A method and device for calculating electromagnetic field absorption boundary conditions

Abstract

This invention discloses a method and apparatus for calculating electromagnetic field absorption boundary conditions, belonging to the field of electromagnetic field calculation technology. It includes: transforming the Maxwell equations for perfectly matched layer absorption boundary conditions by adding error terms to obtain Maxwell equations for efficient absorption boundary conditions; setting an absorption boundary layer at the boundary of a preset electromagnetic field calculation region based on the efficient absorption boundary conditions of the Maxwell equations; and calculating the electromagnetic field components of the electromagnetic wave in the absorption boundary layer after it enters the absorption boundary layer according to the efficient absorption boundary conditions of the Maxwell equations. This invention has the advantages of small reflection error, fast energy absorption, fast calculation speed, and small memory footprint.

Description

Technical Field

[0001] This invention relates to a method and apparatus for calculating electromagnetic field absorption boundary conditions, belonging to the field of electromagnetic field calculation technology. Background Technology

[0002] In electromagnetic field calculations, the computational domain for simulation is always finite, so the infinite computational space must be truncated before numerical simulation can be performed. If absorbing boundary conditions (ABC) are not added to the boundaries of the computational domain, electromagnetic waves will be emitted upon encountering the boundaries, leading to significant errors in the time-domain waveform at the monitoring points. Good absorbing boundary conditions can eliminate non-physical reflections of electromagnetic waves at the truncated points, facilitating a better electromagnetic field computational environment.

[0003] Existing Mur absorbing boundary conditions have the advantages of saving memory and fast computation, but they are not perfectly matched and cannot meet the accuracy requirements of electromagnetic field calculations in many cases, and the reflection error is relatively large. On the other hand, traditional perfectly matched layer (PML) absorbing boundary conditions can reduce reflection error, but they require solving large sparse matrices during the calculation process, resulting in high memory consumption and slow calculation speed. This places certain demands on electromagnetic field computing equipment and computational requirements, thus limiting the application of electromagnetic field calculations. Summary of the Invention

[0004] The purpose of this invention is to provide a method and apparatus for calculating electromagnetic field absorption boundary conditions. It improves upon the existing fully matched layer absorption boundary conditions and proposes a new absorption boundary condition. This absorption boundary condition is fully matched with the medium inside the calculation region. Within the absorption boundary condition, the electric field and magnetic field are calculated according to the method set by this invention. It has the advantages of small reflection error, fast energy absorption, fast calculation speed, and small memory footprint.

[0005] To achieve the above objectives / to solve the above technical problems, the present invention is implemented using the following technical solution:

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

[0007] Based on the Maxwell equations for the fully matched layer absorbing boundary conditions, the Maxwell equations for the efficient absorbing boundary conditions are obtained by adding error terms.

[0008] Based on the Maxwell equations with efficient absorbing boundary conditions, an absorbing boundary layer is set at the boundary of the preset electromagnetic field calculation region.

[0009] When an electromagnetic wave enters the absorbing boundary layer, the changes in the electromagnetic field components under the absorption of the electromagnetic wave in the absorbing boundary layer are calculated according to Maxwell's equations for efficient absorbing boundary conditions.

[0010] In conjunction with the first aspect, the Maxwell equations for the perfectly matched layer absorbing boundary conditions are further as follows:

[0011]

[0012] Where ε0 is the permittivity, μ0 is the free permeability, and E x 、E y H represents the components of the electric field along the x and y directions. z H represents the component of the magnetic field along the z-direction. zx H zy For H z Subcomponents satisfying H z =H zx +H zy , σ x σ y ρ represents the electrical losses in the x and y directions, respectively. x ρ y denoted as , and respectively as , where x, y, and z represent the three directions in the three-dimensional coordinate system, and t is the time variable.

