A grid sequence iterative convergence acceleration method, device, medium and system

Abstract

The present invention discloses a grid sequence iterative convergence acceleration method, device, medium and system, which belongs to the field of numerical simulation of computational electromagnetics time domain finite volume method, and includes the steps of: iteratively solving the time-varying electromagnetic field of Maxwell equations in an implicit dual time step method based on time iterative advancement of conserved electromagnetic field and spatial flux residual; the outer layer of the simulation model is a physical time step cycle until the calculation converges; the inner layer of the simulation model is a virtual time step sub-iteration cycle until the sub-iteration converges; in each virtual time sub-iteration process, according to the grid sequence cycle mode, the spatial flux and residual calculations are performed on each structural grid mesh block and each grid unit of the hierarchical grid in turn, implicit iterative calculations, adjacent grid layer flux residuals, conserved variables, forcing functions, electromagnetic parameters interpolation transmission, and updating the next level of virtual time sub-iteration step number conserved electromagnetic field numerical value. The present invention improves the calculation efficiency.

Description

Technical Field

[0001] The present invention relates to the field of computational electromagnetics time-domain finite volume method numerical simulation, and more specifically, to a grid sequence iterative convergence acceleration method, device, medium and system. Background Art

[0002] Many electronic engineering problems involve time domain solutions to Maxwell's equations, such as radio frequency microwave components, communications, radar, mixed signal integrated circuits, electromagnetic wave diffraction, plasma physics, medical imaging, electromagnetic scattering of complex shaped targets, electromagnetic interference in complex electromagnetic environments, etc. A single calculation in the time domain can obtain broadband information of the system and accurately simulate the time history, so it is widely used in electromagnetic field problems.

[0003] One type of time domain method is the frequency domain-time domain numerical transformation method, which first calculates in the frequency domain and then transforms the solution into the time domain solution through Fourier transformation. The other type is the numerical method for directly solving time domain problems, including the time domain integral equation method, the finite difference time domain method, the finite element time domain method, the finite volume time domain method, etc. Among them, the time domain method for directly solving the Maxwell equations of electromagnetic fields is an important branch. The finite volume time domain method (Finite Volume Time Domain, FVTD) is a numerical method for integrating the divergence equation in the control volume and then converting the volume integral to the surface normal flux area integral. It can maintain the diversity of format construction and can use almost all the design ideas of the difference method; and the finite volume method has no restrictions on meshing and unit shape, and it is easy to handle complex structures. It is currently a general numerical method for computational fluid dynamics.

[0004] In actual engineering applications, as the scale of the grid becomes larger and larger, how to improve the computational efficiency and speed up iterative convergence is a very important issue. In addition to accuracy, computational efficiency is also a key link in numerical applications. Usually, explicit methods have defects. Due to the stability restriction, the space must adopt a unified minimum global step size. The stable time-varying electromagnetic field requires a long calculation time and the computational efficiency is not high. On the other hand, the implicit method can relax the stability (CFL number) restriction, but it is usually accompanied by a decrease in time accuracy and matrix inversion operations, and physical time simulation cannot be used directly. For this reason, the present invention uses a double time cycle to improve the computational efficiency, and adopts the addition of a constant virtual time sub-iteration to meet the stability requirements. The physical time step is determined by the numerical accuracy to break through the time step constraint. At the same time, a fully implicit algorithm and implicit time advancement are used to amplify the CFL number, increase the time step, and use the local time step to accelerate the convergence process to a certain extent.

[0005] Classic Gauss-Seidel, Jaccobi, SOR methods, etc., the error decays very quickly in the first few iterations, among which the high-frequency error decays quickly and the low-frequency error decays slowly. They can quickly smooth out the local high-frequency oscillation error, but the global low-frequency smooth error decays slowly, and the error becomes smooth after several iterations. The grid sequence or multigrid method can smooth out errors of different frequencies and is an effective acceleration method, which has been confirmed by computational fluid dynamics.

[0006] In the field of time-domain electromagnetic calculation, there are few studies on grid sequence methods or geometric multigrid methods, which are mostly applied in the frequency-domain finite element method. In the 2008 "Multi-layer grid step-by-step approximation calculation of electromagnetic field based on FDTD", the electromagnetic field was calculated step by step from coarse to fine grids based on FDTD, and the resonant cavity electromagnetic calculation was applied. In 2015 "A Multilevel Numerical Approach with Application in Time-Domain Electromagnetics", an algebraic multigrid FVTD composed of different precision formats was proposed, which was applied to the calculation of two-dimensional cylinder and airfoil scattering. The time-domain electromagnetic calculation FVTD proposed in this patent combines the geometric structure grid sequence and the double implicit time iteration to accelerate the convergence efficiency of the physical time iteration. This patent is different from the frequency-domain finite volume method in the control equation (time domain / frequency domain), variable type (real number / complex number), incident electromagnetic wave waveform (broadband / single-frequency simple harmonic wave), etc., and has not been reported at home or abroad.

[0007] In summary, the following technical problems exist: the efficiency of electromagnetic field calculation for large grid volume and complex electromagnetic engineering problems, as well as the iterative convergence speed of time-domain electromagnetic fields need to be improved. Summary of the invention

[0008] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a grid sequence iterative convergence acceleration method, equipment, medium and system. On the one hand, an efficient time-domain electromagnetic numerical method is implemented to solve large-scale electromagnetic scattering problems of complex-shaped, high-frequency, electrically large-sized conductor targets, and the calculation efficiency is improved under the premise of ensuring high precision of time and space calculation formats; on the other hand, based on the scheme of the present invention, a structured grid and a time-varying electromagnetic field grid sequence acceleration FVTD algorithm are provided, which involves a body-fitting conformal space grid, a dual-time-step time advancement, an electromagnetic flux residual fully implicit algorithm to relax the CFL number restriction, a forward and backward iterative implicit inversion algorithm, and a grid sequence with different geometric size coarseness to eliminate numerical errors of different frequencies in the iterative process, and an electromagnetic numerical method that achieves an accelerated convergence effect by a grid sequence cycle.

