High-precision field mapping method for specific absorption rate based on non-uniform mesh conformal FDTD

Abstract

The application discloses a high-precision field mapping method for specific absorption rate based on non-uniform mesh conformal FDTD, and belongs to the technical field of electromagnetic field numerical simulation; the method comprises the following steps: performing non-uniform mesh division on a three-dimensional calculation region; identifying conformal edges and performing weighted calculation on material electromagnetic parameters according to the lengths of the conformal edges located in a model region and a background region; performing iterative solution on electric field by using a time domain finite difference algorithm; converting time domain electric field into frequency domain electric field and performing weighted mapping correction on the conformal edges; calculating local specific absorption rate of a target mesh; and determining spatial average specific absorption rate by using a volume weight compensation algorithm; the application organically combines the conformal technology and the non-uniform mesh technology, optimizes the allocation of calculation resources while ensuring the calculation precision, realizes the unification of high efficiency and high precision, and improves the engineering applicability under a complex electromagnetic exposure scene.

Description

Technical Field

[0001] This invention relates to a high-precision field mapping method based on specific absorptivity, and more particularly to a high-precision field mapping method based on non-uniform mesh conformal FDTD. Background Technology

[0002] With the widespread application of 5G mobile communication, the Internet of Things, and wearable devices, the safety assessment of radio frequency electromagnetic radiation exposure to human tissues has become a core issue for public health and equipment compliance regulation. Specific Absorption Rate (SAR), as a core dosimetric indicator for quantifying radio frequency energy absorption, is crucial for the accurate calculation of wireless terminal equipment to meet international safety standards. The Finite-Difference Time-Domain (FDTD) method, due to its ability to handle complex non-uniform media and broadband problems, has become the mainstream method for simulating human electromagnetic exposure environments and calculating SAR distribution. However, for bioelectromagnetic models containing multi-scale fine structures, improving simulation efficiency while ensuring computational accuracy remains a critical challenge.

[0003] Traditional standard FDTD uses a regular Yee grid (orthogonal hexahedron) to discretize the computational space. When simulating physical models with curved surfaces, complex geometries, or fine structures, the uniform Yee grid can only fit the geometric boundaries through "staircasing." This inevitably introduces geometric distortion of the boundary shape, leading to significant errors in the electromagnetic field calculations at the boundaries. To improve the accuracy of electromagnetic field calculations at the boundaries, conformal FDTD technology has emerged. This technology achieves high-fidelity fitting of curved and inclined boundaries by correcting the update coefficients of some boundary grids or the electromagnetic parameters of equivalent materials. However, this technology also introduces a new problem: within a conformal grid containing multiple media, discrete electric field values ​​defined based on the grid edges or center cannot be directly and accurately used to characterize the overall energy absorption state of the biological tissue corresponding to that grid. This results in inherent systematic biases in SAR calculations directly based on the conformal grid electric field results, especially in SAR indices that require spatial averaging of local fields, i.e., spatially averaged SAR.

[0004] To address the low computational efficiency of traditional FDTD (Fixed-Field Detection and Replication) due to the global use of uniform meshes, especially when the simulation model contains local fine structures, non-uniform mesh FDTD technology effectively optimizes the allocation of computational resources by setting fine meshes in critical regions (such as medium interfaces and fine structures) and coarse meshes in non-critical regions. This significantly improves overall simulation efficiency while maintaining the accuracy of the core region. However, when combining conformal techniques aimed at improving accuracy with non-uniform mesh techniques aimed at improving efficiency to construct a high-precision and efficient simulation system called "non-uniform mesh conformal FDTD," existing methods face a double challenge: first, the field value deviation problem within the conformal mesh still exists; second, and more importantly, the traditional average SAR calculation process suitable for uniform meshes is no longer applicable to the irregular system of non-uniform meshes, lacking an accurate and universal calculation method.

[0005] In mainstream international standards guiding FDTD simulation of SAR calculations, the demonstration procedures and algorithms are all based on uniform Yee grids. While these standards detail the steps for spatially averaged SAR calculations within such uniform Yee grid systems, they do not provide methodological guidance or optimization suggestions on ensuring the accuracy of spatially averaged SAR calculations using non-uniform grids, particularly those combined with conformal techniques. This gap in standards results in a severe lack of a complete field mapping and data processing method for achieving high-precision spatially averaged SAR calculations using the advanced simulation system of "non-uniform grid conformal FDTD" in engineering practice. This constitutes a core technical bottleneck that urgently needs to be addressed in the practical application of this technology. Summary of the Invention

