Electromagnetic field absorption boundary condition calculation method and device

Abstract

The invention discloses an electromagnetic field absorption boundary condition calculation method and device, and belongs to the technical field of electromagnetic field calculation. The method comprises the following steps: obtaining a Maxwell equation set of an efficient absorption boundary condition by increasing error term transformation according to a Maxwell equation set of a complete matching layer absorption boundary condition; based on the Maxwell equation set of the efficient absorption boundary condition, a circle of absorption boundary layer is arranged at the boundary of a preset electromagnetic field calculation area; and after the electromagnetic wave enters the absorption boundary layer, calculating the electromagnetic field component of the electromagnetic wave in the absorption boundary layer according to the Maxwell equation set of the efficient absorption boundary condition. The method has the advantages of being small in reflection error, fast in energy absorption, fast in calculation speed and small in occupied memory.

Description

Technical Field

[0001] The invention relates to a method and a device for calculating electromagnetic field absorption boundary conditions, belonging to the technical field of electromagnetic field calculation. Background Art

[0002] In the process of electromagnetic field calculation, since the calculation area of ​​simulation is always limited, the infinite calculation space must be truncated to perform numerical simulation. If the absorbing boundary conditions (ABC) are not added to the boundary of the calculation area, the electromagnetic waves will be emitted when they hit the boundary, resulting in a large error in the time domain waveform of the monitoring point. Good absorbing boundary conditions can eliminate the non-physical reflection of electromagnetic waves at the truncation point and help achieve a better electromagnetic field calculation environment.

[0003] The existing Mur absorbing boundary condition has the advantages of saving memory and fast calculation, but it is not completely matched. In many cases, it cannot meet the requirements of electromagnetic field calculation accuracy, and the reflection error is large. Although the traditional perfectly matched layer (PML) absorbing boundary condition can reduce the reflection error, it needs to solve a large sparse matrix during the calculation process, resulting in a large amount of memory usage and slow calculation speed. It puts forward certain conditions for electromagnetic field calculation equipment and calculation requirements, which limits the application of electromagnetic field calculation. Summary of the invention

[0004] The purpose of the present invention is to provide a method and device for calculating electromagnetic field absorption boundary conditions, to improve the existing perfectly matched layer absorption boundary conditions, and to propose a new absorption boundary condition, which is completely matched with the medium inside the calculation area. Within the absorption boundary condition, the electric field and the magnetic field are calculated according to the method set by the present invention, which has the advantages of small reflection error, fast energy absorption, fast calculation speed, and small memory occupation.

[0005] In order to achieve the above purpose / solve the above technical problems, the present invention is implemented by adopting the following technical solutions:

[0006] In a first aspect, the present invention provides a method for calculating electromagnetic field absorption boundary conditions, comprising the following steps:

[0007] According to the Maxwell equations of perfectly matched layer absorbing boundary conditions, the Maxwell equations of efficient absorbing boundary conditions are obtained by adding error terms.

[0008] Based on the Maxwell equations with efficient absorbing boundary conditions, a circle of absorbing boundary layer is set at the boundary of the preset electromagnetic field calculation area;

[0009] When the electromagnetic wave enters the absorbing boundary layer, the Maxwell equations of the efficient absorbing boundary conditions are used to calculate the changes in the electromagnetic field components of the electromagnetic wave under the absorption of the absorbing boundary layer.

[0010] In combination with the first aspect, further, the Maxwell equations of the perfectly matched layer absorbing boundary condition are:

[0011]

[0012] Among them, ε 0 is the dielectric constant, μ 0 is the vacuum permeability, E x 、E y is the component of the electric field along the x and y directions, H z is the component of the magnetic field along the z direction, H zx , H zy H z The subcomponents satisfy H z =H zx +H zy , σ x , σ y are the electrical losses in the x and y directions, ρ x , y are the magnetic losses in the x and y directions respectively. x, y, z represent the three directions in the three-dimensional coordinate system respectively, and t is the time variable.