[0009] The object of the present invention is achieved through the following solutions:

[0010] A grid sequence iterative convergence acceleration method comprises the following steps:

[0011] The time-varying electromagnetic field of Maxwell's equations is iteratively solved by an implicit dual-time-step method based on time iterative advancement of the conservative electromagnetic field and spatial flux residuals; the outer layer of the simulation model is a physical time step cycle until the calculation converges; the inner layer of the simulation model is a virtual time step sub-iteration cycle until the sub-iteration converges; in each virtual time sub-iteration process, according to the grid sequence cycle mode, the spatial flux and residual calculations are performed on each structural grid block and each grid cell of the hierarchical grid in turn, and the implicit iterative calculations are performed, the flux residuals, conservative variables, forcing functions, and electromagnetic parameters of adjacent grid layers are interpolated and transferred, and the conservative electromagnetic field values ​​of the next virtual time sub-iteration step are updated.

[0012] Furthermore, the outer layer of the simulation model is a physical time step loop until the calculation converges; the inner layer of the simulation model is a virtual time step sub-iteration loop until the sub-iteration converges, which specifically includes the following sub-steps:

[0013] Among them, the physical time step cycle and virtual time step sub-iteration cycle process is:

[0014] Add virtual time derivative , the passive time-domain Maxwell equations of real variables are modified to be:

[0015] (1);

[0016] (2);

[0017] in, is the time domain real number scattering electromagnetic field conservation variable, It's virtual time. is the normalized physical time, , , is the electromagnetic flux in rectangular coordinates , , Quantity, is the real scattered magnetic induction intensity vector, is the real-valued electric displacement vector of the scattered field;

[0018] Virtual Iteration , the equations are reduced to the original equations, virtual time The subiteration table is:

[0019] (3);

[0020] in, yes The value of the electromagnetic field conservation variable after virtual time iteration, yes The approximate value of , the superscript * represents the value of the conserved variable corresponding to the virtual time sub-iteration, is the flux residual, is the number of physical time steps; is the physical time step, It is The electromagnetic conservation variables at the physical time step, It is Electromagnetic conservation variables at the physical time step; for The corresponding intermediate state flux residual; the physical time derivative uses the backward second-order difference;

[0021] Subiteration (3) uses a fully implicit algorithm and performs Virtual time step flux linearization expansion:

[0022] ;

[0023] (4);

[0024] (5);

[0025] in, is the virtual time step; , , Corresponding to the curvilinear coordinate system Directional difference operator; , , Corresponding to the curvilinear coordinate system Directional electromagnetic flux Jacobian coefficient matrix; is the difference of conservation variables of scattering fields in adjacent physical times; It is Physical time step spatial flux residual, It is the total spatial flux residual of the previous physical time step plus the double time step correction; It is Grid unit Electromagnetic conservation variables for virtual time steps; It is Grid unit Electromagnetic conservation variables for virtual time steps; , , They are the corresponding curvilinear coordinate systems Directional electromagnetic flux;

[0026] Among them, the spatial flux in each level of the grid in the structured grid sequence is calculated as follows:

[0027] First, the Steger-Warming splitting method is used to calculate the interface flux of the grid cells;

[0028] Finally, the forward and backward iterative calculation of the electromagnetic field difference is achieved based on LUSGS in each level of the structural grid sequence. :

[0029] During the structural grid sequence cycle, the adjacent level grid calculation process:

[0030] Step (a) is to iteratively solve the discrete equations in the densest grid to obtain the electromagnetic field quantity , electromagnetic field increment and residuals, store these quantities and pass the electromagnetic field quantities and residuals to the coarse grid through the "restriction operator";

[0031] (6);

[0032] (7);

[0033] (8);

[0034] In the formula, the subscript Represents the geometric scale of the grid at this level, the subscript Represents the geometric scale of the grid at this level, the subscript For the summation variable, 4 is used for two-dimensional and 8 for three-dimensional; yes The upper triangular matrix of the level grid, yes Level grid diagonal matrix The inverse matrix of yes The triangular matrix of the lower level grid, is the virtual time step, yes Level grid spatial flux residual; yes The initial value of the electromagnetic field on the grid level, yes Level Grid to Volume weighted interpolation operator for level grids, yes The volume of the grid cells participating in the summation on the level grid, is the residual error transferred from the densest grid, yes Level grid spatial flux residual, yes The residuals involved in the summation on the level grid, yes Calculation of spatial flux residuals on grids at the upper level Level grid flux residual operator;

[0035] Step (2), switch to the next dense grid layer iteration, in the first step of the iteration, find the forcing function , which means the difference between the initial field and the transmitted residual on the sub-dense grid obtained by restriction:

[0036] (9);

[0037] In the formula, is the residual error transferred from the densest grid, The residuals calculated by the explicit scheme are calculated for the first iteration of the coarse grid; in this iteration, will remain unchanged; if W loop is used, then in the downward calculation, The previous value will be used; the actual residual for the iteration on the coarse grid is the residual calculated by the format plus the forcing term

[0038] (10);

[0039] yes Level Grid The actual residual of the second sub-iteration, yes The residual obtained by calculating the spatial format flux on the coarse grid, the electromagnetic field variables after the coarse grid iteration are recorded as , repeat step (a);

[0040] Step (3), switch to a more sparse grid calculation, same as step (2), repeat steps (1) to (3) until the sparsest grid is reached;

[0041] Step (iv), after the iterative calculation of the sparsest grid, the correction amount is interpolated back to the upper grid in sequence until the densest grid; the interpolation process is then performed in the current grid layer for "post-iteration", and the "forcing term" is still added to the iteration;

[0042] (11);

[0043] (12);

[0044] In the formula, yes The electromagnetic field quantity on the grid level, is the interpolation operator that transfers the correction from the lower grid to the upper grid, yes Electromagnetic field increment on the grid , yes After the first iteration on the level grid, the electromagnetic field quantities are, yes Initial values ​​of electromagnetic field quantities of level grid; The “quasi-trilinear” interpolation method is adopted. Specifically, the correction amount is first interpolated from the grid center to the node through volume weighted interpolation, and then the correction amount is interpolated to the grid center of the dense grid through linear interpolation.

[0045] Furthermore, before the iterative solution of the Maxwell equations time-varying electromagnetic field in the implicit dual time-step method based on the conserved electromagnetic field time iterative advancement and the spatial flux residual, the method further includes the following steps:

[0046] The grid density ensures 15-20 grid points per wavelength, the wall density is >300 points / local wavelength, and the density is encrypted to 50-100 grid points / local wavelength at geometric singularities. For two-dimensional grids, one layer is advanced according to the right-hand rule in the plane perpendicular to the two-dimensional grid, and it is calculated uniformly as a special case of three-dimensional problems. The grid data file includes the number of structural grid blocks and the dimensions of each block in the three curvilinear coordinate system.