[0013] In conjunction with the first aspect, the Maxwell equations for the efficient absorbing boundary conditions are further as follows:

[0014]

[0015] in, These represent the electrical losses σ, respectively. x σ y Intermediate quantities in the calculation They represent the values ​​based on magnetic loss ρ x ρ y The intermediate quantities calculated are: s, the time factor of the Laguerre transform; r, the spatial variable; ε0, the permittivity; and μ0, the free permeability. These are the time-domain electric field components E x (r,t), E y The k-th order Laguerre coefficients of (r,t), These are the time-domain electric field components E x (r,t), E y Laguerre coefficients of order q for (r,t) For the electric field components of the Laguerre domain intermediate process variables, For the electric field components of the Laguerre domain The intermediate process quantity, H is the time-domain magnetic field component z Laguerre coefficients of order q for (r,t) H represents the time-domain magnetic field subcomponent, respectively. zx (r,t),H zy The q-th order Laguerre coefficients of (r,t) H represents the time-domain magnetic field subcomponent, respectively. zx (r,t),H zy The k-th order Laguerre coefficients of (r,t), where x, y, z represent the three directions in the three-dimensional coordinate system.

[0016] In conjunction with the first aspect, further, the thickness, electrical 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 anisotropic, where the electrical loss and magnetic loss along the x-direction are respectively set to σ x and ρ x The electrical and magnetic losses along the y-direction are respectively set as σ y and ρ y .

[0017] In conjunction with the first aspect, furthermore, after the electromagnetic wave enters the absorbing boundary layer, according to Maxwell's equations for efficient absorbing boundary conditions, starting from order q = 0, each order of electromagnetic field component in the absorbing boundary layer is calculated in a step-by-step manner until the highest order q is reached. max q max ≥2BT f +1, where B is the frequency bandwidth of the signal, T f The duration of the signal in the time domain.

[0018] In conjunction with the first aspect, the Maxwell equations for efficient absorbing boundary conditions are further discretized using the central difference method to obtain a discretized calculation formula for 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 electromagnetic waves in the absorbing boundary layer are efficiently solved using the chasing method. The Laguerre domain expressions of the electric and magnetic field components of electromagnetic waves in the absorbing boundary layer are obtained, and then the changes of electromagnetic field components under the absorption of electromagnetic waves in the absorbing boundary layer are obtained.

[0020] Building upon the first aspect, we further utilize the inverse Laguerre transform to obtain the time-domain waveform of the electromagnetic wave in the absorbing boundary layer, as shown in the following expression:

[0021]

[0022] Among them, E x (r,t) represents the time-domain electric field component in the x-direction at time t in space r, E y (r,t) represents the time-domain electric field component in the y-direction at time t in space r, H z (r,t) represents the time-domain magnetic field component in the z-direction at time t in space r, H zx (r,t) represents the time-domain magnetic field component in the zx direction at time t in space r, H zy The time-domain magnetic field component in the zy direction at time t in r space. For p-order Laguerre basis functions, These are the time-domain electric field components E x (r,t), E y p-order Laguerre coefficients of (r,t) These are the time-domain magnetic field components H z (r,t),H zx (r,t),H zy The p-order Laguerre coefficients 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 transform the Maxwell equations with efficient absorbing boundary conditions by adding error terms based on the Maxwell equations with perfectly matched layer absorbing boundary conditions; and to set an absorbing boundary layer at the boundary of the preset electromagnetic field calculation region based on the Maxwell equations with efficient absorbing boundary conditions.

[0025] The absorbing boundary layer calculation module is used to calculate the changes in electromagnetic field components under the absorption of electromagnetic waves in the absorbing boundary layer, based on Maxwell's equations for efficient absorbing boundary conditions, after electromagnetic waves enter the absorbing boundary layer.