[0013] In combination with the first aspect, further, the Maxwell equations of the efficient absorption boundary condition are:

[0014]

[0015] in, Respectively represent the electrical loss σ x , σ y The intermediate process quantity calculated, They are respectively expressed according to the magnetic loss ρ x , y The intermediate process quantity of the calculation, s is the time factor of Laguerre transformation, r is the spatial variable, ε 0 is the dielectric constant, μ 0 is the vacuum permeability, They are the time domain electric field components E x (r,t),E y The k-th Laguerre coefficient of (r,t), They are the time domain electric field components E x (r,t),E y The q-order Laguerre coefficient of (r,t), is the Laguerre domain electric field component The intermediate process variables, is the Laguerre domain electric field component The intermediate process quantity, is the time domain magnetic field component H z The q-order Laguerre coefficient of (r,t), They represent the time domain magnetic field subcomponents H zx (r,t),H zy The q-order Laguerre coefficient of (r,t), They represent the time domain magnetic field subcomponents H zx (r,t),H zy (r, t) is the k-order Laguerre coefficient, where x, y, and z represent the three directions in the three-dimensional coordinate system.

[0016] In combination with the first aspect, further, the thickness, electric loss and magnetic loss of the absorbing boundary layer are set according to the electromagnetic field absorption rate requirements; the thickness d = nΔ, where n is the number of grids in the absorbing boundary layer and Δ is the grid size; the absorbing boundary layer is set to be anisotropic, where the electric loss and magnetic loss along the x direction are set to σ respectively x and ρ x , the electric loss and magnetic loss along the y direction are set to σ y and ρ y .

[0017] In combination with the first aspect, further, when the electromagnetic wave enters the absorbing boundary layer, according to the Maxwell equations of the efficient absorbing boundary condition, starting from the order q=0, the electromagnetic field components of each order of the electromagnetic wave in the absorbing boundary layer are calculated in a step-by-step manner until the highest order q max ,q max ≥2BT f +1, where B is the frequency domain bandwidth of the signal, T f is the duration of the signal in the time domain.

[0018] Combined with the first aspect, further, the Maxwell equations of the efficient absorbing boundary conditions are discretized using the central difference method to obtain the discretized calculation formula of electromagnetic propagation in the absorbing boundary layer;

[0019] Based on the discretized calculation formula of electromagnetic propagation in the absorbing boundary layer, the electromagnetic field components of the electromagnetic wave in the absorbing boundary layer are efficiently solved using the pursuit method, and the Laguerre domain expressions of the electric field and magnetic field components of the electromagnetic wave in the absorbing boundary layer are obtained, and then the changes of the electromagnetic field components of the electromagnetic wave under the absorption of the absorbing boundary layer are obtained.

[0020] In combination with the first aspect, the inverse Laguerre transform is further used to obtain the time domain waveform of the electromagnetic wave in the absorbing boundary layer, and the expression is as follows:

[0021]

[0022] Among them, E x (r, t) represents the time domain electric field component in the x direction at time t and r space, E y (r, t) represents the time domain electric field component in the y direction at time t and r space, H z (r, t) represents the time domain magnetic field component in the z direction at time t and r space, H zx (r, t) represents the time domain magnetic field component in the zx direction at time t and r space, H zy (r,t)t time, the time domain magnetic field component in the zy direction in r space, is the p-order Laguerre basis function, They are the time domain electric field components E x (r,t),E y The p-order Laguerre coefficient of (r,t), They are the time domain magnetic field components H z (r,t),H zx (r,t),H zy p-th order Laguerre coefficient of (r,t).