[0047] Furthermore, before the iterative solution of the Maxwell equations time-varying electromagnetic field in the implicit dual time-step method based on the conserved electromagnetic field time iterative advancement and the spatial flux residual, the method further includes the following steps:

[0048] The physical time step is pre-set. For two-dimensional problems, a physical time step of the order of 0.01 of the incident electromagnetic wave period is used. For three-dimensional problems, a physical time step of the order of 0.001 of the incident electromagnetic wave period is used. At the same time, the sub-iteration convergence standard criterion value is set as the absolute value of the second-order moment of the difference in magnetic field amplitudes between adjacent sub-iteration time steps in the full grid space decreases by two orders of magnitude, that is, the ratio of the second-order moment after the first sub-iteration is <0.01, which is considered convergence. The maximum number of sub-iteration steps is set to 30.

[0049] A computer device comprises a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is loaded by the processor, any of the above methods is executed.

[0050] A readable storage medium stores a computer program, and when the computer program is loaded by the processor, any of the above methods is executed.

[0051] A grid sequence iterative convergence acceleration system comprises the computer device as described above.

[0052] The beneficial effects of the present invention include:

[0053] 1. The present invention relaxes the physical time step restriction by using the dual (physical and virtual) time iterative advancement of the conserved electromagnetic field and the implicit calculation of the space flux in the time domain finite volume method, and uses the implicit time domain finite volume method to efficiently obtain the 2D and 3D electromagnetic field space-time distribution.

[0054] 2. The present invention directly numerically simulates the Maxwell equations of the time-domain electromagnetic field. In the sub-iteration, the flux residuals, conservation variables, forcing functions, and electromagnetic parameters of adjacent grid layers are interpolated and transferred at each grid level in a specific cycle mode. The high-frequency errors are first eliminated on the densest grid, and then the low-frequency errors are eliminated on the coarse grid. In this way, errors of different frequencies are iteratively eliminated on a series of grids of different coarsenesses to achieve the purpose of accelerated convergence.

[0055] The example shows that in the entire real-number electromagnetic field physical time unsteady calculation, the virtual time-steady sub-iteration of each physical time step ends the sub-iteration calculation when the convergence standard is met, saving the amount of calculation; and the convergence curve shows that the use of multiple grid sequence iterations, whether V-shaped or W-shaped cycles, converges faster than single grid calculations, and the W-shaped is optimal, with convergence acceleration of up to 36%, and efficiency improvement of more than 50%. And the numerical accuracy of the time-domain electromagnetic field physical time and radar scattering cross-section output is guaranteed. Therefore, the time-domain finite volume method accelerated by the structured grid sequence that implicitly combines the time double time step and the space flux corresponding to the present invention can stably, accurately and efficiently obtain the time and space distribution of the electromagnetic field, and is suitable for numerical simulation of electromagnetic wave propagation, reflection and other phenomena, and is particularly suitable for large-scale, large-volume electromagnetic field calculations and scattering stealth characteristics calculations of electrically large-sized targets.

[0056] 3. The structural grid and geometric grid sequence of the present invention are simple to implement and have a clear structure. An appropriate number of grid levels can be selected, and the grid sequence cycle mode can be arbitrarily selected, such as a W-shaped cycle or a V-shaped cycle, to achieve optimal acceleration efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0058] Figure 1 It is a software flow chart of the present invention;

[0059] Figure 2a It is a complex W-shaped grid sequence cyclic mode;

[0060] Figure 2b It is a V-shaped grid sequence cycle mode;

[0061] Figure 3a It is the densest grid of the metal ball grid sequence ign=1;

[0062] Figure 3b is the metal ball grid sequence ign=2 grid;

[0063] Figure 3c It is the metal ball grid sequence ign=3 grids;

[0064] Figure 3d It is the most sparse grid of the metal ball grid sequence ign=4;

[0065] Figure 4a It is the sub-iteration convergence curve in the last three physical time steps before the unsteady calculation converges;

[0066] Figure 4b It is the sub-iteration convergence process of the last physical time step process; Figure 4a~Figure 4b Among them, the vertical axis Epselon represents the total residual of the entire grid electromagnetic field virtual time iterative calculation process, and the horizontal axis ITER represents the number of iterative calculation steps; Lu-Sgs Single Grid represents the calculation case using a single grid and Lu-Sgs algorithm, 4 level V-MultiGrid represents the calculation case using a 4-grid and V-shaped grid sequence cyclic algorithm, and 4 level W-MultiGrid represents the calculation case using a 4-grid and W-shaped grid sequence cyclic algorithm;

[0067] Figure 5 is the electromagnetic scattering surface induced current of the metal sphere (ka=2); where Jx represents the x component of the target surface induced current density vector;

[0068] Figure 6It is a comparison of radar cross section distribution of a metal sphere (ka=2) calculated by three iterative methods. Wherein, the abscissa degree represents the azimuth of the dual-station radar; the ordinate RCS represents the radar scattering cross-section; Exact (E-Plane) represents the exact solution of the E-plane; Exact (H-Plane) represents the exact solution of the H-plane; Single Grid Computation (E-Plane) represents the E-plane result calculated by using the algorithm of the present invention and a single grid; Single Grid Computation (H-Plane) represents the H-plane result calculated by using the algorithm of the present invention and a single grid; 3 level W-Multigrid Computation (E-Plane) represents the E-plane calculation result using a 3-grid and W-shaped grid sequence cyclic algorithm; 3level W-Multigrid Computation (H-Plane) represents the H-plane calculation result using a 3-grid and W-shaped grid sequence cyclic algorithm; 3 level V-Multigrid Computation (E-Plane) represents the E-plane calculation result using a 3-grid and V-shaped grid sequence cyclic algorithm; 3 level V-Multigrid Computation (H-Plane) represents the H-plane calculation result using a 3-grid and V-shaped grid sequence cyclic algorithm. DETAILED DESCRIPTION

[0069] All features disclosed in all embodiments in this specification, or steps in all methods or processes implicitly disclosed, except for mutually exclusive features and / or steps, can be combined and / or expanded or replaced in any manner.