[0006] This invention aims to address the inaccuracy of spatial average SAR calculations caused by field value deviations within the conformal mesh in existing non-uniform mesh conformal FDTD simulation systems. It provides a high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD. This method improves the accuracy of spatial average SAR calculations while maintaining high computational efficiency, thus solving the core technical bottleneck of the advanced "non-uniform mesh conformal FDTD" simulation system in practical applications.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD, comprising the following steps: S1: Perform non-uniform meshing on the 3D computational region containing the model, and determine the model region and background region; specifically: establish a model including the geometric features of the target to be simulated and the geometric features of the radiation source in the 3D Cartesian coordinate system O-xyz; determine the 3D computational region in the 3D Cartesian coordinate system O-xyz based on the model, the 3D computational region being able to completely cover the region where the model is located; perform non-uniform meshing on the 3D computational region to form a meshed 3D computational region with multiple meshes distributed along the 3D plane; divide the meshed 3D computational region into a model region and a background region; wherein, the model region represents the space where the model is located in the meshed 3D computational region, and the background region is the other region in the meshed 3D computational region besides the model region; S2: In each mesh, edges that are partially located in the model region and partially located in the background region are marked as conformal edges, and other edges, i.e., edges that are entirely located in the model region or entirely in the background region, are marked as regular edges; and the length of each conformal edge in the model region and the length in the background region are determined; meshes containing conformal edges are defined as conformal meshes; for each regular edge located in the model region, the electromagnetic parameters of its material are the same as those of the material in the model region, and for each regular edge located in the background region, the electromagnetic parameters of its material are the same as those of the material in the background region. S3: For each conformal edge, the electromagnetic parameters of its material are determined by weighted calculation based on its length in the model region and its length in the background region, as well as the electromagnetic parameters of the material in the model region. S4: The electric field on each edge is iteratively calculated using the finite-difference time-domain algorithm to obtain the time-domain electric field of each edge; S5: At the preset calculation frequency, for each regular edge, its time-domain electric field is converted into a frequency-domain electric field value. For each conformal edge, its time-domain electric field is first converted into an initial frequency-domain electric field value. Then, based on its length in the model region and its length in the background region, its initial frequency-domain electric field value is weighted and mapped to obtain its frequency-domain electric field value. S6: Each grid that is partially located in the model region and partially located in the background region, as well as each grid that is entirely located in the model region, are all considered as target grids; for each target grid, its local specific absorption rate is calculated based on the frequency domain electric field values ​​of its conformal edges and all regular edges located in the model region. S7: For each target grid, its spatial average specific absorptivity is determined by a volume weight compensation algorithm based on its local specific absorptivity.

[0008] Compared with the prior art, the advantages of the present invention are as follows: (i) This invention solves the problem of spatial average SAR calculation accuracy in non-uniform grid conformal FDTD systems. Through a three-level processing mechanism of conformal edge identification, weighted electromagnetic parameter calculation, and weighted frequency domain electric field mapping, this invention effectively corrects the electric field calculation deviation at the conformal grid boundary, reduces the systematic error introduced by the field value deviation at the conformal grid boundary to the spatial average SAR calculation, and significantly improves the accuracy of spatial average SAR calculation.

[0009] (II) A spatial average SAR calculation method applicable to non-uniform grid systems has been established. Existing international standards only provide spatial average SAR calculation procedures for uniform Yee grids, lacking methodological guidance for non-uniform grids, especially grid systems combined with conformal techniques. This invention establishes a complete spatial average SAR calculation procedure applicable to non-uniform grids through a volume weight compensation algorithm, providing a feasible technical path for spatial average SAR calculation in non-uniform grid systems.

[0010] (III) Balancing simulation efficiency and computational accuracy. This invention organically combines conformal technology and non-uniform mesh technology, optimizing the allocation of computational resources while ensuring computational accuracy, achieving a balance between high efficiency and high accuracy, and improving the engineering applicability in complex electromagnetic exposure scenarios.

[0011] In a further technical solution, the specific process of performing non-uniform mesh division on the three-dimensional computational region in step S1 is as follows: S1.1 Determine the maximum and minimum allowable step size for mesh generation; S1.2. Based on the geometric characteristics of the model, the three-dimensional computational region is divided into a minimum step size grid region, a maximum step size grid region, and a grid transition region. S1.3 Set the grid step size of the minimum step size grid region to the minimum allowable step size, set the grid step size of the maximum step size grid region to the maximum allowable step size, and change the step size of the grid transition region in a gradient manner according to the preset adaptive step size to achieve the connection with the minimum step size grid region; S1.4. The three axes of the three-dimensional rectangular coordinate system are respectively denoted as... x axis, y shaft and z Axis; in x axis, y shaft and z Discretization segments are divided along the axial direction using the minimum allowable step size, the maximum allowable step size, and the adaptive step size, respectively. S1.5 After the segmentation is completed, x axis, y shaft and z The boundaries of each axis overlap orthogonally in space, generating a non-uniformly distributed grid. S1.6, will x The total number of axis boundary divisions is denoted as M x , y The total number of axis boundary divisions is denoted as M y , z The total number of axis boundary divisions is denoted as M z Using spatial indexes ( i , j , k The node coordinates of the calibrated mesh are as follows: i =1,2,……, M x , j =1,2,……, M y , k =1,2,……, M z ;( i , j , k )express x Axis No. i A dividing boundary, y Axis No. j Each dividing boundary and z Axis No. k The intersection points of the dividing boundaries are used to indicate the location of the boundary. x Axis No. i Individual, in y Axis No. j Individual and in z Axis No. k The node coordinates of a certain grid are used to establish a mapping relationship between the node coordinates of the grid and the spatial position, thereby realizing the non-uniform grid division of the three-dimensional computing region.

[0012] In a further technical solution, in step S1, the meshed three-dimensional computational region is divided into a model region and a background region using ray tracing. Specifically, this involves dividing the mesh into the three coordinate planes O-xyz of the three-dimensional Cartesian coordinate system. x O y noodle, x O z Face to face y O z The nodes on the surface serve as source points. Rays are emitted from each source point perpendicular to its coordinate plane. These rays coincide with multiple mesh edges. If a ray intersects the geometric surface of the model, there will be at least one pair of intersection points. Each pair of intersection points is located on the model interface, and the area enclosed by all the intersection points is the model region.