[0023] In a second aspect, the present invention provides an electromagnetic field absorption boundary condition calculation device, comprising:

[0024] The absorbing boundary layer setting module is used to obtain the Maxwell equations of efficient absorbing boundary conditions by adding error terms according to the Maxwell equations of the perfectly matched layer absorbing boundary conditions; based on the Maxwell equations of efficient absorbing boundary conditions, a circle of absorbing boundary layer is set at the boundary of the preset electromagnetic field calculation area;

[0025] The absorbing boundary layer calculation module is used to calculate the change of the electromagnetic field component of the electromagnetic wave under the absorption of the absorbing boundary layer according to the Maxwell equations of the efficient absorbing boundary conditions after the electromagnetic wave enters the absorbing boundary layer.

[0026] In combination with the second aspect, further, the Maxwell equations of the efficient absorption boundary condition are:

[0027]

[0028]

[0029] in, Respectively represent the electrical loss σ x , σ y The intermediate process quantity calculated, They are respectively expressed according to the magnetic loss ρ x , y The intermediate process quantity of the calculation, s is the time factor of Laguerre transformation, r is the spatial variable, ε 0 is the dielectric constant, μ 0 is the vacuum permeability, They are the time domain electric field components E x (r,t),E y The k-th Laguerre coefficient of (r,t), They are the time domain electric field components E x (r,t),E y The q-order Laguerre coefficient of (r,t), is the Laguerre domain electric field component The intermediate process variables, is the Laguerre domain electric field component The intermediate process quantity, is the time domain magnetic field component H z The q-order Laguerre coefficient of (r,t), They represent the time domain magnetic field subcomponents H zx (r,t),H zy The q-order Laguerre coefficient of (r,t), They represent the time domain magnetic field subcomponents H zx (r,t),H zy (r, t) is the k-order Laguerre coefficient, where x, y, and z represent the three directions in the three-dimensional coordinate system.

[0030] In a third aspect, the present invention provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the steps of the method for calculating electromagnetic field absorption boundary conditions provided in the first aspect.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] The present invention proposes a method and device for calculating electromagnetic field absorption boundary conditions, improves the existing perfectly matched layer absorption boundary conditions, and proposes a new high-efficiency absorption boundary condition, which is completely matched with the internal medium of the calculation area. Based on the high-efficiency absorption boundary condition, an absorption boundary layer is set in the electromagnetic wave calculation area. After the electromagnetic wave enters the absorption boundary layer, it is restricted by the high-efficiency absorption boundary condition, and the energy is gradually absorbed, thereby achieving the effect of truncating the infinite calculation space of the electromagnetic wave into a limited one.

[0033] The invention obtains the Maxwell equations of efficient absorption boundary conditions through a special derivation process, and its wave impedance can be completely matched with the incident end medium, and the reflection error is small. With the appropriate numerical setting of electric loss and magnetic loss, the energy loss of electromagnetic waves in the absorption boundary layer can be faster. Compared with the existing absorption boundary conditions, the calculation method of the invention can achieve the advantages of smaller reflection error, faster energy absorption, faster calculation speed, and less memory usage. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 FIG. 1 is a schematic diagram of the steps of a method for calculating electromagnetic field absorption boundary conditions provided by an embodiment of the present invention;

[0035] Figure 2 Shown is a schematic diagram of an absorbing boundary layer in an embodiment of the present invention;

[0036] Figure 3 The figure shows a schematic diagram of the positional relationship of each electromagnetic field component in the central difference format in an embodiment of the present invention;

[0037] Figure 4 The figure shows a schematic diagram of a two-dimensional dielectric square column scattering structure in an embodiment of the present invention;

[0038] Figure 5 FIG. 1 is a schematic diagram of relative reflection error at an observation point calculated using different absorbing boundary conditions in an embodiment of the present invention;

[0039] Figure 6 Shown is a schematic structural diagram of an electromagnetic field absorption boundary condition calculation device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. The embodiments of the present invention and the technical features in the embodiments may be combined with each other unless there is a conflict.

[0041] Example 1

[0042] This embodiment introduces an efficient method for calculating electromagnetic field absorption boundary conditions. Figure 1 As shown, the specific steps include:

[0043] Step 1: Based on the existing Maxwell equations for perfectly matched layer absorbing boundary conditions, a new Maxwell equations for efficient absorbing boundary conditions is obtained by adding error terms and solving them step by step.