[0070] In view of the problems in the background, in order to improve the efficiency of electromagnetic field calculation for large grid volume and complex electromagnetic engineering problems, accelerate the iterative convergence speed of electromagnetic fields, and achieve the purpose of FVTD numerical tools to solve more practical electromagnetic engineering needs, the present invention proposes an efficient structured grid sequence accelerated FVTD method for directly solving the time-domain Maxwell equations. By adding a double time cycle of constant virtual time sub-iteration, the physical time step is determined by the numerical accuracy and the small time step constraint limited by stability is eliminated; at the same time, a fully implicit algorithm and implicit time advancement are used to amplify the CFL number, increase the time step and adopt the local time step; in particular, a geometric grid sequence accelerated convergence algorithm is proposed to further enhance the iterative convergence efficiency of the time-domain electromagnetic field. The innovative points of the present invention include: unlike the finite element and moment method, the FVTD of the present invention does not have large storage requirements and large dense matrix iterative calculations, and FVTD only requires iterative operations on variables of several adjacent grid units; unlike the FDTD multi-layer grid method in the literature, the present invention adopts an implicit finite volume method with body-fitting conformal grids and co-location of electromagnetic field quantities; unlike the algebraic multi-grid in the 2015 Chatterjee literature, the present invention combines the successful experience in the CFD field and accelerates convergence only on the structural grid geometry sequence. The present invention can accurately simulate complex shape targets and adopt an implicit time-marching algorithm, so that while maintaining high numerical accuracy, it can also use a larger iterative physical time step, and combined with a variety of iterative acceleration techniques can improve computing performance and efficiency. Specifically, the specific implementation process of the present invention is as follows:

[0071] In a preferred embodiment, the present invention particularly relates to how to improve the efficiency of solving Maxwell's equations in the form of scattered fields, a dual time-step method for maintaining the accuracy of time-varying electromagnetic field calculations, implicit calculation of electromagnetic flux residuals for each grid sequence, and interpolation and transmission of flux residuals, conserved variables, and electromagnetic parameters of adjacent grid layers, and a fully implicit FVTD calculation method for iteratively accelerating the solution through grid sequence cycles. Specifically, the present invention provides a grid sequence iterative convergence acceleration method in the structured grid time-varying electromagnetic field finite volume time domain (Finite Volume Time Domain, FVTD) method. The method comprises the following steps: performing simulation modeling according to the physical background of the electromagnetic problem to be simulated by the target and combining boundary condition information; dividing the numerical calculation region into two-dimensional quadrilateral or three-dimensional hexahedral structure grids, encrypting the grids at the walls and geometric singularities, and gradually making the grids sparser away from the scattering walls; outputting grid data files and boundary condition files; inputting target calculation electromagnetic parameters and numerical calculation control parameters; inputting grid data and boundary condition information files, and initializing the calculation space electromagnetic field; advancing based on dual-time-step virtual time sub-iterations, implicitly calculating the electromagnetic flux residuals in each grid sequence in a specific cyclic manner in each sub-iteration, and interpolating and transferring the flux residuals, conserved variables, and electromagnetic parameters of adjacent grid layers, so as to iteratively solve the time-varying electromagnetic field. The present invention directly numerically calculates the Maxwell equations in the time domain. On the one hand, by introducing a constant virtual time derivative term in the control equation, the physical time step is selected according to the numerical calculation accuracy without being restricted by stability; the forward and backward iterative implicit inversion algorithm is used to relax the CFL (Courant-Friedrichs-Lewy) number restriction, and finally, through a grid sequence with different geometric size coarseness, the numerical errors of different frequencies in the iterative process are eliminated, and the grid sequence cycle is used to achieve the effect of accelerated convergence. The present invention can solve large-scale electromagnetic scattering problems of large-scale targets with arbitrary complex shapes and high frequency electricity.

[0072] Furthermore, if Figure 1 As shown in the figure, the entire software for calculating electromagnetic fields using the finite volume method in the time domain can be divided into three parts according to its structure: preprocessing, electromagnetic field calculation, and postprocessing. Preprocessing mainly includes three modules: grid data input, calculation parameter data input, and control parameter input. It is mainly used to read in grid data, calculation parameter data input, and control parameter files, and on this basis, preprocessing is performed to provide calculation support for electromagnetic field calculation; electromagnetic field calculation includes: spatial electromagnetic field MUSCL format interpolation, unit interface flux calculation, time advancement, each sub-iteration performs implicit calculation of electromagnetic flux residuals in each grid sequence in a specific loop mode, adjacent grid layer flux residuals, conservation variables, electromagnetic parameter interpolation transfer, and convergence judgment modules; postprocessing is mainly used to output the time and spatial distribution of the electromagnetic field, the induced current density on the target surface, and the radar scattering cross section output.

[0073] Next, we combine the two curl equations of the passive Maxwell equations to be numerically simulated. , ,in is the gradient symbol, is the real-numbered scattered field magnetic induction intensity vector, is the real-valued electric displacement vector of the scattered field, is the real-valued electric field intensity vector of the scattered field, is the real-valued scattered field magnetic field intensity vector, is the normalized physical time.

[0074] The double time-step time-domain finite volume method is introduced to iteratively calculate the target electromagnetic scattering process. The scattered field form, the time-domain Maxwell equations of real variables are expressed in rectangular coordinates as follows:

[0075]

[0076]

[0077]

[0078] in, is the conservation variable of the scattered electromagnetic field, It's virtual time. is the normalized physical time, , , is the electromagnetic flux in rectangular coordinates , , Quantity, is the real scattered magnetic induction intensity vector, is the real-valued electric displacement vector of the scattered field, is the electric field intensity vector of the scattered field, Scattering field magnetic field intensity vector, including subscripts , , The scalars are the rectangular coordinates of the corresponding vectors , , Quantity.

[0079] For objects with complex shapes, the computational space body-fitting multi-block structure grid is used, so there is a coordinate transformation:

[0080]

[0081] in Represents a curvilinear coordinate system Three directions, respectively One of them. The conservation form of Maxwell's equations in the curvilinear coordinate system for numerical simulation is obtained:

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] Where V is the Jacobian matrix of the coordinate transformation, and the superscript variables represent the values ​​in the curvilinear coordinate system, which are obtained by the coordinate transformation. is the conserved variable of the curvilinear coordinate system, , , That is when Take the direction of the curve coordinate system respectively The electromagnetic flux in the curvilinear coordinate system at one time.

