this interval fit,j-1 . The error of this interval is obtained by the following formula: j-1,t

[0033]

[0034] Step 7, from the interval \(W\) with the largest error maxErr and the error \(\varepsilon\) max , find a new sampling point or end the fitting.

[0035] If \(\varepsilon\) max \(\geq \varepsilon\) threshold and \(n < N\) max , where \(\varepsilon\) threshold is the error threshold and \(N\) max is the upper limit of the number of sampling points. Then: \(j = j + 1\), \(f\) new \(= (f\) l , \(f\) r ) / 2\), where \([f\) l , \(f\) r = \(W\) maxErr , that is, the next loop obtains a new sampling point from the \(W\) maxErr interval, and returns to execute the next round of adaptive loop starting from Step 3.

[0036] Otherwise, end the adaptation, output the sampling point set \(K\) (j) as the sampling result, and the fitting function \(H\) fit,j (s) as the interpolation sweep result.

[0037] The adaptive sampling of the present invention can effectively improve the selection efficiency of sampling points in the interpolation sweep of transmission scattering parameters. In a section with drastic changes, when the number of sampling points is insufficient, the difference between two fittings is relatively large, and this adaptive method will naturally tend to insert new sampling points into this section. Conversely, in a section with gentle changes, the difference between the two fittings before and after is small, and there is no need to insert new sampling points. Compared with some adaptive strategies based on single-point error comparison, the present invention uses the difference between the integrals of two fitting functions within a sub-interval, which better reflects the degree of change of the transmission scattering parameters within the interval; compared with some methods based on a set of sampling points, repeatedly selecting points from them for fitting comparison, it reduces the number of fittings and is simple and easy to implement. In this way, through the reasonable selection of sampling points, both the insertion of redundant sampling points is reduced, and the fitting accuracy for sections with drastic changes is improved. Thus, the efficiency and accuracy of interpolation sweep are improved.

[0038] In summary, the interpolation sweep method of transmission scattering parameters with adaptive sampling provided by the present invention is based on rational function fitting, reasonably inserts new sampling points according to the results of the previous step, and is accurate and easy to implement. It effectively solves the problems of poor adaptive sampling effect and complexity in existing methods. Brief Description of the Drawings

[0039] Figure 1 is the flowchart of the present invention.

[0040] Figure 2 is the finite element model diagram of the embodiment.

[0041] Figure 3 is the result comparison diagram between the embodiment of the present invention and discrete sweep.

[0042] Figure 4 is the absolute value of the error between the embodiment of the present invention and the result of discrete sweep. Detailed Embodiment

[0043] The technical solution of the present invention will be described in detail below in conjunction with the drawings and embodiments.

[0044] A method for interpolation sweep of transmission scattering parameters with adaptive sampling, as Figure 1 shown, includes the following steps:

[0045] Step 1: Model the target waveguide, add materials, boundaries and excitations, and then extract the corresponding calculation model to obtain the corresponding solution domain V. The finite element model of this embodiment is as Figure 2 shown.

[0046] Step 2: Use tetrahedral mesh division for the solution domain V obtained in Step 1 to obtain the corresponding discrete domain.

[0047] Using tetrahedral meshing for the solution domain is a well-known process in the finite element method. After meshing, the solution domain is discretized into numerous tetrahedral meshes.

[0048] Step 3: Add new sampling points to the sampling point set K (j-1) , obtaining the sampling point set K (j) , and calculating the transmission scattering parameters of each port corresponding to the newly added sampling point; where j represents the number of the adaptive loop, and K (j) represents the sampling point set corresponding to the j-th adaptive loop. It should be noted that special treatment is required when j = 1.

[0049] When j = 1 (i.e., the first adaptive loop), from f min and f max two sampling points generate the sampling point set K (1) , f min is the minimum frequency of the frequency band W to be solved, and f max is the maximum frequency of the frequency band W to be solved. Using the finite element method for the discrete domain obtained in Step 2, calculate its transmission scattering parameters H(s min ) and H(s max ).

[0050] When j ≠ 1, the newly added sampling point f new to the sampling point set K (j-1) obtains the sampling point set K (j) , and using the finite element method for the discrete domain obtained in Step 2, calculate its transmission scattering parameters H(s new ).