[0044] In a lossless, homogeneous, isotropic medium, the existing Maxwell equations for perfectly matched layer absorbing boundary conditions are:

[0045]

[0046] Among them, ε 0 is the dielectric constant, μ 0 is the vacuum permeability, E x 、E y is the component of the electric field along the x and y directions, H z is the component of the magnetic field along the z direction, H zx , H zy Yes H z subcomponents that satisfy H z =H zx +H zy , σ x , σ y are the electrical losses in the x and y directions, ρ x , y are the magnetic losses in the x and y directions respectively. x, y, z represent the three directions in the three-dimensional coordinate system respectively, and t is the time variable.

[0047] The existing Maxwell equations of perfectly matched layer absorbing boundary conditions are expanded into the Laguerre domain, and the expanded Maxwell equations are transformed using pre-constructed intermediate variables to obtain the Maxwell equations in matrix form.

[0048] In the embodiment of the present invention, the pre-constructed intermediate variables are:

[0049]

[0050]

[0051] in, is a vector consisting of unknown electric field components of order q, and the superscript T represents the transposition operation. is a vector consisting of unknown electric field components of order q, D E , D H is a custom matrix consisting of partial differential symbols, is a vector consisting of known electric and magnetic field components below (q-1) order, They are the time domain electric field components E x (r,t),E y The q-order Laguerre coefficient of (r,t), is the time domain magnetic field component H z The q-order Laguerre coefficient of (r,t), Respectively represent the electrical loss σ x , σ y The intermediate process quantity calculated, They are respectively expressed according to the magnetic loss ρ x , y The intermediate process quantity calculated, s is the time factor of Laguerre transformation, r is the spatial variable, They are the time domain electric field components E x (r,t),E y The k-order Laguerre coefficient of (r, t), the time domain magnetic field component H z (r, t) can be further divided into subcomponents H zx (r,t),H zy (r,t), They represent the time domain magnetic field subcomponents H zx (r,t),H zy The k-th Laguerre coefficient of (r,t).

[0052] According to the pre-constructed intermediate variables, the expanded Maxwell equation can be written as the matrix equation Where I is the identity matrix equation.

[0053] Let D H D E =M+N, where M and N are constructed as the following two matrices:

[0054]

[0055] Then the formula Maxwell's equations can be transformed into matrix form:

[0056]

[0057] Actively add a high-order small error term to the left side of the Maxwell equation in matrix form The coefficient matrix on the left side of the Maxwell equation can be decomposed into the form of the product of two square matrices; the transformed Maxwell equation is decomposed into three steps using a step-by-step solution method, and finally a new Maxwell equation with efficient absorption boundary conditions is obtained.

[0058] In an embodiment of the present invention, the Maxwell equations for efficient absorption boundary conditions are as follows:

[0059]

[0060] in, They are the time domain magnetic field subcomponents H zx (r,t),H zy (r, t) and the time domain magnetic field component H z The q-order Laguerre coefficient of (r,t), yes The subcomponent of is the Laguerre domain electric field component The intermediate process variables, is the Laguerre domain electric field component The intermediate process quantity has no practical significance.

[0061] In the present invention, It only depends on the spatial position and has nothing to do with time.

[0062]

[0063] in, Respectively represent the corresponding intermediate process quantities The value at the field point x=i, y=j, σ x | i,j , σ y | i,j They represent the corresponding electrical losses σ x , σ y The value at the field point x=i, y=j, ρ x | i,j , y | i,j They represent the corresponding magnetic loss ρ x , y The value at the field point x=i, y=j.

[0064] Step 2: Based on the Maxwell equations of efficient absorption boundary conditions, a circle of absorption boundary layer is set at the boundary of the preset electromagnetic field calculation area. The absorption boundary layer adopts the split field technology and is similar to a virtual absorbing medium.