[0090] In order to get rid of the drawback of large computational complexity caused by the limitation of the global minimum physical time step of the traditional explicit time-domain finite volume, a fully implicit dual-time-step calculation method is invented to improve the time advancement efficiency of the target time-varying electromagnetic field. The dual time step is used to ensure the time accuracy while selecting the physical time step according to the physical characteristics. The implicit spatial flux residual is combined to obtain a stable and efficient calculation process. In actual implementation, the following steps are specifically included:

[0091] Step 1: Based on the physical background of the electromagnetic problem being simulated, simulation modeling is performed in combination with boundary condition information.

[0092] Step 2: Use quadrilateral (two-dimensional) or hexahedral structure (three-dimensional) to mesh the simulation model. The mesh is encrypted on the wall and geometric singularity. The mesh gradually becomes sparse away from the scattering wall; numerically calculate the mesh of the corresponding area, output the mesh data file, set and output the boundary condition file. The mesh density ensures 15-20 grid points per wavelength, the wall density is >300 points / per wavelength, and the geometric singularity is encrypted to 50-100 grid points / per wavelength. The two-dimensional grid is advanced by 1 layer according to the right-hand rule in the plane perpendicular to the plane, and is calculated uniformly as a special case of the three-dimensional problem. The mesh data file includes the number of structural grid blocks and the dimensions of each block in the three curvilinear coordinate system.

[0093] Step 3: Preprocessing part, input the target calculation electromagnetic parameters and numerical calculation control parameters. The virtual time sub-iteration is implicit because the CFL number is not subject to the above explicit stability requirements. The physical time step is pre-set. For two-dimensional problems, the physical time step of the incident electromagnetic wave period is dimensionless. The calculation accuracy is good enough, and the three-dimensional problem is selected At the same time, set the sub-iteration convergence standard criterion value (for example, the absolute value of the second-order moment of the magnetic field amplitude difference of the full grid space sub-iteration time step decreases by two orders of magnitude, that is, the ratio of the second-order moment after the first sub-iteration is <0.01, which is considered convergence), and set the maximum number of sub-iteration steps (for example: isubmax=30).

[0094] Step 4: Input the grid data and boundary condition information file to initialize the calculation of the spatial electromagnetic field. The grid data dimension meets the semi-coarsening requirement of the grid sequence, that is, the three spatial direction dimensions of the spatial grid block are , is an integer.

[0095] Step 5: The time-varying electromagnetic field of the dielectric Maxwell equations is iteratively solved using an implicit dual time-stepping method based on the time iterative advancement of the conserved electromagnetic field and the spatial flux residual.

[0096] Step 5-1: The outer physical time step cycle ends when the calculation converges.

[0097] Step 5-2: Inner virtual time step sub-iteration loop, until the sub-iteration converges or the maximum sub-iteration step number condition is met. The time accuracy of the dual-time method unsteady calculation is also restricted by the number of sub-iteration steps in each physical time step. The time accuracy can be guaranteed only when the number of iteration steps is large and the convergence control is strict. If the real time step is small, the sub-iteration can be obtained less. In numerical calculation, in order to prevent the field from changing violently and the sub-iteration CFL number from being too large, the residual is likely to fail to decrease to convergence and fall into an infinite loop, and the maximum number of sub-iteration steps is given. On the other hand, the sub-iteration convergence is judged and controlled, and the iteration is terminated as soon as possible under the premise of ensuring a certain time accuracy. The sub-iteration convergence criterion uses the absolute value of the second-order moment of the sub-iteration time step amplitude difference of the full grid space to decrease by two orders of magnitude.

[0098] In each virtual time sub-iteration process, according to the grid sequence loop mode, the spatial flux and residual calculations are performed on each structural grid block and each grid cell of the hierarchical grid in turn, implicit iterative calculations are performed, the flux residuals, conservation variables, forcing functions, and electromagnetic parameters of adjacent grid layers are interpolated and transferred, and the conserved electromagnetic field values ​​of the next virtual time sub-iteration step are updated.

[0099] The specific algorithms of step 5-1 and step 5-2 are introduced below: MUSCL (Monotonic Upstream Schemes for Conservation Laws, MUSCL) interpolation is used.

[0100] Add virtual time derivative , the time-domain Maxwell equations to be solved in the form of scattered field are modified to:

[0101]

[0102] Obviously, when When converged, the system of equations is restored to the original system of equations, and the virtual time The sub-iteration is represented as:

[0103]

[0104]

[0105] in, yes The value of the electromagnetic field conservation variable after virtual time iteration, yes The approximate value of , the superscript * represents the value of the conserved variable corresponding to the virtual time sub-iteration, is the flux residual, is the flux residual Added the residual after the physical time derivative term and source term; is the number of physical time steps; is the physical time step, It is The electromagnetic conservation variables at the physical time step, It is Electromagnetic conservation variables at the physical time step; for The corresponding intermediate state flux residual; the physical time derivative of the backward second-order difference is the second-order time accuracy; the constant sub-iteration part adopts the implicit algorithm:

[0106]

[0107] in, is the structural grid curve coordinate system direction 1, is the structural grid curve coordinate system direction 2, is the structural grid curve coordinate system direction 3; They correspond to the curvilinear coordinate system Directional electromagnetic flux; is an implicit control parameter, The fully implicit form of the other parameters corresponds to the explicit and implicit mixed format; subscript is the grid cell number, It is Grid unit Electromagnetic conservation variables for virtual time steps, It is Grid unit Electromagnetic conservation variables for virtual time steps, It is The electromagnetic conservation variables for the physical time step, It is The electromagnetic conservation variables for the physical time step, It is The electromagnetic conservation variables for the physical time step, It is Grid unit The spatial flux residual at the virtual time step, It is Grid unit The spatial flux residual at the virtual time step, It is a virtual time step controlled by stability, calculated by the CFL number and the local grid unit geometric scale and eigenvalue, which is significantly different from the explicit method. Different grid units in the steady-state calculation have different local virtual time sub-iteration steps, thereby accelerating the convergence of the electromagnetic field of the unit.

[0108] The implicit time-marching iteration equations in each level of the structured grid sequence are:

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] in, is the virtual time step; , , Corresponding to the curvilinear coordinate system Directional difference operators; , , Corresponding to the curvilinear coordinate system Jacobian coefficient matrix of directional electromagnetic flux; is the difference of conservation variables of scattering fields in adjacent physical times; It is Physical time step spatial flux residual, is the total spatial flux residual of the previous physical time step plus the double time step correction.