[0051] Solving waveguide problems by the finite element method is a well-known method, which is only briefly described here. For the newly added sampling points (when j = 1, it is for f min and f max respectively to calculate the corresponding transmission scattering parameters), using the mesh information, from the weak solution form of the problem:

[0052]

[0053] In the formula, p1 represents the non-excited port number, p2 represents the excited port number, P is the number of ports, V is the solution domain in Step 2, S p1 and S p2 represent the cross-sections of the corresponding ports, S0 is the non-port truncation boundary, is the outward normal, is the Hamiltonian operator, × represents the cross product, and · represents the dot product. is the basis function, is the electric field, represents the incident electric field of port p2, is the magnetic field. ω is the angular frequency, i is the imaginary unit, μ0 and ε0 are the magnetic permeability and permittivity in vacuum respectively, and ε r is the relative permittivity, η is the wave impedance, and Z p1 and Z p2 represent the relevant mode impedances of the corresponding ports..

[0054] First, the computational domain is discretized into tetrahedral meshes, and then the vector finite element method is adopted. According to the mesh information, the finite element matrix is integrated to obtain the linear equation to be solved

[0055] Ax = b

[0056] where A is the left - hand side part of the above formula (2), b is the source (the right - hand side term of the equal sign) of the above formula (2), and x is the coefficient of the basis function.

[0057] Solve this equation to obtain the coefficient x. Combining the tetrahedral mesh and the basis function, the electromagnetic field at the corresponding frequency can be obtained.

[0058] Extract the electromagnetic field on the port and use the following formula:

[0059]

[0060]

[0061] In the formula, s p1,p2 , s p1,p1 is the transmission scattering parameter between ports, S p1 is the port cross - section, is the outward unit normal of the port cross - section, is the transverse electric field on the port, represents the transverse magnetic field on port p1, represents the incident electric field.

[0062] That is, the transmission scattering parameters of each port are calculated, that is, H(s new ); when j = 1, then the two values of H(s min ) and H(s max ) are obtained respectively.

[0063] Step 4: Use the set of sampling points K (j) of the current adaptive loop and the calculated values of the transmission scattering parameters of the sampling points H(s k ) to perform rational function fitting to obtain the fitting function H fit,j (s). In the formula, the subscript fit indicates that this function is a fitting function, j represents the number of the adaptive loop, and s represents the complex - frequency domain variable.

[0064] The fitting is based on the complex - frequency domain state space of the transmission scattering parameters under passivity:

[0065]

[0066] In the formula, \(x(s)\) is the state vector, \(y(s)\) is the output vector, \(u(s)\) is the input vector, \(A\) is the state matrix, \(B\) is the input matrix, \(C\) is the output matrix, and \(D\) and \(D1\) are the feedforward matrices, where \(D\) corresponds to the input vector itself, and \(D1\) corresponds to the first derivative of the input vector in the time domain.

[0067] Fitting iteration format:

[0068] H fit (s) = σ(s)H(s) (1)

[0069] Among them, \(s\) represents the complex frequency domain variable, and \(s\) k corresponds to the value transformed to the complex frequency domain at the \(k\)th sampling point \(f\) k , \(H(s\) k ) corresponds to the calculated value of the transmission scattering parameter at the sampling point \(f\) k , \(H\) fit (s k ) is the fitting function, and σ(s k ) is the iteration factor. The form is as follows:

[0070]

[0071]

[0072] In the formula, \(m\) is the set order, initialized to 1. \(a\) i , \(i = 1, 2, \ldots, m\) are the current poles, and they are initialized to a set of complex numbers.

[0073] The fitting iteration is divided into two nested loops:

[0074] Inner loop: Continuously substitute the sampling point data and solve the least squares of the above iteration format (3), then the corresponding \(c\) in the formula can be solved i , \(w\) i , \(d\), \(h\), , \(i = 1, 2, \ldots, m\). Then, according to the σ(s) expression (5), the zeros \(z\) i , \(i = 1, 2, \ldots, m\) are obtained. At this time, if \(z\) i changes very little compared to \(a\) i , \(i = 1, 2, \ldots, m\), such as the root mean square error is less than the given value (RMS pole ≤RMS poleMax ). Then proceed to the next step. Otherwise, as the new poles, update the values of \(a\) i to \(z\) i , \(i = 1, 2, \ldots, m\), that is, use the obtained zeros as the new poles. Repeat the inner loop until the poles converge.

[0075] Outer loop: Starting from the order m = 1, if RMS ≤ RMS max or m ≥ m max , the fitting is terminated to obtain the fitting function H fit,j (s). Otherwise, let m = m + 1 and restart the inner loop. Where m max is the maximum allowable order and should satisfy 2n ≥ (2m max +3), where n represents the number of sampling points in the sampling point set K (j) ; RMS is the root mean square error of the fitting function domain at the sampling points, and RMS max is the error limit, using the following formula:

[0076]

[0077] Step 5: Use the frequency points in the sampling point set K (j) to divide the frequency band W. It should be noted that when j = 1, special processing is required.