[0065] Absorbing boundary layer Figure 2 As shown in the figure, the parameters of the absorbing boundary layer are set as follows: thickness d = nΔ, where n is the number of grids in the absorbing boundary layer and Δ is the grid size; the absorbing boundary layer is set to be anisotropic, where the electric loss and magnetic loss along the x direction are set to σ x and ρ x, the electric loss and magnetic loss along the y direction are set to σ y and ρ y In the embodiment of the present invention, the values ​​of parameters such as the thickness of the absorbing boundary layer, the electric loss, and the magnetic loss are set according to actual needs.

[0066] Step 3: When the electromagnetic wave enters the absorbing boundary layer, the propagation process of the electromagnetic wave in the absorbing boundary layer is calculated according to the Maxwell equations of the efficient absorbing boundary conditions to obtain the change of the electromagnetic field component under the absorption of the electromagnetic wave by the absorbing boundary layer.

[0067] After the electromagnetic wave enters the absorbing boundary layer, its propagation process needs to be calculated according to formula (13) to formula (22). During the calculation, the equation is calculated step by step, starting from the order q = 0 to the highest order q max , generally take q max ≥2BT f +1, where B is the frequency domain bandwidth of the signal, T f is the duration of the signal in the time domain.

[0068] In the calculation of each order q, the first step is to use formula (13) to find the intermediate process quantity The right side of formula (13) is the accumulation of low-order field quantities, which are known at this time; the second step is to use formula (14) to calculate the electric field component The right side of formula (14) In the first step, it has been found and is a known quantity; in the third step, the electric field component is found using formula (15) Similarly, all the variables on the right side of formula (15) are known. In the fourth step, use formulas (16) and (17) to calculate the magnetic field subcomponents: Step 5: Use formula (18) to find the magnetic field component

[0069] By solving the problem step by step, it is possible to continuously calculate the electromagnetic field components of the next order. Since energy is continuously absorbed in the absorbing boundary layer, the electromagnetic field components will continue to decrease until they are 0.

[0070] The algorithm equation provided by the present invention can form two tridiagonal matrix equations after being discretized by the central difference method, and then the chasing method is used to efficiently solve them to obtain the Laguerre domain expressions of the electric field and magnetic field components of the electromagnetic wave in the absorbing boundary layer.

[0071] The central difference method is used to discretize the Maxwell equations of the efficient absorbing boundary conditions, and the discretized calculation formula of electromagnetic propagation in the absorbing boundary layer is obtained. Taking formula (13) to formula (15) as an example, the difference equation is:

[0072]

[0073] Where i and j are the grid coordinates in the x and y directions, Δy represents the grid size of the absorbing boundary layer in the y direction, represents the electric field component with direction x and order k, represents the magnetic field subcomponent with direction zx and order k, represents the electric field component with direction y and order k, are the intermediate process quantities of discretization calculation, The calculation formula is as follows:

[0074]

[0075] Among them, Δ x is the absorbing boundary layer mesh size in the x-direction.

[0076] The position relationship of each electromagnetic field component in the central difference format is as follows: Figure 3 As shown, the embodiment of the present invention takes the solution of formula (24) as an example for explanation. In formula (24), the left side of the equation is are coefficients calculated based on the parameters of the absorbing boundary layer and are known quantities. The right side of the equation is also known quantities. The unknown quantity in the equation is The positional relationship of these three unknown quantities is as follows: Figure 3 shown.

[0077] make:

[0078]

[0079] Among them, a i 、b i 、c i They are The coefficient of .