[0116] In each level of the grid in the structured grid sequence, the spatial flux is calculated as follows:

[0117] The Steger-Warming splitting method is used to calculate the interface flux of the grid cells.

[0118]

[0119]

[0120]

[0121] Subscript Take the curvilinear coordinate system One of the directions, corresponding That is the corresponding The direction of the electromagnetic flux, Represents a curvilinear coordinate system The electromagnetic flux obtained by splitting the positive eigenvalue in the Steger-Warming splitting in the corresponding direction; Represents a curvilinear coordinate system The electromagnetic flux obtained by splitting the negative eigenvalue in the Steger-Warming splitting in the corresponding direction; is the similarity matrix, are diagonal matrices consisting of positive and negative eigenvalues, respectively. They represent the left and right state variables at the interface respectively, and they can use the MUSCL format to achieve the highest third-order accuracy.

[0122]

[0123] in, is a limiter, subscript is the grid cell number, Corresponding unit interface, is the control parameter in third-order precision format, and are the post-difference and pre-difference operators respectively; Represented in grid cells The left state electromagnetic field conservation variable at the interface, Represented in grid cells Conservation variables of the right-state electromagnetic field at the interface; It is The conservation variables of the electromagnetic field scattered by each grid cell are: It is The grid cells scatter the electromagnetic field conservation variables.

[0124] In each level of the structured grid sequence, the spatial flux implicit iteration and the splitting and forward iteration of the Jacobian coefficient matrix are used to solve the problem. The Jacobian coefficient Steger-Warming splitting generated by the flux partial derivative conservation variable is obtained.

[0125]

[0126] in is the coefficient matrix after splitting, is the spatial flux residual calculated at the previous iterative time step, is the implicit sub-iteration electromagnetic field difference.

[0127] Will Expressed as LDU approximation factorization

[0128] .

[0129] Among them, the subscript is the grid cell number, is the maximum eigenvalue splitting parameter of the Jacobi coefficient matrix, is the largest eigenvalue of the Jacobian coefficient matrix. is the unit diagonal matrix, is a diagonal matrix, is an upper triangular matrix, is a lower triangular matrix, is the difference of the electromagnetic conservation variables corresponding to the upper triangular matrix, is the difference of electromagnetic conservation variables corresponding to the lower triangular matrix; refer to The difference of electromagnetic conservation variables in adjacent iteration time steps of the grid cells; refer to The difference of electromagnetic conservation variables in adjacent iteration time steps of the grid cells; refer to The difference of electromagnetic conservation variables in adjacent iteration time steps of the grid cells; refer to The difference of electromagnetic conservation variables in adjacent iteration time steps of the grid cells; refer to The difference of electromagnetic conservation variables in adjacent iteration time steps of the grid cells; refer to The difference of electromagnetic conservation variables in adjacent iteration time steps of the grid cells; It refers to adjacent The coefficient matrix after the grid cell splitting; means The coefficient matrix after the adjacent grid cells are split; It refers to adjacent The coefficient matrix after the grid cell splitting; It refers to adjacent The coefficient matrix after the grid cell splitting; means The coefficient matrix after the adjacent grid cells are split; means The coefficient matrix after the adjacent grid cells are split;

[0130] Finally, the electromagnetic field difference calculated by forward and backward iteration is obtained :

[0131]

[0132]

[0133]

[0134] in, is a diagonal matrix The inverse matrix of , According to , The calculated upper triangular matrix and lower triangular matrix;

[0135] Forward loop:

[0136] Backward loop:

[0137] in, It is the intermediate transition variable of the difference of electromagnetic conservation variables.

[0138] During the structured grid sequence cycle (V cycle), the previously set grid sequence parameters are applied, including the maximum multiplicity of the multigrid (such as Figure 3a~Figure 3d As shown, generally up to 4 is good), number of iterations per grid, grid sequence loop method (such as Figure 2a~Figure 2b As shown, V-shaped or complex W-shaped). Adjacent level grid calculation steps:

[0139] (I) Iteratively solve the discrete equations on the densest grid to obtain the electromagnetic field quantities , electromagnetic field increment and residuals, store these quantities and pass the electromagnetic field quantities and residuals to the coarse grid through the "limit operator".

[0140]

[0141]

[0142]

[0143] Subscript Represents the geometric scale of the grid at this level (dense grid), subscript Represents the geometric scale of the grid at this level (sparse grid, relative to the previous subscript dense grid, each dimension of the grid is halved), subscript For the summation variable, take 4 for two-dimensional and 8 for three-dimensional. yes The upper triangular matrix of the level grid, yes Level grid diagonal matrix The inverse matrix of yes The triangular matrix of the lower level grid, is the virtual time step, yes Level grid spatial flux residual. yes The initial value of the electromagnetic field on the grid level, yes Level Grid to Volume weighted interpolation operator for level grids, yes The volume of the grid cells participating in the summation on the level grid, is the residual error transferred from the densest grid, yes Level grid spatial flux residual, yes The residuals involved in the summation on the level grid.

[0144] (ii) Switch to the next dense grid layer iteration. In the first step of the iteration, find the forcing function , which means the difference between the initial field and the transmitted residual on the sub-dense grid obtained by restriction:

[0145]

[0146] In the formula is the residual error transferred from the densest grid, The residuals calculated by the explicit scheme are calculated for the first iteration of the coarse grid. In this iteration, Will remain unchanged. If W loop is used, in the downward calculation, The previous value will be used. The actual residual for the iteration on the coarse grid is the residual computed by the scheme plus the forcing term.

[0147]

[0148] yes Level Grid The actual residual of the second sub-iteration, yes The residual obtained by calculating the spatial format flux on the coarse grid, the electromagnetic field variables after the coarse grid iteration are recorded as , repeat (a).

[0149] (iii) Switch to a more sparse grid calculation, same as step (ii), repeat (i) to (iii) until the sparsest grid is reached.

[0150] (iv) After the iterative calculation of the sparsest grid, the correction amount is interpolated back to the upper grid in sequence until the densest grid. In order to avoid uploading the high-frequency error component during the interpolation process, "post-iteration" can be performed on the current grid layer. At this time, the iteration still needs to add a "forcing term".