[0078] When j = 1, it corresponds to the first adaptive loop. At this time, there are only two sampling points f (1) and f min in the sampling point set K max . Therefore, let the new sampling point f new to be inserted = (f min +f max ) / 2, j = j + 1, and then jump to Step 3 to start the next round of adaptive loop.

[0079] When j ≠ 1, use the frequency points in the sampling point set K (j) to divide the frequency band W into a total of n - 1 intervals:

[0080] W1 = [f1, f2], W2 = [f2, f3], …, W n-1 = [f n-1 , f n

[0081] Step 6: Traverse all intervals W1, W2, …, W n-1 , and for the fitting functions H fit,j (s) and H fit,j-1 (s), find the interval W maxErr with the largest error, and the corresponding error ε max .

[0082] For the interval W t , perform Gaussian integration (Gaussian integration is a well-known method) to obtain the integral F fit,j of H j,t (s) in this interval, and the integral F fit,j-1 of H j-1,t ​This interval error is obtained as follows:

[0083]

[0084] Step 7: From the maximum error interval W maxErr and the error ε max , find a new sampling point or end the fitting.

[0085] If ε max ≥ε threshold and n < N max , where ε threshold is the error threshold and N max is the upper limit of the number of sampling points. Then: j = j + 1, f new =(f l , f r ) / 2, where [f l , f r =W maxErr , that is, the next cycle obtains a new sampling point from the W maxErr interval, and returns to execute from step C.

[0086] Otherwise, end the self - adaptation, output the sampling point set K as the sampling result, and the fitting function H fit,j as the interpolation sweep result.

[0087] Figure 3 is the comparison graph of the results of this embodiment and the discrete sweep. It can be seen that except for the obvious error near 2.2 GHz, the two almost coincide in other cases, indicating high precision. At the same time, it can be seen that the sampling points are concentrated in the section from 1.2 GHz to 1.8 GHz, that is, the section with relatively large changes, which reflects the advantage of the present invention. Figure 4 is the absolute value of the error between the results of this embodiment and the discrete sweep, and corresponds to Figure 3 . It can be seen that the whole range from 0.6 GHz to 2.4 GHz is at a relatively low level (below 0.01), which once again reflects the high precision of the present invention.

[0088] In summary, the present invention first performs finite element modeling on the target waveguide, adds materials, boundaries and excitations, establishes a corresponding calculation model, and uses tetrahedral mesh to divide the solution domain to obtain a discrete domain; then performs an adaptive sampling loop. For the sampling points, by selecting vector basis finite elements, the corresponding electromagnetic fields are solved, and then the corresponding transmission and scattering parameters are obtained therefrom; then, based on all the current sampling points, rational function fitting is performed to obtain a fitting function; then, based on the sampling points, the entire frequency band is divided into a group of sub-intervals; then, using the fitting functions obtained from the current and previous adaptive sampling loops, the integral differences are calculated for all the divided sub-intervals, and the interval with the largest difference is selected as the new sampling interval, and the new sampling points are determined. The adaptive sampling loop is repeated until the error is satisfied or the sampling point upper limit is reached. Finally, the final set of sampling points and the corresponding fitting function are obtained. Thus, interpolation frequency sweeping with adaptive selection of sampling points is realized, effectively solving the problems of poor adaptive sampling effect and complexity in the existing methods.