[0026] In conjunction with the second aspect, the Maxwell equations for the efficient absorbing boundary conditions are further as follows:

[0027]

[0028]

[0029] in, These represent the values ​​based on electrical loss σ. x σ y Intermediate quantities in the calculation They represent the values ​​based on magnetic loss ρx ρ y The intermediate quantities calculated are: s, the time factor of the Laguerre transform; r, the spatial variable; ε0, the permittivity; and μ0, the free permeability. These are the time-domain electric field components E x (r,t), E y The k-th order Laguerre coefficients of (r,t), These are the time-domain electric field components E x (r,t), E y Laguerre coefficients of order q for (r,t) For the electric field components of the Laguerre domain intermediate process variables, For the electric field components of the Laguerre domain The intermediate process quantity, H is the time-domain magnetic field component z Laguerre coefficients of order q for (r,t) H represents the time-domain magnetic field subcomponent, respectively. zx (r,t),H zy The q-th order Laguerre coefficients of (r,t) H represents the time-domain magnetic field subcomponent, respectively. zx (r,t),H zy The k-th order Laguerre coefficients of (r,t), where x, y, z represent the three directions in the three-dimensional coordinate system.

[0030] Thirdly, the present invention provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the electromagnetic field absorption boundary condition calculation method provided in the first aspect.

[0031] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0032] This invention proposes a method and apparatus for calculating electromagnetic field absorption boundary conditions. It improves upon the existing perfectly matched layer absorption boundary conditions by proposing a new, highly efficient absorption boundary condition. This highly efficient absorption boundary condition is perfectly matched with the medium inside the computational region. Based on the highly efficient absorption boundary condition, an absorption boundary layer is set in the electromagnetic wave computational region. After the electromagnetic wave enters the absorption boundary layer, it is restricted by the highly efficient absorption boundary condition, and its energy is gradually absorbed, thus achieving the effect of truncating the infinite computational space of electromagnetic waves into a finite one.

[0033] This invention derives a highly efficient Maxwell equation set for absorbing boundary conditions through a special derivation process. The wave impedance of this set perfectly matches the incident medium, resulting in minimal reflection error. With appropriate electrical and magnetic loss values, the energy dissipation of electromagnetic waves in the absorbing boundary layer can be accelerated. Compared to existing absorbing boundary conditions, the method described in this invention offers advantages such as smaller reflection error, faster energy absorption, faster computation speed, and lower memory footprint. Attached Figure Description

[0034] Figure 1 The diagram shows the steps of a method for calculating electromagnetic field absorption boundary conditions according to an embodiment of the present invention.

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

[0036] Figure 3 The diagram shown is a schematic representation of the positional relationship of each electromagnetic field component under the central difference scheme in an embodiment of the present invention.

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

[0038] Figure 5 The diagram shows the relative reflection error at the observation point calculated using different absorption boundary conditions in an embodiment of the present invention.

[0039] Figure 6 The diagram shown is a structural schematic of an electromagnetic field absorption boundary condition calculation device provided in an embodiment of the present invention. Detailed Implementation

[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. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0041] Example 1

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

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

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

[0045]

[0046] Where ε0 is the permittivity, μ0 is the free permeability, and E x E y H represents the components of the electric field along the x and y directions. z H represents the component of the magnetic field along the z-direction. zx H zy It is H z Subcomponents satisfying H z =H zx +H zy , σ x σ y ρ represents the electrical losses in the x and y directions, respectively. x ρ y denoted as , and respectively as , where x, y, and z represent the three directions in the three-dimensional coordinate system, and t is the time variable.

[0047] The existing Maxwell equations with 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 matrix form of the Maxwell equations.