[0013] In a further technical solution, the electromagnetic parameters of the material include relative permittivity and conductivity. The background region material is a vacuum, with a relative permittivity of 1 and a conductivity of 0 S / m.

[0014] In a further technical solution, for each conformal edge, its relative permittivity and conductivity are determined using formulas (1) and (2), respectively: (1) (2) in, The relative permittivity of the conformal edge. The conductivity of the conformal edge, Let be the relative permittivity of the material in the model region. The relative permittivity of the material in the background region is . The length of the conformal edge in the model region. The length of the conformal edge in the background region. The electrical conductivity of the material in the model region. The background region material has electrical conductivity.

[0015] In a further technical solution, in step S5, for each conformal edge, its initial frequency domain electric field value is weighted and mapped according to its length in the model region and its length in the background region. The specific method for obtaining its frequency domain electric field value is as follows: If the length of the conformal edge in the model region accounts for less than 50% of its total length, then the adjacent regular edge that is collinear with the conformal edge and located in the background region is taken as the weighted edge, and its frequency domain electric field value is obtained using formula (3). If the length of the conformal edge in the model region accounts for not less than 50% of its total length, then the adjacent regular edge that is collinear with the conformal edge and located in the model region is taken as the weighted edge, and its frequency domain electric field value is obtained using formula (4). (3) (4) in, Let be the frequency domain electric field value of the conformal edge. Let be the initial frequency domain electric field value on the conformal edge. The frequency domain electric field value of the weighted edge. This represents the length of the weighted edge.

[0016] In a further technical solution, in step S6, the local specific absorption rate (SAR) of each target grid is calculated using formula (5). loc ; (5) in, σvoxel ρ is the average conductivity of all conformal edges of the target mesh and all regular edges located in the model region. voxel E represents the density of the material in the model region (kg / m³). x E is the average frequency domain electric field value of all edges along the x-direction among all conformal edges of the target mesh and all regular edges located in the model region. y E is the average frequency domain electric field value of all edges along the y-direction among all conformal edges of the target mesh and all regular edges located in the model region. z The average value of the frequency domain electric field along the z-direction is the value of all conformal edges and all regular edges located in the model region of the target mesh. This is the modulo symbol.

[0017] In a further technical solution, the specific process of determining the spatial average specific absorptivity of each target grid based on its local specific absorptivity using a volume weight compensation algorithm in step S7 is as follows: Step (1): Expand the cube outward from the center of each target mesh until the model quality inside the cube reaches the preset quality value; wherein, the center of the expanding cube coincides with the center of the target mesh, and the expansion direction is along the three-dimensional direction of the three-dimensional rectangular coordinate system O-xyz; Step (2): Based on the relative position of the cube and the background region, the target mesh is divided into valid meshes and invalid meshes; wherein, if the volume of the cube of a target mesh located in the background region exceeds 10% of its total volume, or if at least one face is completely located in the background region, then the target mesh is an invalid mesh, otherwise it is a valid mesh. Step (3): For each effective grid, calculate its spatial average specific absorption and mark the portion of the grid within its cube; Specifically, for each valid mesh, the meshes that are completely contained within their cube and located locally within the model region, or entirely within the model region, are called their containing meshes, and each containing mesh is marked "used". The meshes that are partially contained within their cube and located locally or entirely within the model region are called boundary meshes. Then, the total volume of each boundary mesh and the volume of its portion contained within the cube, i.e., the sub-volume, are obtained, and the formula R = ... V part,total / V total,edge Calculate the overall volume weighting coefficients for all boundary meshes, where V part,total The sum of the sub-volumes of all boundary meshes. V total,edgeThe total volume of all boundary meshes is summed. Then, based on the local specific absorptivity of all contained meshes, and the local specific absorptivity of all boundary meshes combined with the overall volume weighting coefficient, the spatial average specific absorptivity of the cube is calculated by volume-weighted averaging. This spatial average specific absorptivity of the cube is then used as the spatial average specific absorptivity of the effective mesh. SAR avg ; Step (4): For each invalid grid, the invalid grid with the label is treated as a "used" grid, and the maximum value of the spatial average specific absorptivity of the valid grids that have been labeled is taken as its spatial average specific absorptivity. Specifically, iterate through all invalid grids, define invalid grids with at least one "use" tag as "used" grids, and define invalid grids without a "use" tag as "unused" grids; for each "used" grid, find all valid grids that have added a "use" tag to the "used" grid, and take the maximum value of the spatial average specific absorption of these valid grids as the spatial average specific absorption of the "used" grid. Step (5): For invalid meshes without markings, expand cubes outward from each surface in multiple directions, take the expanded cube with the smallest volume as the reference, retain other expanded cubes whose volume difference from the reference cube is within a preset range, and take the maximum value of the spatial average specific absorptivity of all retained cubes as its spatial average specific absorptivity. Specifically, for each "unused" mesh, starting from each of its surfaces, a cube is expanded in a direction away from the center of the "unused" mesh until the model quality inside the expanded cube reaches a preset quality value; at this time, each "unused" mesh is expanded to obtain 6 cubes; the smallest of these 6 cubes is taken as the minimum cube, and the other 5 cubes whose volume difference from the minimum cube does not exceed 5% of the minimum cube's volume are taken as the reserved cubes; for each reserved cube, its spatial average specific absorption rate is calculated in the same way as in step (3), but no "used" mark is added to any mesh during this calculation process, and the spatial average specific absorption rate of each reserved cube is obtained; the maximum value is selected from all the spatial average specific absorption rates of the reserved cubes, and this maximum value is taken as the spatial average specific absorption rate of the "unused" mesh.