Claims

1. An adaptive sampling-based interpolation sweep frequency method for transmission scattering parameters, characterized in that Including the following steps: Step 1: Perform 3D modeling on the target waveguide, add materials, boundaries, and excitations, then extract the corresponding computational model to obtain the corresponding solution domain V; Step 2: Use tetrahedral mesh division for the solution domain V obtained in Step 1 to obtain the corresponding discrete domain; Step 3: Add a new sampling point to the sampling point set K (j-1) , to obtain the sampling point set K (j) , and calculate the transmission scattering parameters of each port corresponding to the newly added sampling point; where j represents the j-th adaptive loop, and K (j) represents the sampling point set corresponding to the j-th adaptive loop; When j = 1, from f min and f max two sampling points generate a sampling point set K (1) , f min is the minimum frequency of the frequency band W to be obtained, f max is the maximum frequency of the frequency band W to be obtained; for the discrete domain obtained in step 2, use the finite element method to calculate its transmission scattering parameters H(s min ) and H(s max ), s min and s max correspond to the values after the newly added sampling points f min and f max are transformed into the complex frequency domain; When j≠1, the newly added sampling point f new to the sampling point set K (j-1) obtains the sampling point set K (j) , and uses the finite element method for the discrete domain obtained in step 2 to calculate its transmission scattering parameter H(s new ), where s new is the value after the newly added sampling point f new is transformed to the complex frequency domain; Step 4: Use the sampling point set K of the current adaptive loop (j) and the calculated value H(s k ) of the transmission scattering parameter of the sampling points, where k is the number of the sampling points in the sampling point set K (j) , s k corresponds to the value of the k-th sampling point f k transformed to the complex frequency domain, and H(s k ) corresponds to the calculated value of the transmission scattering parameter of the sampling point f k . Perform rational function fitting to obtain the fitting function H fit,j (s); the subscript fit indicates that this function is a fitting function, and the subscript j indicates that this fitting function corresponds to the j-th adaptive loop; The fitting method is based on the complex frequency domain state space of the transmission scattering parameters under passive conditions: In the formula, x(s) is the state vector, y(s) is the output vector, u(s) is the input vector, A is the state matrix, B is the input matrix, C is the output matrix; D and D1 are feedforward matrices, where D corresponds to the input vector itself, and D1 corresponds to the first derivative of the input vector in the time domain; Fitting iteration format: H fit (s) = σ(s)H(s) (1) where s represents the complex frequency domain variable, H(s) correspondingly represents the actual frequency response function, H fit (s) is the fitting function, and σ(s) is the iteration factor; By substituting the sampling point set K (j) and the calculated values of the corresponding transmission scattering parameters H(s k ), a least-squares problem for fitting the iterative format (1) is established; The fitting iteration is divided into two-layer loops: Inner loop: At the q-th inner loop, substitute the sampling point set K (j) data, and perform least squares solution on the fitting iteration format (1). Take the iteration factor σ of the q-th memory loop obtained (q) (s) zeros as new poles to start the (q + 1)-th inner loop, and repeat the inner loop until the poles converge; Outer loop: Starting from the order m = 1, if RMS ≤ RMS max or m ≥ m max , then end the fitting and obtain the fitting function H fit,j (s); otherwise, let m = m + 1 and restart the inner loop; where RMS is the root mean square error of the fitting function domain at the sampling points, and RMS max is the error limit, m is the order of the fitting function; m max is the maximum allowed order, satisfying 2n ≥ (2m max + 3), and n represents the number of sampling points in the sampling point set K (j) ; Step 5: Use the frequency points in the sampling point set K (j) to divide the frequency band W; When j = 1, the sampling point set K (1) contains only two sampling points f min and f max . Therefore, at this time, let the new sampling point f new to be inserted be f min + f max ) / 2, j = j + 1, and then jump to step 3 to start the next round of adaptive loop; When j ≠ 1, the sampling point set K (j) intermediate frequency points are used to divide the frequency band W into a total of n - 1 intervals: W1 = [f1, f2], W2 = [f2, f3], …, W n-1 = [f n-1 , f n ​ Step 6. Traverse all intervals \(W_1, W_2, \ldots, W\) n-1 , for the fitting functions \(H\) fit,j (s) and \(H\) fit,j-1 (s), find the interval \(W\) maxErr with the largest error, and the corresponding error \(\varepsilon\) max ; For the interval W t , where t is the t-th frequency band, t = 1, 2, …, n - 1; Gaussian integration is performed to obtain the integral F of H fit,j (s) over this interval j,t , and the integral F of H fit,j-1 (s) over this interval j-1,t ; The error for this interval is obtained by the following formula: Step 7. From the maximum error range W maxErr and the error ε max , find a new sampling point or end the fitting; If ε max ≥ ε threshold and n < N max , where ε threshold is the error threshold and N max is the upper limit of the number of sampling points; then: j = j + 1, f new =(f l , f r ) / 2, where [f l , f r =W maxErr , that is, the new sampling point is obtained from the W maxErr interval in the next cycle, and return to execute the next round of adaptive cycle starting from step 3; Otherwise, end the adaptation and output the set of sampling points K (j) As the sampling result, the fitting function H fit,j (s) is used as the interpolation sweep result.

2. The interpolation sweep frequency method for transmission scattering parameters with adaptive sampling according to claim 1, characterized in that: The specific process of calculating the transmission scattering parameters in Step 3 is as follows: For the newly added sampling point f new , when j = 1, it is for f min and f max respectively for calculation; First, for the discrete domain generated in step 2, the vector finite element method is adopted, and the finite element matrix is integrated according to the grid information to obtain the linear equation to be solved Ax = b; where, b corresponds to the source, and x is the coefficient of the basis function; Solve this equation to obtain the coefficient x; combined with the basis function of the tetrahedral element, the electromagnetic field at the corresponding frequency can be obtained; Extract the electromagnetic field on the ports and calculate the transmission scattering parameters of each port, that is, H(s new ); when j = 1, then we get two values of H(s min ) and H(s max ) respectively.

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