[0048] In this embodiment of the invention, the pre-constructed intermediate variable is:

[0049]

[0050]

[0051] in, Let be a vector composed of unknown electric field components of order q, with the superscript T indicating the transpose operation. Let D be a vector composed of unknown electric field components of order q. E D H A custom matrix consisting of partial differential symbols. Let be a vector composed of known electric and magnetic field components of order (q-1) and below. These are the time-domain electric field components E x (r,t), E y Laguerre coefficients of order q for (r,t) H is the time-domain magnetic field component z Laguerre coefficients of order q for (r,t) These represent the values ​​based on electrical loss σ. x σ yIntermediate quantities in the calculation They represent the values ​​based on magnetic loss ρ x ρ y The intermediate process quantities are calculated, where s is the time factor of the Laguerre transform and r is the spatial variable. These are the time-domain electric field components E x (r,t), E y The k-th order Laguerre coefficients of (r,t), the time-domain magnetic field component H z (r,t) can be further divided into sub-components H zx (r,t),H zy (r,t), H represents the time-domain magnetic field subcomponent, respectively. zx (r,t),H zy The k-th order Laguerre coefficients of (r,t).

[0052] Based on the pre-constructed intermediate variables, the expanded Maxwell equation can be written as a 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] A higher-order small error term is actively added to the left-hand side of the matrix form of Maxwell's equation. This allows the coefficient matrix on the left side of the Maxwell equation to be decomposed into the product of two square matrices. The transformed Maxwell equation is then decomposed into a three-step solution using a step-by-step method, ultimately yielding a new, highly efficient Maxwell equation that absorbs boundary conditions.

[0058] In this embodiment of the invention, the Maxwell equation for efficiently absorbing boundary conditions is as follows:

[0059]

[0060] in, These 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-th order Laguerre coefficients of (r,t) yes Subcomponents, For the electric field components of the Laguerre domain intermediate process variables, For the electric field components of the Laguerre domain The intermediate process quantities are meaningless.

[0061] In this invention, It is only related to spatial location, not to time.

[0062]

[0063] in, These represent the corresponding intermediate process quantities. The value of σ at the field points x = i and y = j x | i,j σ y | i,j These represent the corresponding electrical losses σ. x σ y The value of ρ at the field points x = i and y = j x | i,j ρ y | i,j These represent the corresponding magnetic losses ρ. x ρ y The values ​​at the field points x = i and y = j.

[0064] Step 2: Based on the Maxwell equations with efficient absorbing boundary conditions, an absorbing boundary layer is set at the boundary of the preset electromagnetic field calculation region. This absorbing boundary layer adopts the split field technique, which is similar to a virtual absorbing medium.

[0065] Absorbing boundary layer, such as Figure 2 As shown, 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 anisotropic, where the electric loss and magnetic loss along the x-direction are set to σ. x and ρ x The electrical and magnetic losses along the y-direction are respectively set as σ y and ρ y In this embodiment of the invention, the values ​​of parameters such as the thickness of the absorbing boundary layer, electrical loss, and magnetic loss are set according to actual needs.

[0066] Step 3: After the electromagnetic wave enters the absorbing boundary layer, the propagation process of the electromagnetic wave in the absorbing boundary layer is calculated according to Maxwell's equations for efficient absorbing boundary conditions, and the changes in the electromagnetic field components under the absorption of the electromagnetic wave in the absorbing boundary layer are obtained.

[0067] After an electromagnetic wave enters the absorbing boundary layer, its propagation process needs to be calculated according to formulas (13) to (22). During the calculation, the equations are performed step-by-step, starting from order q = 0 and continuing up to the highest order q. max Generally, q is taken. max ≥2BT f +1, where B is the frequency bandwidth of the signal, T f The duration of the signal in the time domain.

[0068] In the calculation of q at each order, the first step is to use formula (13) to find the intermediate process quantities. The right side of formula (13) is all the accumulation of low-order field quantities, which is known at this point; the second step is to use formula (14) to find the electric field components. The right side of formula (14) The electric field components have been determined in the first step and are known quantities; in the third step, the electric field components are calculated using formula (15). Similarly, the right side of formula (15) consists entirely of known quantities; in the fourth step, use formulas (16) and (17) to calculate the subcomponents of the magnetic field. Fifth step, use formula (18) to calculate the magnetic field components.