[0018] In a further technical solution, based on the local specific absorptivity of all grid-containing areas, and the local specific absorptivity of all boundary grids combined with the overall volume weighting coefficient, the spatial average specific absorptivity of the cube is calculated by volume-weighted averaging. SAR avg The calculation formula is as follows: (6) in, N e The total number of boundary grids, N i The total number of grid cells. For the first n e Local specific absorption of each boundary grid, For the first n i Local specific absorption rate containing a grid, SAR avg is the spatial average specific absorptivity of the cube. Attached Figure Description

[0019] Figure 1 This is a flowchart of the high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD of the present invention; Figure 2 This is a schematic diagram of the ray tracing method for generating non-uniform meshes in the high-precision field mapping method for specific absorptivity based on conformal FDTD of non-uniform meshes of the present invention. Figure 3 This is a schematic diagram of the frequency domain electric field mapping principle of the conformal mesh in the high-precision field mapping method of specific absorptivity based on non-uniform mesh conformal FDTD of the present invention; wherein, (a) is a schematic diagram of the conformal mesh including the model region and the background region; (b) is a schematic diagram of the three-dimensional calculation region corresponding to the model region; Figure 4 This is a schematic diagram of the electromagnetic radiation scene of a human body model in a ship deck environment in the high-precision field mapping method of specific absorptivity based on non-uniform mesh conformal FDTD of the present invention. Figure 5 This is a simplified schematic diagram of a human body model subjected to plane wave radiation on a deck in the high-precision field mapping method based on non-uniform mesh conformal FDTD of the present invention. Figure 6 In the high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD of the present invention, the spatial average specific absorptivity is calculated. SAR avg A schematic diagram of the time boundary grid; Figure 7 This is a schematic diagram of the mesh division of the human body model in the high-precision field mapping method based on non-uniform mesh conformal FDTD of the present invention. Figure 8This diagram illustrates the local specific absorptivity comparison analysis of the x-direction profile passing through the center of the model in the high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD of the present invention; where the black solid line represents the result of the commercial electromagnetic simulation software CST (Computer Simulation Technology), the red dashed line represents the result of the traditional FDTD method, and the blue dashed line represents the result of the method of the present invention; Figure 9 In the high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD of the present invention, the central cross-sectional view of the spatial average specific absorptivity of the human body model under oblique incident plane wave illumination is shown; wherein, (a) is the result of the method of the present invention; (b) is the result of the commercial electromagnetic simulation software CST. Figure 10 In the high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD of the present invention, the central cross-sectional view of the spatial average specific absorptivity of the human body model under oblique incident plane wave illumination is shown; wherein, (a) is the result of the method of the present invention; (b) is the result of the commercial electromagnetic simulation software CST. Figure 11 The image shows the central cross-sectional view of the spatial average specific absorptivity in the z-direction of a human body model under oblique plane wave irradiation in the high-precision field mapping method of specific absorptivity based on non-uniform mesh conformal FDTD of the present invention; where (a) is the result of the method of the present invention; and (b) is the result of the commercial electromagnetic simulation software CST. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail and completely below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can understand and implement them. The embodiments described in this section are only used to illustrate the technical solutions of this invention and are not intended to limit the scope of protection of this invention.