[0151]

[0152]

[0153] In the formula yes The electromagnetic field quantity on the grid level, It is an interpolation operator that transfers the correction amount from the lower grid to the upper grid (sparse grid to dense grid). yes Electromagnetic field increment on the grid , yes After the first iteration on the level grid, the electromagnetic field quantities are, yes Initial values ​​of electromagnetic field quantities at the grid level. A "quasi-trilinear" interpolation method is adopted. Specifically, the correction amount is first interpolated from the grid center to the node through volume weighted interpolation, and then the correction amount is linearly interpolated to the grid center of the dense grid. This interpolation can decouple the three directions and proceed in each direction. It is simple to implement and easy to program.

[0154] The above is the iterative process of using structured grids and grid sequences to accelerate the FVTD algorithm to calculate the Maxwell equations to control the time-varying electromagnetic field.

[0155] Step 6: Convergence judgment, post-processing process, output of time and space distribution of electromagnetic field, output of surface induced current and radar cross section spatial distribution data, etc.

[0156] like Figure 2a~Figure 2bAs shown in the figure, the two main grid sequence calculation cycle modes, the W-shaped cycle and the V-shaped cycle, both start from the densest grid to quickly filter out high-frequency errors, and then calculate the geometric coarse and fine grids generated by semi-coarsening to filter out smooth high-frequency errors.

[0157] like Figure 3a~Figure 3d As shown in the figure, the scatterer (metal ball) surface and space profile are distributed in a 4-fold structured grid sequence. The grid data dimension meets the semi-coarsening requirement of the grid sequence, that is, the three spatial direction dimensions of the spatial grid block are , is an integer. In this example, the grid dimension is 57X81X41 to meet this condition. The far-field boundary is outside 3 wavelengths, with a total of 57 grid points in the normal direction. The wall surface is encrypted to 500 grid points per wavelength, and then gradually becomes sparse to 4 grid points per wavelength along the radiation direction. The other two directions are evenly distributed, with an average of about 40 grid points per wavelength.

[0158] like Figure 4a~Figure 4b The following is a comparison of the convergence characteristics of the four-grid sequence for electromagnetic scattering calculation of a metal sphere (ka=2). Figure 3a~Figure 3d The grid sequence shown is calculated under the following conditions: maximum grid multiplicity = 4, CFL number = 1000, physical time step dt = 0.04, maximum sub-iteration step number = 30, Figure 4a The figure shows the comparison of the sub-iteration convergence curves in the last three physical time steps before the entire unsteady calculation converges. Each physical time step is a steady sub-iteration of the virtual time step described above. If the sub-iteration convergence standard is met, the sub-iteration loop will be jumped out even if it is less than the maximum number of sub-iteration steps. The calculation shows that the use of 4-grid sequence iteration, whether V-shaped or W-shaped cycle, converges faster than single-grid calculation. Figure 4b For the last physical time step process, the sub-iteration convergence process requires 22 iterations for single grid iteration, 16 iterations for V-shaped grid sequence, and 14 iterations for W-shaped grid sequence. It can be seen that the V-shaped grid sequence in this example is 27.3% faster than the single grid in convergence, and the efficiency is improved by 37.5%; the W-shaped grid sequence is 36.4% faster than the single grid in convergence, and the efficiency is improved by 57%.

[0159] Figure 5 It is the electromagnetic scattering surface induced current of the metal ball (ka=2), which is one of the outputs of the present invention.

[0160] Figure 6 This is a comparison of radar cross section distributions calculated by three iterations of a metal sphere (ka=2), which is one of the outputs of the present invention. It can be seen that compared with the precise analytical MIE series solution, the three are almost completely consistent, indicating that both V-shaped and W-shaped grid sequence iterations can ensure the calculation accuracy of the entire radar cross section output, and the reliability is guaranteed.

[0161] These numerical examples show that the structured grid time-varying electromagnetic field grid sequence accelerated FVTD algorithm corresponding to the invention, combined with the physical / virtual dual time step and fully implicit forward and backward iterative implicit inversion algorithm, can not only relax the time step restrictions while ensuring the numerical accuracy of the format and accurately obtaining the time and spatial distribution of the target electromagnetic scattering field, but also improve the time advancement efficiency and save computing costs.

[0162] The units involved in the embodiments of the present invention may be implemented by software or hardware, and the units described may also be arranged in a processor. The names of these units do not, in some cases, limit the units themselves.

[0163] According to one aspect of an embodiment of the present invention, a computer program product or a computer program is provided, the computer program product or the computer program includes a computer instruction, and the computer instruction is stored in a computer-readable storage medium. A processor of a computer device reads the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes the method provided in the above various optional implementations.

[0164] As another aspect, an embodiment of the present invention further provides a computer-readable medium, which may be included in the electronic device described in the above embodiment; or may exist independently without being assembled into the electronic device. The above computer-readable medium carries one or more programs, and when the above one or more programs are executed by an electronic device, the electronic device implements the method described in the above embodiment.