[0080] And let the right side of formula (24) equal to the process quantity β i , then formula (24) can be simplified to

[0081]

[0082] Assume that the total number of grids in the x and y directions is N respectively. x 、N y In the solution process, for each fixed j=M, the value range of i is [1,N x For different values ​​of i, a x The system of equations consists of:

[0083]

[0084] The system of equations (34) can be written in matrix form AX=B, where:

[0085]

[0086]

[0087] Since AX=B is a tridiagonal equation, the pursuit method can be used to efficiently solve it. When j=M, the q-order electric field component of each point is When j is in (1,N y ) changes, we can calculate the electric field components at all points in the absorbing boundary layer

[0088] Similarly, the q-order electromagnetic field components of all points in the absorbing boundary layer can also be obtained by discretizing the other equations in formulas (13) to (18) using the central difference method: In this way, the q-order equation is solved, and we can step to the q+1 order to solve it until q max Step.

[0089] Step 4: Use the inverse Laguerre transform to obtain the time domain waveform of the electromagnetic wave in the absorbing boundary layer for observation by the user.

[0090] After the calculation in step 3, the electromagnetic waves entering the absorbing boundary layer have been completely absorbed without reflection. In order to observe the time domain waveform of the electromagnetic waves entering the absorbing boundary layer, the inverse Laguerre transform can be used to calculate the time domain waveform of a certain observation point in the absorbing boundary layer. The specific formula is as follows:

[0091]

[0092] The embodiment of the present invention is Figure 4 As an example, the double grid technology is used to test the absorption effect of the method of the present invention and Mur's first-order absorption boundary condition on the outward wave. The present invention sets the basic calculation space Ω B The number of grids is 180×180, and the experimental calculation space Ω T The number of grids is 30×30, and the grid size of the two calculation spaces is 1cm×1cm. The scatterer (dielectric square column) is placed in the middle of the calculation area, with a size of 6cm×6cm. The uniform plane wave is introduced at the boundary connecting the total field / scattering field, and the incident angle is The calculation space is truncated using Mur's first-order absorbing boundary condition and the efficient absorbing boundary condition proposed in this invention, and the observation point is located at a distance Ω T P at one grid point on the boundary 1 .

[0093] The incident electric field is a modulated Gaussian pulse, and the expression is as follows:

[0094]

[0095] Among them, E i (t) is the time domain expression of the incident electromagnetic wave, f c =1.0GHz, T d =1 / 2f c , T c =1.5T d , the highest frequency is 4GHz. Calculate the time length T f = 6ns, calculation order q = 60, time scale factor s = 6.0 × 10 10 .

[0096] Relative reflection error R dB Defined as:

[0097]

[0098] in, is the amplitude of the field component at the observation point calculated using the basic grid space, is the amplitude of the field component at the observation point calculated using the test grid space.

[0099] Figure 5 is the observation point P 1 The relative reflection error under two absorbing boundary conditions is Figure 5 It can be seen that the absorption performance of the high-efficiency absorbing boundary condition adopted in the present invention is significantly better than that of the Mur first-order absorbing boundary condition.

[0100] Example 2

[0101] Based on the same inventive concept as that of Example 1, this embodiment introduces a device for calculating electromagnetic field absorption boundary conditions, such as Figure 6 As shown, it mainly includes an absorbing boundary layer setting module and an absorbing boundary layer calculation module.

[0102] The absorbing boundary layer setting module is used to transform the Maxwell equations of the perfectly matched layer absorbing boundary conditions into the Maxwell equations of the efficient absorbing boundary conditions by adding error terms; based on the Maxwell equations of the efficient absorbing boundary conditions, a circle of absorbing boundary layer is set at the boundary of the preset electromagnetic field calculation area.

[0103] The absorbing boundary layer calculation module is used to calculate the electromagnetic field components of the electromagnetic wave in the absorbing boundary layer according to the Maxwell equations of the efficient absorbing boundary conditions when the electromagnetic wave enters the absorbing boundary layer.

[0104] In addition, the device also includes a waveform observation module, which is used to obtain the time domain waveform of the electromagnetic wave in the absorption boundary layer by using the inverse Laguerre transform for observation by the user.

[0105] The specific functional implementation of each of the above modules can be found in the relevant contents of the method in Example 1 and will not be elaborated here.