[0021] Example: This example provides a high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD, and its flowchart is as follows. Figure 1 As shown. This high-precision field mapping method based on specific absorptivity includes the following steps: S1: Model building and non-uniform mesh generation First, a model including the geometric features of the target to be simulated and the geometric features of the radiation source is established in a three-dimensional rectangular coordinate system O-xyz. Based on the model, a three-dimensional calculation region is determined in the three-dimensional rectangular coordinate system O-xyz. The three-dimensional calculation region can completely cover the area where the model is located. The target to be simulated is the human body, that is, the model is a human body model. Next, the three-dimensional computational domain is divided into non-uniform meshes to form a meshed three-dimensional computational domain with multiple meshes distributed along the three dimensions, specifically: S1.1 Determine the maximum and minimum allowable step size for mesh generation based on the frequency of the radiation source; S1.2 Based on the geometric characteristics of the model (the complexity of the model structure), the three-dimensional computational region is divided into the minimum step size mesh region (such as the head and fine organization), the maximum step size mesh region, and the mesh transition region. S1.3 Set the grid step size of the minimum step size grid region to the minimum allowable step size, set the grid step size of the maximum step size grid region to the maximum allowable step size, and change the step size of the grid transition region in a gradient manner according to the preset adaptive step size to achieve the connection with the minimum step size grid region; S1.4. The three axes of the three-dimensional rectangular coordinate system are respectively denoted as... x axis, y shaft and z Axis; in x axis, y shaft and z Discretization segments are divided along the axial direction using the minimum allowable step size, the maximum allowable step size, and the adaptive step size, respectively. S1.5 After the segmentation is completed, x axis, y shaft and z The boundaries of each axis overlap orthogonally in space, generating a non-uniformly distributed grid. S1.6, will x The total number of axis boundary divisions is denoted as M x , y The total number of axis boundary divisions is denoted as M y , z The total number of axis boundary divisions is denoted as M z Using spatial indexes ( i , j , k The node coordinates of the calibrated mesh are as follows: i =1,2,……, M x , j =1,2,……, M y , k =1,2,……, M z ;( i , j , k )express x Axis No. i A dividing boundary,y Axis No. j Each dividing boundary and z Axis No. k The intersection points of the dividing boundaries are used to indicate the location of the boundary. x Axis No. i Individual, in y Axis No. j Individual and in z Axis No. k The node coordinates of a certain grid are used to establish the mapping relationship between the node coordinates of the grid and the spatial position, thereby realizing the non-uniform grid division of the three-dimensional computing region. Then, the gridded three-dimensional computing region is divided into a model region and a background region. The model region represents the space in which the model is located in the gridded three-dimensional computing region, and the background region is the other regions in the gridded three-dimensional computing region other than the model region. S2: Region Identification Based on Ray Tracing The mesh is placed in the three coordinate planes O-xyz of the three-dimensional Cartesian coordinate system. x O y noodle, x O z Face to face y O z The nodes on the surface serve as source points. A ray is emitted from each source point perpendicular to its coordinate plane. This ray coincides with multiple mesh edges. If the ray intersects the geometric surface of the model, there will be at least one pair of intersection points. Each pair of intersection points is located on the model interface, and the area enclosed by all intersection points is the model region. S3: Material Parameter Determination For each conformal edge, its electromagnetic parameters are determined by weighted calculation based on its length in the model region and its length in the background region, as well as the electromagnetic parameters of the material in the model region. The electromagnetic parameters of the material include the relative permittivity and conductivity. The material in the background region is a vacuum, with a relative permittivity of 1 and a conductivity of 0 S / m. Specifically, its relative permittivity and conductivity are determined using formulas (1) and (2): (1) (2) in, The relative permittivity of the conformal edge. The conductivity of the conformal edge, Let be the relative permittivity of the material in the model region. The relative permittivity of the material in the background region is . The length of the conformal edge in the model region. The length of the conformal edge in the background region. The electrical conductivity of the material in the model region. The electrical conductivity of the material in the background region; S4: Time-domain electric field calculation The electric field on each edge is iteratively calculated using the finite-difference time-domain algorithm to obtain the time-domain electric field of each edge; S5: Calculation of frequency domain electric field value At the preset calculation frequency (1.1 GHz in this embodiment), for each conventional edge, its time-domain electric field is converted into a frequency-domain electric field value; for each conformal edge, its time-domain electric field is first converted into an initial frequency-domain electric field value, and then its initial frequency-domain electric field value is weighted and mapped according to its length in the model region and its length in the background region to obtain its frequency-domain electric field value. Specifically, if the length of the conformal edge in the model region accounts for less than 50% of its total length, then the adjacent conventional edges that are collinear with the conformal edge and located in the background region are taken as weighted edges, and their frequency-domain electric field value is obtained using formula (3); if the length of the conformal edge in the model region accounts for not less than 50% of its total length, then the adjacent conventional edges that are collinear with the conformal edge and located in the model region are taken as weighted edges, and their frequency-domain electric field value is obtained using formula (4). (3) (4) in, Let be the frequency domain electric field value of the conformal edge. Let be the initial frequency domain electric field value on the conformal edge. The frequency domain electric field value of the weighted edge. The length of the weighted edge; Thus, this weighted mapping optimizes the physical property description at the medium interface and reduces the boundary error caused by the traditional step approximation. S6: Calculation of local specific absorption rate Each grid cell that is partially located in the model region and partially located in the background region, as well as each grid cell that is entirely located in the model region, are considered as target grid cells. For each target grid cell, its local specific absorption rate (SAR) is calculated using formula (5). loc ; (5) in, σ voxel ρ is the average conductivity of all conformal edges of the target mesh and all regular edges located in the model region. voxel E represents the density of the material in the model region (kg / m³). x E is the average frequency domain electric field value of all edges along the x-direction among all conformal edges of the target mesh and all regular edges located in the model region.y E is the average frequency domain electric field value of all edges along the y-direction among all conformal edges of the target mesh and all regular edges located in the model region. z The average value of the frequency domain electric field along the z-direction is the value of all conformal edges and all regular edges located in the model region of the target mesh. The modulo symbol; S7: Calculation of Spatial Average Specific Absorption For each target grid, its spatial average specific absorptivity is determined based on its local specific absorptivity using a volume weight compensation algorithm, specifically as follows: Step (1): Expand the cube outward from the center of each target mesh until the model mass inside the cube reaches the preset mass value (such as 1g or 10g); wherein the center of the expanding cube coincides with the center of the target mesh, and the expansion direction is along the three-dimensional direction of the three-dimensional rectangular coordinate system O-xyz; Step (2): Based on the relative position of the cube and the background region, the target mesh is divided into valid meshes and invalid meshes; wherein, if the volume of the cube of a target mesh located in the background region exceeds 10% of its total volume, or if at least one face is completely located in the background region, then the target mesh is an invalid mesh, otherwise it is a valid mesh. Step (3): For each effective grid, calculate its spatial average specific absorption and mark the portion of the grid within its cube; Specifically, for each valid mesh, the meshes that are completely contained within their cube and located locally within the model region, or entirely within the model region, are called their containing meshes, and each containing mesh is marked "used". The meshes that are partially contained within their cube and located locally or entirely within the model region are called boundary meshes. Then, the total volume of each boundary mesh and the volume of its portion contained within the cube, i.e., the sub-volume, are obtained, and the formula R = ... V part,total / V total,edge Calculate the overall volume weighting coefficients for all boundary meshes, where V part,total The sum of the sub-volumes of all boundary meshes. V total,edge The total volume of all boundary meshes is summed. Then, based on the local specific absorptivity of all contained meshes, and the local specific absorptivity of all boundary meshes combined with the overall volume weighting coefficient, the spatial average specific absorptivity of the cube is calculated by volume-weighted averaging. This spatial average specific absorptivity of the cube is then used as the spatial average specific absorptivity of the effective mesh. SAR avg Spatial average specific absorptivity SARavg The calculation formula is as follows: (6) in, N e The total number of boundary grids, N i The total number of grid cells. For the first n e Local specific absorption of each boundary grid, For the first n i Local specific absorption rate containing a grid, SAR avg The spatial average specific absorptivity of the cube; Step (4): For each invalid grid, the invalid grid with the label is treated as a "used" grid, and the maximum value of the spatial average specific absorptivity of the valid grids that have been labeled is taken as its spatial average specific absorptivity. Specifically, iterate through all invalid grids, define invalid grids with at least one "use" tag as "used" grids, and define invalid grids without a "use" tag as "unused" grids; for each "used" grid, find all valid grids that have added a "use" tag to the "used" grid, and take the maximum value of the spatial average specific absorption of these valid grids as the spatial average specific absorption of the "used" grid. Step (5): For invalid meshes without markings, expand cubes outward from each surface in multiple directions, take the expanded cube with the smallest volume as the reference, retain other expanded cubes whose volume difference from the reference cube is within a preset range, and take the maximum value of the spatial average specific absorptivity of all retained cubes as its spatial average specific absorptivity. Specifically, for each "unused" mesh, starting from each of its surfaces, a cube is expanded in a direction away from the center of the "unused" mesh until the model quality inside the expanded cube reaches a preset quality value; at this time, each "unused" mesh is expanded to obtain 6 cubes; the smallest of these 6 cubes is taken as the minimum cube, and the other 5 cubes whose volume difference from the minimum cube does not exceed 5% of the minimum cube's volume are taken as the reserved cubes; for each reserved cube, its spatial average specific absorption rate is calculated in the same way as in step (3), but no "used" mark is added to any mesh during this calculation process, and the spatial average specific absorption rate of each reserved cube is obtained; the maximum value is selected from all the spatial average specific absorption rates of the reserved cubes, and this maximum value is taken as the spatial average specific absorption rate of the "unused" mesh.