Claims

1. A grid sequence iterative convergence acceleration method, characterized in that: The following steps are involved: The time-varying electromagnetic field of the Maxwell equations is iteratively solved by an implicit dual-time-step method based on the time iterative advancement of the conserved electromagnetic field and the spatial flux residual. The outer layer of the simulation model is a physical time step cycle until the calculation converges. The inner layer of the simulation model is a virtual time step sub-iteration cycle until the sub-iteration converges. In each virtual time sub-iteration process, the spatial flux and residual calculations are performed on each structural grid block and each grid unit of the grid at that level in turn according to the grid sequence cycle mode. The implicit iterative calculations, the flux residuals of adjacent grid layers, the conserved variables, the forcing functions, and the electromagnetic parameters are interpolated and transferred, and the conserved electromagnetic field values ​​of the next virtual time sub-iteration step are updated. The outer layer of the simulation model is a physical time step loop until the calculation converges; the inner layer of the simulation model is a virtual time step sub-iteration loop until the sub-iteration converges, which specifically includes the following sub-steps: The physical time step cycle and virtual time step iteration cycle process is: Add virtual time derivative , the passive time-domain Maxwell equations of real variables are modified to be: ；(1) ；(2) in, is the time domain real number scattering electromagnetic field conservation variable, It's virtual time. is the normalized physical time, , , is the electromagnetic flux in rectangular coordinates , , Quantity, is the real scattered magnetic induction intensity vector, is the real-valued electric displacement vector of the scattered field; Virtual Iteration , the equations are reduced to the original equations, and the constant virtual The subiteration table is: ；(3) in, yes The value of the electromagnetic field conservation variable after virtual time iteration, yes The superscript * represents the value of the conserved variable corresponding to the virtual time sub-iteration. is the flux residual, is the number of physical time steps; is the physical time step, It is The electromagnetic conservation variables at the physical time step, It is Electromagnetic conservation variables at the physical time step; for The corresponding intermediate state flux residual; the physical time derivative uses the backward second-order difference; The constant subiteration (3) uses a fully implicit algorithm and performs Virtual time step flux linearization expansion: ；(4) ； ； in, is the virtual time step; , , Corresponding to the curvilinear coordinate system Directional difference operator; , , Corresponding to the curvilinear coordinate system Directional electromagnetic flux Jacobian coefficient matrix; is the difference of conservation variables of scattering fields in adjacent physical times; It is Physical time step spatial flux residual, It is the total spatial flux residual of the previous physical time step plus the double time step correction; It is Grid unit Electromagnetic conservation variables for virtual time steps; It is Grid unit Electromagnetic conservation variables for virtual time steps; , , They are the corresponding curvilinear coordinate systems Directional electromagnetic flux; Among them, the spatial flux in each level of the grid in the structured grid sequence is calculated as follows: First, the Steger-Warming splitting method is used to calculate the interface flux of the grid cells; Finally, the forward and backward iterative calculation of the electromagnetic field difference is achieved based on LUSGS in each level of the structural grid sequence. : During the structural grid sequence cycle, the adjacent level grid calculation process: Step (a) is to iteratively solve the discrete equations in the densest grid to obtain the electromagnetic field quantity , electromagnetic field increment and residuals, store these quantities and pass the electromagnetic field quantities and residuals to the coarse grid through the "restriction operator"; ； (6) ；(7) ；(8) In the formula, the subscript Represents the geometric scale of the grid at this level, the subscript Represents the geometric scale of the grid at this level, the subscript For the summation variable, 4 is used for two-dimensional and 8 for three-dimensional; yes The upper triangular matrix of the level grid, yes Level grid diagonal matrix The inverse matrix of yes The triangular matrix of the lower level grid, is the virtual time step, yes Level grid spatial flux residual; yes The initial value of the electromagnetic field on the grid level, yes Level Grid to Volume weighted interpolation operator for level grids, yes The volume of the grid cells participating in the summation on the level grid, is the residual error transferred from the densest grid, yes Level grid spatial flux residual, yes The residuals involved in the summation on the level grid, yes Calculation of spatial flux residuals on grids at the upper level Level grid flux residual operator; Step (2), switch to the next dense grid layer iteration, in the first step of the iteration, find the forcing function , which means the difference between the initial field and the transmitted residual on the sub-dense grid obtained by restriction: ；(9) In the formula, is the residual error transferred from the densest grid, The residuals calculated by the explicit scheme are calculated for the first iteration of the coarse grid; in this iteration, will remain unchanged; if W loop is used, then in the downward calculation, The previous value will be used; the actual residual for the iteration on the coarse grid is the residual calculated by the format plus the forcing term ；(10) yes Level Grid The actual residual of the second sub-iteration, yes The residual obtained by calculating the spatial format flux on the coarse grid, the electromagnetic field variables after the coarse grid iteration are recorded as , repeat step (a); Step (3), switch to a more sparse grid calculation, same as step (2), repeat steps (1) to (3) until the sparsest grid is reached; Step (iv), after the iterative calculation of the sparsest grid, the correction amount is interpolated back to the upper grid in sequence until the densest grid; the interpolation process is then "post-iterated" in the current grid, and the "forcing term" is still added to the iteration; ；(11) ；(12) In the formula, yes The electromagnetic field quantity on the grid level, is the interpolation operator that transfers the correction from the lower grid to the upper grid, yes Electromagnetic field increment on the grid , yes After the first iteration on the level grid, the electromagnetic field quantities are, yes Initial values ​​of electromagnetic field quantities of level grid; The "quasi-trilinear" interpolation method is adopted. The specific method is to first interpolate the correction amount from the grid center to the node through volume weighted interpolation, and then interpolate the correction amount to the grid center of the dense grid through linear interpolation.

2. The grid sequence iterative convergence acceleration method according to claim 1, characterized in that: Before the iterative solution of the Maxwell equations time-varying electromagnetic field in the implicit dual time-step method based on the conserved electromagnetic field time iterative advancement and the spatial flux residual, the method further includes the following steps: The grid density ensures 15-20 grid points per wavelength, the wall density is >300 points / local wavelength, and the density is encrypted to 50-100 grid points / local wavelength at geometric singularities. For two-dimensional grids, one layer is advanced according to the right-hand rule in the plane perpendicular to the two-dimensional grid, and it is calculated uniformly as a special case of three-dimensional problems. The grid data file includes the number of structural grid blocks and the dimensions of each block in the three curvilinear coordinate system.

3. The grid sequence iterative convergence acceleration method according to claim 1, characterized in that: Before the iterative solution of the Maxwell equations time-varying electromagnetic field in the implicit dual time-step method based on the conserved electromagnetic field time iterative advancement and the spatial flux residual, the method further includes the following steps: The physical time step is set in advance. For two-dimensional problems, the physical time step of 0.01, which is the dimensionless physical time step of the incident electromagnetic wave period, is used to ensure sufficient calculation accuracy. For three-dimensional problems, the order of magnitude is 0.

001. At the same time, the sub-iteration convergence standard criterion value is set as the absolute value of the second-order moment of the difference in magnetic field amplitudes in adjacent sub-iteration time steps in the full grid space decreases by two orders of magnitude, that is, the ratio of the second-order moment after the first sub-iteration is <0.01, which is considered convergence. The maximum number of sub-iteration steps is set to 30.

4. A computer device, characterized in that: The computer device comprises a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is loaded by the processor, the method according to any one of claims 1 to 3 is executed.

5. A readable storage medium, characterized in that: A computer program is stored in a readable storage medium, and when the computer program is loaded by a processor, the method according to any one of claims 1 to 3 is executed.

6. A grid sequence iterative convergence acceleration system, characterized in that: A computer device comprising the method of claim 4.

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