[0106] Example 3

[0107] Based on the same inventive concept as other embodiments, this embodiment introduces a computer-readable storage medium on which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, the steps of the electromagnetic field absorption boundary condition calculation method introduced in Embodiment 1 are implemented.

[0108] In summary, the method of the present invention improves the existing perfectly matched layer absorption boundary conditions, introduces a perturbation term into the two-dimensional PML equation group without spatial discretization, and uses intermediate variables and step-by-step calculation technology to solve the large sparse matrix equation into two tridiagonal equations and a simple explicit equation to obtain a new efficient absorption boundary condition, whose wave impedance can be completely matched with the incident end medium, and the reflection error of the absorption boundary layer is smaller than the traditional Mur absorption boundary. With the appropriate setting of the electric loss and magnetic loss values, the energy loss of the electromagnetic wave in the absorption boundary layer can be faster.

[0109] The tridiagonal matrix equation obtained by the discretization calculation of the present invention has a much smaller dimension than the matrix equation of the traditional Laguerre-based perfectly matched layer, thereby greatly reducing the demand for computer physical memory for electromagnetic field calculations and improving the calculation efficiency. After the electromagnetic wave enters the absorption boundary layer, it is restricted by the efficient absorption boundary conditions, and the energy is gradually absorbed, which can quickly and efficiently achieve the effect of truncating the infinite calculation space of the electromagnetic wave into a limited space.

[0110] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0111] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0112] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0113] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0114] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which all fall within the protection of the present invention.

Claims

1. A method for calculating electromagnetic field absorption boundary conditions, characterized in that: The steps include: According to the Maxwell equations of perfectly matched layer absorbing boundary conditions, the Maxwell equations of efficient absorbing boundary conditions are obtained by adding error terms. Based on the Maxwell equations with efficient absorbing boundary conditions, a circle of absorbing boundary layer is set at the boundary of the preset electromagnetic field calculation area; When the electromagnetic wave enters the absorbing boundary layer, the Maxwell equations of the efficient absorbing boundary conditions are used to calculate the changes in the electromagnetic field components of the electromagnetic wave under the absorption of the absorbing boundary layer.

2. The method for calculating electromagnetic field absorption boundary conditions according to claim 1, characterized in that: The Maxwell equations for the perfectly matched layer absorbing boundary condition are: ； ； ； ； in, is the dielectric constant, is the vacuum permeability, , are the components of the electric field along the x and y directions, is the component of the magnetic field along the z direction, , for The subcomponent of , , are the electrical losses in the x and y directions respectively, , are the magnetic losses in the x and y directions respectively. x, y, z represent the three directions in the three-dimensional coordinate system respectively, and t is the time variable.

3. The method for calculating electromagnetic field absorption boundary conditions according to claim 1, characterized in that: The Maxwell equations for the efficient absorbing boundary conditions are: ； ； ； ； ； ； in, , Respectively represent the power loss , The intermediate process quantity calculated, , Respectively represent the magnetic loss , The intermediate process quantity of the calculation, s is the time factor of Laguerre transformation, r is the spatial variable, is the dielectric constant, is the vacuum permeability, , are the time domain electric field components , The k-th order Laguerre coefficient, , are the time domain electric field components , The q-order Laguerre coefficient, , is the Laguerre domain electric field component , The intermediate process variables, is the Laguerre domain electric field component The intermediate process quantity, is the time domain magnetic field component The q-order Laguerre coefficient, , Represent the time domain magnetic field subcomponents , The q-order Laguerre coefficient, , Represent the time domain magnetic field subcomponents , The k-order Laguerre coefficient of , x, y, z represent the three directions in the three-dimensional coordinate system.

4. The method for calculating electromagnetic field absorption boundary conditions according to claim 1, characterized in that: According to the electromagnetic field absorption rate requirements, the thickness, electrical loss and magnetic loss of the absorption boundary layer are set; thickness ,in, is the number of grids in the absorbing boundary layer, is the mesh size; the absorbing boundary layer is set to be anisotropic, where the electric loss and magnetic loss along the x direction are set to and , the electric loss and magnetic loss along the y direction are set to and .