[0069] By solving in stepwise order, the electromagnetic field components of the next order can be continuously calculated. Since energy is continuously absorbed in the absorbing boundary layer, the electromagnetic field components will continuously decrease until they become 0.

[0070] The algorithm equations provided by this invention can be discretized by the central difference method to form two tridiagonal matrix equations, which can then be efficiently solved using the chasing method to obtain the Laguerre domain expressions for the electric and magnetic field components of electromagnetic waves in the absorbing boundary layer.

[0071] The Maxwell equations for efficient absorbing boundary conditions are discretized using the central difference method, resulting in discretized calculation formulas for electromagnetic propagation in the absorbing boundary layer. Taking equations (13) to (15) as examples, the difference equations are:

[0072]

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

[0074]

[0075] Where, Δ x denoted as the mesh size of the absorbing boundary layer in the x-direction.

[0076] The positional relationship of each electromagnetic field component under the central difference scheme is as follows: Figure 3 As shown, this embodiment of the invention uses the solution of formula (24) as an example for illustration. In formula (24), the left side of the equation... All coefficients are derived from the parameters of the absorbing boundary layer and are known quantities. The right-hand side of the equation also contains known quantities. The unknowns in the equation are... The positional relationship of these three unknowns is as follows: Figure 3 As shown.

[0077] make:

[0078]

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

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

[0081]

[0082] Let the total number of grid cells in the x and y directions be N respectively. x N y In the solution process, for each fixed j = M, the range of values ​​for i is [1, N]. x For different values ​​of i, a set of N can be constructed. x A system of equations consisting 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, it can be solved efficiently using the chasing method, yielding the q-order electric field components at each point when j = M. When j is in (1, N) yWhen the electric field changes, we can calculate the electric field components at all points in the absorbing boundary layer.

[0088] Similarly, by discretizing the other equations in equations (13) to (18) using the central difference method, the q-order electromagnetic field components at all points in the absorbing boundary layer can also be obtained. This completes the solution to the q-th order equation. We can then proceed to the (q+1)-th order equation, and so on, until we reach 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 the user to observe.

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

[0091]

[0092] The embodiments of the present invention are based on Figure 4 For example, the absorption effect of the method of this invention and the Mur first-order absorbing boundary condition on outward waves is verified using dual-grid technology. This invention sets up a basic computational space Ω. B The grid size is 180×180, and the experimental computation space is Ω. T The grid size is 30×30, and the grid size for both computational spaces is 1cm×1cm. A scatterer (medium prism) with dimensions of 6cm×6cm is placed in the center of the computational domain. A uniform plane wave is introduced from the boundary connecting the total field and the scattered field, with an incident angle of... The computational space is truncated using Mur's first-order absorbing boundary condition and the efficient absorbing boundary condition proposed in this invention, with the observation point located at a distance Ω. T P1 at a grid point on the boundary.

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

[0094]

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

[0096] Relative reflection error R dB Defined as:

[0097]

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

[0099] Figure 5 The relative reflection error at observation point P1 under two absorption boundary conditions is calculated from... Figure 5 It can be seen that the absorption performance of the efficient absorption boundary condition used in this invention is significantly better than that of the first-order absorption boundary condition of Mur.

[0100] Example 2

[0101] Based on the same inventive concept as Embodiment 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 with efficient absorbing boundary conditions by adding error terms, based on the Maxwell equations with perfectly matched layer absorbing boundary conditions. Based on the Maxwell equations with efficient absorbing boundary conditions, an absorbing boundary layer is set at the boundary of the preset electromagnetic field calculation region.

[0103] The absorbing boundary layer calculation module is used to calculate the electromagnetic field components of electromagnetic waves in the absorbing boundary layer based on Maxwell's equations for efficient absorbing boundary conditions after electromagnetic waves enter the absorbing boundary layer.

[0104] In addition, the device also includes a waveform observation module, which uses the inverse Laguerre transform to obtain the time-domain waveform of electromagnetic waves in the absorbing boundary layer for user observation.