[0022] Table 1 shows the uniform and non-uniform mesh partitioning of the above human body model with a minimum mesh size of 0.005m. The uniform mesh has 743,512,500 meshes with a minimum mesh size of 0.005m, while the non-uniform mesh has only 90,051,870 meshes with a minimum mesh size of 0.005m. This significantly reduces the computational load and storage requirements. The method of this invention has a higher computational speed than the uniform mesh FDTD method, and also shortens the specific absorption rate calculation time.

[0023] Table 1

[0024] Figure 2 This is a schematic diagram of the ray tracing method provided in an embodiment of the present invention. For example... Figure 2 As shown, in ray tracing, frequent ray-geometric patch intersection tests are required to determine whether the ray interacts with the model, which can effectively generate high-quality FDTD meshes. The plane equation of the triangular element is as follows:

[0025] In the formula, A, B, and C are the components of the normal vector n=(A,B,C) of the triangular facet plane, which determine the direction of the plane; D is a constant that determines the position of the plane in space. The intersection point between the ray and the triangular facet can be obtained from the above formula, and the length of the edge occupied by the conformal mesh and different media can be determined from the intersection point.

[0026] Figure 3 This is a schematic diagram illustrating the principle of conformal mesh frequency domain electric field mapping provided in an embodiment of the present invention, as shown below. Figure 3 As shown, because the FDTD algorithm is based on the Yee mesh, we treat the electric field value as the edge and the magnetic field value as the center. Since part of the mesh is air, the electric field value will exhibit a step at the medium interface. We use a weighted linear mapping: when the conformal mesh material accounts for more than 50%, a weighted linear mapping is performed with the model interior; when the conformal mesh material accounts for less than 50%, a weighted linear mapping is performed with the model exterior. This method optimizes the frequency domain electric field distribution at the model boundary, thereby improving the accuracy of the local specific absorptivity calculation. This mapping method is closer to the actual physical meaning and can significantly reduce the error of the local specific absorptivity R at the model boundary, improving the accuracy of the local specific absorptivity.

[0027] Figure 4 This is a schematic diagram illustrating an electromagnetic radiation scenario of a human body on a ship's deck, provided as an embodiment of the present invention. Figure 4 As shown, the main image displays a three-dimensional physical model of the ship, while the enlarged view within the dashed box in the upper left corner shows the specific distribution and spatial proportions of the human body model on the ship's deck, used to define the physical boundaries and exposure environment when calculating the specific absorption rate.

[0028] Figure 5 This is a simplified schematic diagram of a human body model subjected to plane wave radiation on a deck, as provided in an embodiment of the present invention. This embodiment uses numerical simulation of the human body model shown in the figure to further verify the optimization of the conformal FDTD mapping method for calculating the absorptivity of non-uniform meshes.

[0029] This embodiment simulates the spatial average specific absorptivity of a typical human body structure at a frequency of 1.1 GHz under continuous plane wave irradiation with an amplitude of 1000 V / m. The simulation conditions are set as follows: the plane wave is incident along the positive z-direction; the relative permittivity of human tissue is set to 12, the conductivity is set to 0.08, and the density is set to 1000 kg / m³; the metal dielectric plate material is PEC (Perfect Electric Conductor).