5. The method for calculating electromagnetic field absorption boundary conditions according to claim 1, characterized in that: When the electromagnetic wave enters the absorbing boundary layer, according to the Maxwell equations of the efficient absorbing boundary conditions, starting from the order q=0, the electromagnetic field components of each order of the electromagnetic wave in the absorbing boundary layer are calculated step by step until the highest order , ,in, is the frequency domain bandwidth of the signal, is the duration of the signal in the time domain.

6. The method for calculating electromagnetic field absorption boundary conditions according to claim 5, characterized in that: The Maxwell equations of efficient absorbing boundary conditions are discretized by using the central difference method, and the discretized calculation formula of electromagnetic propagation in the absorbing boundary layer is obtained. Based on the discretized calculation formula of electromagnetic propagation in the absorbing boundary layer, the electromagnetic field components of the electromagnetic wave in the absorbing boundary layer are efficiently solved using the pursuit method, and the Laguerre domain expressions of the electric field and magnetic field components of the electromagnetic wave in the absorbing boundary layer are obtained, and then the changes of the electromagnetic field components of the electromagnetic wave under the absorption of the absorbing boundary layer are obtained.

7. The method for calculating electromagnetic field absorption boundary conditions according to claim 1 or 6, characterized in that: The inverse Laguerre transform is used to obtain the time domain waveform of the electromagnetic wave in the absorbing boundary layer. The expression is as follows: ； ； ； ； ； in, represents the time domain electric field component in the x direction at time t and in r space, represents the time domain electric field component in the y direction at time t and in space r, represents the time domain magnetic field component in the z direction at time t and in r space, represents the time domain magnetic field component in the zx direction in r space at time t, The time domain magnetic field component in the zy direction at time t and in space r, for Laguerre basis functions of order, , are the time domain electric field components , The p-order Laguerre coefficient, , , They are the time domain magnetic field components , , The p-order Laguerre coefficient of .

8. An electromagnetic field absorption boundary condition calculation device, characterized in that: include: The absorbing boundary layer setting module is used to obtain the Maxwell equations of efficient absorbing boundary conditions by adding error terms according to the Maxwell equations of the perfectly matched layer absorbing boundary conditions; based on the Maxwell equations of efficient absorbing boundary conditions, a circle of absorbing boundary layer is set at the boundary of the preset electromagnetic field calculation area; The absorbing boundary layer calculation module is used to calculate the change of the electromagnetic field component of the electromagnetic wave under the absorption of the absorbing boundary layer according to the Maxwell equations of the efficient absorbing boundary conditions after the electromagnetic wave enters the absorbing boundary layer.

9. The electromagnetic field absorption boundary condition calculation device according to claim 8, characterized in that: The Maxwell equations for the efficient absorbing boundary conditions are: ； ； ； ； ； ； in, , Respectively represent the power loss , The intermediate process quantity calculated, , Respectively represent the magnetic loss , The intermediate process quantity of the calculation, s is the time factor of Laguerre transformation, r is the spatial variable, is the dielectric constant, is the vacuum permeability, , are the time domain electric field components , The k-th order Laguerre coefficient, , are the time domain electric field components , The q-order Laguerre coefficient, , is the Laguerre domain electric field component , The intermediate process variables, is the Laguerre domain electric field component The intermediate process quantity, is the time domain magnetic field component The q-order Laguerre coefficient, , Represent the time domain magnetic field subcomponents , The q-order Laguerre coefficient, , Represent the time domain magnetic field subcomponents , The k-order Laguerre coefficient of , x, y, z represent the three directions in the three-dimensional coordinate system.

10. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instruction is executed by a processor, the steps of the method for calculating electromagnetic field absorption boundary conditions described in any one of claims 1-7 are implemented.

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