[0105] The specific functions of each module described above are explained in the relevant content of the method in Embodiment 1, and will not be repeated here.

[0106] Example 3

[0107] Based on the same inventive concept as other embodiments, this embodiment introduces a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps of the electromagnetic field absorption boundary condition calculation method described in Embodiment 1.

[0108] In summary, the present invention improves upon existing perfectly matched layer absorbing boundary conditions by introducing a perturbation term into the undiscretized two-dimensional PML equations. Using intermediate variables and step-by-step computation techniques, the large sparse matrix equations are reduced to two tridiagonal equations and a simple explicit equation for solution, resulting in a new, highly efficient absorbing boundary condition. This condition achieves perfect matching of wave impedance with the incident medium, and the reflection error of the absorbing boundary layer is less than that of the traditional Mur absorbing boundary. With appropriate electrical and magnetic loss values, the energy dissipation of electromagnetic waves in the absorbing boundary layer can be accelerated.

[0109] The tridiagonal matrix equation obtained during discretization in this invention has a much smaller dimension than the matrix equation of a traditional Laguerreky perfectly matched layer, thus greatly reducing the physical memory requirements of the computer for electromagnetic field calculations and improving computational efficiency. After electromagnetic waves enter the absorbing boundary layer, they are constrained by the highly efficient absorbing boundary conditions, and their energy is gradually absorbed, enabling the rapid and efficient truncation of the infinite computational space of electromagnetic waves into a finite one.

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

[0111] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. 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 storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0113] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[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 guidance 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 are all protected by the present invention.

Claims

1. A method for calculating electromagnetic field absorption boundary conditions, characterized in that, Includes the following steps: Based on the Maxwell equations for the fully matched layer absorbing boundary conditions, the Maxwell equations for the efficient absorbing boundary conditions are obtained by adding error terms. Based on the Maxwell equations with efficient absorbing boundary conditions, an absorbing boundary layer is set at the boundary of the preset electromagnetic field calculation region. When an electromagnetic wave enters the absorbing boundary layer, the changes in the electromagnetic field components under the absorption of the electromagnetic wave in the absorbing boundary layer are calculated according to Maxwell's equations for efficient absorbing boundary conditions. The Maxwell equations for the efficient absorbing boundary conditions are as follows: ； ； ； ； ； ； in, , These represent the differences based on electrical losses. , Intermediate quantities in the calculation , They represent the values ​​based on magnetic loss. , The intermediate process quantities in the calculation are: s, which is the time factor of the Laguerre transform, and r, which is the spatial variable. Where is the dielectric constant. The permeability of free space, , These are the time-domain electric field components. , The k-th order Laguerre coefficients, , These are the time-domain electric field components. , The q-th order Laguerre coefficients, , For the electric field components of the Laguerre domain , intermediate process variables, For the electric field components of the Laguerre domain The intermediate process quantity, For time-domain magnetic field components The q-th order Laguerre coefficients, , Representing the time-domain magnetic field subcomponents respectively , The q-th order Laguerre coefficient, , Representing the time-domain magnetic field subcomponents respectively , The k-th order Laguerre coefficients, where x, y, z represent the three directions in the three-dimensional coordinate system; Once the electromagnetic wave enters the absorbing boundary layer, according to Maxwell's equations for efficient absorbing boundary conditions, starting from order q=0, the electromagnetic field components of each order in the absorbing boundary layer are calculated in a step-by-step manner until the highest order is reached. , ,in, The frequency bandwidth of the signal. The duration of the signal in the time domain; The Maxwell equations for efficient absorbing boundary conditions are discretized using the central difference method, resulting in a discretized calculation formula for electromagnetic propagation in the absorbing boundary layer. Based on the discretized calculation formula of electromagnetic propagation in the absorbing boundary layer, the electromagnetic field components of electromagnetic waves in the absorbing boundary layer are efficiently solved using the chasing method. The Laguerre domain expressions of the electric and magnetic field components of electromagnetic waves in the absorbing boundary layer are obtained, and then the changes of electromagnetic field components under the absorption of electromagnetic waves in the absorbing boundary layer are obtained.