[0030] Figure 6 This is a schematic diagram illustrating the local average specific absorptivity at the boundary of a cube during the calculation of the average specific absorptivity in a non-uniform grid space, as provided in an embodiment of the present invention.

[0031] like Figure 6 As shown, when analyzing the portion of an extended cube using a mesh, it can be observed that the left side occupies only half the volume using a mesh, while the right side occupies more than half. According to the IEEE / IEC calculation standard, averaging the local specific absorptivity of all parts using a mesh based on volume introduces errors in the spatial average specific absorptivity of the central mesh. These errors are particularly pronounced with greater mesh inhomogeneity. To address this, we separate the averaging of different edges and sections using a mesh, averaging the left and right sides separately based on their respective volumes. This reduces the error in spatial average specific absorptivity calculations using non-uniform mesh FDTD.

[0032] Figure 7 This is a schematic diagram of the mesh division of a non-uniform mesh human body model provided in an embodiment of the present invention, as shown below. Figure 7 The image shown is a cross-sectional view of a non-uniform mesh generated using ray tracing based on triangular facets. This ray tracing method generates a high-quality non-uniform mesh, while using a coarser mesh in the homogeneous medium region based on the model and electromagnetic properties, significantly reducing computational load and memory consumption. This results in a substantial improvement in the algorithm's computational efficiency and accuracy.

[0033] Figure 8 This is a schematic diagram illustrating the local specific absorption rate comparison analysis of the x-direction profile passing through the center of the model, provided in an embodiment of the present invention. Figure 8As shown, the black solid line corresponding to CST represents the local specific absorption rate obtained by simulating a conventional conformal test case using the commercial electromagnetic simulation software CST; the red dashed line corresponding to conformal represents the local specific absorption rate obtained by simulating a conventional conformal test case using the traditional FDTD; and the blue dashed line corresponding to modified conformal represents the local specific absorption rate obtained by simulating a conventional conformal test case using the method of this invention.

[0034] analyze Figure 8 It can be seen that the local specific absorptivity results obtained by the method of the present invention are highly consistent with the simulation results of the commercial electromagnetic simulation software CST. The error of the local specific absorptivity results obtained by the method of the present invention is about 6%; while the error of the local specific absorptivity of the uncorrected conformal grid frequency domain electric field is about 40%. This shows that the method of the present invention effectively reduces the local specific absorptivity error of the conformal grid.

[0035] Figure 9 (a) is a spatial average specific absorptivity distribution diagram of the cross section at the center point of the calculation region in the x-direction in the human body model case under oblique plane wave incidence; (a) is a diagram of the method of the present invention for the above Figure 5 (a) Spatial average specific absorption rate results obtained from human body model case simulation; (b) Results of the above using commercial electromagnetic simulation software CST. Figure 5 The spatial average specific absorption rate results obtained from human body model case simulation.

[0036] Depend on Figure 9 As can be seen, the specific absorption rate distribution trend of the calculation results of the method of the present invention is basically consistent with that of the simulation results of the commercial electromagnetic simulation software CST on the distribution map. The high specific absorption rate region is mainly concentrated on the electromagnetic wave incident side and the local boundary region of the human body. The hot spot location and intensity variation law are well matched, indicating that the present invention can accurately characterize the spatial average specific absorption rate distribution on the x-direction section.

[0037] Figure 10 (a) is a spatial average specific absorptivity distribution diagram of the cross section where the center point of the calculation region is located in the y-direction in the human body model case under oblique plane wave incidence; (a) is a diagram of the method of the present invention for the above Figure 5 (a) Spatial average specific absorption rate results obtained from human body model case simulation; (b) Results of the above using commercial electromagnetic simulation software CST. Figure 5 The spatial average specific absorption rate results obtained from human body model case simulation.

[0038] Depend on Figure 10 As can be seen, the specific absorption rate distribution pattern of the calculation results of the method of the present invention is consistent with that of the simulation results of the commercial electromagnetic simulation software CST on the distribution map. The energy absorption distribution on both sides of the human body and at the local curved surface boundary can be effectively captured, indicating that the present invention has good calculation accuracy for the electromagnetic energy deposition distribution in the transverse section.

[0039] Figure 11 (a) is a spatial average specific absorptivity distribution of the cross section at the center point of the calculation region in the z-direction in the human body model case under oblique plane wave incidence; (a) is a diagram of the method of the present invention for the above-mentioned Figure 5 (a) Spatial average specific absorption rate results obtained from human body model case simulation; (b) Results of the above using commercial electromagnetic simulation software CST. Figure 5 The spatial average specific absorption rate results obtained from human body model case simulation.

[0040] Depend on Figure 11 As can be seen, the calculation results of the method of the present invention are consistent with the simulation results of the commercial electromagnetic simulation software CST in terms of specific absorptivity hot spots, attenuation trends and overall distribution patterns on the distribution map. It can reflect the specific absorptivity changes of different tissue regions within the longitudinal section of the human body, further verifying the accuracy of the present invention in calculating the spatial average specific absorptivity under three-dimensional non-uniform grid conditions.