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 conditions are as follows: ； ； ； ； in, Where is the dielectric constant. The permeability of free space, , Let x and y be the components of the electric field along the x and y directions. Let be the component of the magnetic field along the z-direction. , for Subcomponents, satisfying , , These represent electrical losses in the x and y directions, respectively. , denoted as , and respectively as , where x, y, and z represent the three directions in the three-dimensional coordinate system, and t is the time variable.

3. The method for calculating electromagnetic field absorption boundary conditions according to claim 1, characterized in that, The thickness, electrical loss, and magnetic loss of the absorption boundary layer are set according to the electromagnetic field absorption rate requirements; thickness ,in, To absorb the number of grid cells in the boundary layer, The mesh size is [size missing]; the absorbing boundary layer is set to anisotropic, where the electric loss and magnetic loss along the x-direction are set to [values ​​missing]. and The electrical and magnetic losses along the y-direction are respectively set as and .

4. The method for calculating electromagnetic field absorption boundary conditions according to claim 1, characterized in that, The time-domain waveform of electromagnetic waves in the absorbing boundary layer is obtained using the inverse Laguerre transform, as shown in the following expression: ； ； ； ； ； in, Let represent the time-domain electric field component in the x-direction at time t in space r. Let represent the time-domain electric field component in the y-direction at time t in space r. Let represent the time-domain magnetic field component in the z-direction at time t in space r. Let represent the time-domain magnetic field component in the zx direction at time t in r space. The time-domain magnetic field component in the zy direction at time t in space r. for Laguerre basis functions of order 1 , These are the time-domain electric field components. , p-th order Laguerre coefficients, , , These are the time-domain magnetic field components. , , The p-order Laguerre coefficients.

5. A device for calculating electromagnetic field absorption boundary conditions, characterized in that, The device is used to implement the steps of the electromagnetic field absorption boundary condition calculation method according to claim 1, including: The absorbing boundary layer setting module is used to transform the Maxwell equations with efficient absorbing boundary conditions by adding error terms based on the Maxwell equations with perfectly matched layer absorbing boundary conditions; and to set an absorbing boundary layer at the boundary of the preset electromagnetic field calculation region based on the Maxwell equations with efficient absorbing boundary conditions. The absorbing boundary layer calculation module is used to calculate the changes in electromagnetic field components under the absorption of electromagnetic waves in the absorbing boundary layer, based on Maxwell's equations for efficient absorbing boundary conditions, after electromagnetic waves enter the absorbing boundary layer.

6. The electromagnetic field absorption boundary condition calculation device according to claim 5, characterized in that, The Maxwell equations for the efficient absorbing boundary conditions are as follows: ； ； ； ； ； ； in, , These represent the differences based on electrical losses. , Intermediate quantities in the calculation , They represent the values ​​based on magnetic loss. , The intermediate process quantities in the calculation are: s, which is the time factor of the Laguerre transform, and r, which is the spatial variable. Where is the dielectric constant. The permeability of free space, , These are the time-domain electric field components. , The k-th order Laguerre coefficients, , These are the time-domain electric field components. , The q-th order Laguerre coefficients, , For the electric field components of the Laguerre domain , intermediate process variables, For the electric field components of the Laguerre domain The intermediate process quantity, For time-domain magnetic field components The q-th order Laguerre coefficients, , Representing the time-domain magnetic field subcomponents respectively , The q-th order Laguerre coefficient, , Representing the time-domain magnetic field subcomponents respectively , The k-th order Laguerre coefficients, where x, y, and z represent the three directions in the three-dimensional coordinate system.

7. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the electromagnetic field absorption boundary condition calculation method according to any one of claims 1-4.

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