Claims

1. A high-precision field mapping method based on conformal FDTD of non-uniform mesh, characterized in that, Includes the following steps: S1: Perform non-uniform meshing on the 3D computational region containing the model, and determine the model region and background region; S2: In each mesh, the edges that are locally located in the model region and locally located in the background region are marked as conformal edges, and the other edges are marked as regular edges; S3: For each conformal edge, the electromagnetic parameters of its material are determined by weighted calculation based on its length in the model region and the background region, as well as the electromagnetic parameters of the material in the model region. S4: The electric field on each edge is iteratively calculated using the finite-difference time-domain algorithm to obtain the time-domain electric field of each edge; S5: At the preset calculation frequency, for each regular edge, its time-domain electric field is converted into its frequency-domain electric field value; for each conformal edge, after its time-domain electric field is converted into an initial frequency-domain electric field value, the initial frequency-domain electric field value is weighted and mapped according to its length in the model region and the background region to obtain its frequency-domain electric field value. S6: Treat each grid, whether partially or entirely located in the model region, as a target grid; for each target grid, calculate its local specific absorption rate based on the frequency domain electric field values ​​of its conformal edges and all regular edges located in the model region; S7: For each target grid, its spatial average specific absorptivity is determined by a volume weight compensation algorithm based on its local specific absorptivity.

2. The high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD according to claim 1, characterized in that, In step S1, the model is established in a three-dimensional rectangular coordinate system O-xyz; the three-dimensional computational region can completely cover the region where the model is located; the three-dimensional computational region containing the model is divided into a non-uniform mesh to form a meshed three-dimensional computational region; the meshed three-dimensional computational region is divided into a model region and a background region using ray tracing, specifically: the mesh is placed in the three coordinate planes of the three-dimensional rectangular coordinate system O-xyz. x O y noodle, x O z Face to face y O z The nodes on the surface serve as source points. Rays are emitted from each source point perpendicular to its coordinate plane. These rays coincide with multiple mesh edges. If a ray intersects the geometric surface of the model, there will be at least one pair of intersection points. Each pair of intersection points is located on the model interface, and the area enclosed by all the intersection points is the model region.

3. The high-precision field mapping method for specific absorptivity based on conformal FDTD with non-uniform mesh as described in claim 1, characterized in that, The electromagnetic parameters of the material include relative permittivity and conductivity. The background region material is a vacuum with a relative permittivity of 1 and a conductivity of 0 S / m.

4. The high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD according to claim 1, characterized in that, For each conformal edge, its relative permittivity and conductivity are determined using formulas (1) and (2), respectively: （1） （2） in, The relative permittivity of the conformal edge. The conductivity of the conformal edge, Let be the relative permittivity of the material in the model region. The relative permittivity of the material in the background region is . The length of the conformal edge in the model region. The length of the conformal edge in the background region. The electrical conductivity of the material in the model region. The background region material has electrical conductivity.

5. The high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD according to claim 1, characterized in that, In step S5, for each conformal edge, after converting its time-domain electric field into an initial frequency-domain electric field value, its initial frequency-domain electric field value is weighted and mapped according to its length in the model region and its length in the background region. The specific method for obtaining its frequency-domain electric field value is as follows: If the length of the conformal edge in the model region accounts for less than 50% of its total length, then the adjacent regular edges that are collinear with the conformal edge and located in the background region are taken as weighted edges, and their frequency-domain electric field value is obtained using formula (3). If the length of the conformal edge in the model region accounts for not less than 50% of its total length, then the adjacent regular edges that are collinear with the conformal edge and located in the model region are taken as weighted edges, and their frequency-domain electric field value is obtained using formula (4). （3） （4） in, Let be the frequency domain electric field value of the conformal edge. The length of the conformal edge in the model region. The length of the conformal edge in the background region. Let be the initial frequency domain electric field value on the conformal edge. The frequency domain electric field value of the weighted edge. This represents the length of the weighted edge.

6. The high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD according to claim 1, characterized in that, In step S6, the local specific absorption rate of each target grid is calculated based on the average conductivity of all conformal edges and all conventional edges located in the model region, the density of the material in the model region, and the average frequency domain electric field values ​​of all edges along the x-axis, y-axis, and z-axis directions of all conformal edges and all conventional edges located in the model region.

7. The high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD according to claim 1, characterized in that, In step S7, the specific process of determining the spatial average specific absorptivity of each target grid based on its local specific absorptivity using a volume weight compensation algorithm is as follows: Step (1): Expand the cube outward from the center of each target mesh until the model quality inside the cube reaches the preset quality value; Step (2): Based on the relative position of the cube and the background area, the target mesh is divided into valid meshes and invalid meshes; Step (3): For each effective grid, calculate its spatial average specific absorption and mark the portion of the grid within its cube; Step (4): For each invalid grid, the invalid grid with the label is treated as a "used" grid, and the maximum value of the spatial average specific absorptivity of the valid grids that have been labeled is taken as its spatial average specific absorptivity. Step (5): For invalid meshes without markings, expand cubes outward from each surface in multiple directions, take the expanded cube with the smallest volume as the reference, retain other expanded cubes whose volume difference from the reference cube is within a preset range, and take the maximum value of the spatial average specific absorptivity of all retained cubes as its spatial average specific absorptivity.

8. The high-precision field mapping method for specific absorptivity based on non-uniform mesh conformal FDTD according to claim 7, characterized in that, In step (3), the spatial average specific absorption rate of the cube is calculated by volume weighted average based on the grids that are at least partially located in the model region and are partially or entirely contained within the cube, the grids that are partially contained within the cube and are located in the model region, and the volume proportion of these grids contained in the cube.

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