Analysis method, analysis device, and analysis program

Abstract

To reduce the calculation time of an electromagnetic field in the FDTD method and reduce the amount of usage of a memory.SOLUTION: An analysis method of an embodiment is an analysis method for performing electromagnetic field analysis by using the finite-difference time-domain method (FDTD method). The analysis method of the embodiment includes: setting a plurality of voxels in an analysis area; setting at least one of the plurality of voxels as a release voxel based on a model of the analysis area; and repeatedly executing updating a time step and electromagnetic field component calculation processing targeted for each of the plurality of voxels. The calculation processing includes calculation of electric field components targeted for the plurality of voxels and application of an absorption boundary condition to the electric field components. In the calculation processing, calculation of the electric field component targeted for at least one release voxel is omitted.SELECTED DRAWING: Figure 7

Description

Technical Field

[0001] Embodiments relate to an analysis method, an analysis apparatus, and an analysis program.

Background Art

[0002] As the speed of wireless communication systems increases, the need to appropriately analyze the electromagnetic fields generated by devices is increasing. As one method for analyzing electromagnetic fields, the FDTD method (Finite-Difference Time-Domain method) is known. The FDTD method is an electromagnetic field analysis technique that divides an analysis region into a large number of blocks (hereinafter referred to as voxels) and updates the electric field and magnetic field generated by a wave source in the analysis region over time based on Maxwell's equations.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0004] However, the FDTD method requires securing memory for holding the electric field, magnetic field, and medium constants corresponding to each voxel in the analysis region, and performing update formula calculations for the electric field, magnetic field, and absorption boundary, from the start of iterative calculations (time 0) for reproducing the passage of time until the set end time. For this reason, the FDTD method has a problem that it is necessary to secure a large amount of memory and the calculation time becomes long when analyzing a large-scale analysis region or when analyzing propagation characteristics for a high frequency band such as fifth-generation mobile communication.

[0005] Therefore, an object of the present invention is to provide an analysis method, an analysis apparatus, and an analysis program that can shorten the calculation time of the electromagnetic field in the FDTD method and suppress the amount of memory used.

Means for Solving the Problems

[0006] The analysis method of the embodiment is an analysis method for performing electromagnetic field analysis using the FDTD method (Finite-Difference Time-Domain method). The analysis method of the embodiment includes setting a plurality of voxels in the analysis region, setting at least one of the plurality of voxels as a free voxel based on the model of the analysis region, and repeatedly executing the update of the time step and the calculation process of the electromagnetic field components for each of the plurality of voxels. The calculation process includes the calculation of the electric field components for the plurality of voxels and the application of the absorption boundary condition to the electric field components. In the calculation process, the calculation of the electric field components for at least one free voxel is omitted.

Effects of the Invention

[0007] The analysis method of the embodiment can shorten the calculation time of the electromagnetic field in the FDTD method and suppress the amount of memory used.

Brief Description of the Drawings

[0008]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Embodiments for Carrying Out the Invention

[0009] Embodiments will be described below with reference to the drawings. The embodiments illustrate apparatuses and methods for embodying the technical idea of the invention. The drawings are schematic or conceptual. In the following description, components having substantially the same function and configuration are denoted by the same reference numerals. The X direction, Y direction, and Z direction correspond to directions that intersect each other.

[0010] <1>Overview of the FDTD Method FIG. 1 is a perspective view showing an example of an analysis region AR determined by electromagnetic field analysis processing using the FDTD method. As shown in FIG. 1, the analysis region AR is, for example, a three-dimensional region having a width Lx along the X direction, a depth Ly along the Y direction, and a height Lz along the Z direction. The analysis region AR includes, for example, a wave source 1 and at least one object 2. The wave source 1 is a transmission point of radio waves (electromagnetic fields). When the medium constant in the analysis region AR is uniform, the radio waves transmitted from the wave source 1 propagate in a spherical shape (radial shape in the electric field strength contour diagram) centered on the wave source 1. As the medium constant, conductivity, permeability, etc. are used. The object 2 has a medium constant different from that of the space in the analysis region AR. The object 2 is, for example, a building. The number of objects 2 set in the analysis region AR, the shape of the object 2, the medium constant for each object 2, etc. are appropriately set according to the model to be analyzed. A plurality of models can be applied to the analysis region AR.

[0011] FIG. 2 is a perspective view showing an example of the setting of voxels in the electromagnetic field analysis process using the FDTD method. As shown in FIG. 2, in the electromagnetic field analysis process using the FDTD method, the analysis region AR is divided into a plurality of blocks (voxels VX) arranged three-dimensionally. The voxel VX is set to an arbitrary size. Coordinate values (x coordinate, y coordinate, z coordinate) are set for each voxel VX, and medium constants such as the object 2 corresponding to the coordinate values are associated. Note that the analysis region AR is an analysis target with an absorption boundary condition set around it, and the number of voxels VX is finite. In the FDTD method, when performing time updates of the electric field and magnetic field, the electric field and magnetic field calculated at the previous time step and the medium constant for each voxel VX are used. Therefore, in order to calculate the electromagnetic field using the FDTD method, memory for holding the electric field, magnetic field, and medium constant corresponding to the number of voxels VX is required.

[0012] FIG. 3 is a schematic diagram showing an outline of the method for calculating electromagnetic field components using the FDTD method. As shown in FIG. 3, when the calculation of electromagnetic field components starts in the FDTD method (calculation start), arrays for the electric field and magnetic field of each voxel VX in the analysis region AR are set. This "array" corresponds to the memory area used for the calculation of the electric field and magnetic field in the analysis region AR and is assigned to each voxel VX. Then, the three components of the electric field (Ex, Ey, Ez) and the three components of the magnetic field (Hx, Hy, Hz) are updated for each voxel VX at a predetermined time interval. Ex, Ey, and Ez correspond to the electric field components along the x direction, y direction, and z direction, respectively. Hx, Hy, and Hz correspond to the magnetic field components along the x direction, y direction, and z direction, respectively. When each of the electric field components and magnetic field components converges, the calculation of the electromagnetic field components ends (calculation end). Note that when the electromagnetic field is analyzed using a plurality of models, for example, the calculation is executed for each single model. Hereinafter, the calculation of the electromagnetic field components and the number of update times are referred to as the number of time steps. For example, when the number of voxels of one model is M and the number of time steps is T, the number of accesses to the memory when the model is used is M×T times.

[0013] <2>Configuration <2-1>Hardware Configuration of Analysis Device 10 FIG. 4 is a block diagram showing an example of the hardware configuration of the analysis device 10 according to the embodiment. As shown in FIG. 4, the analysis device 10 includes, for example, an input unit 20, an output unit 21, a communication unit 22, a CPU (Central Processing Unit) 23, a ROM (Read Only Memory) 24, a RAM (Random Access Memory) 25, a storage medium 26, and a bus 27. The input unit 20, the output unit 21, the communication unit 22, the CPU 23, the ROM 24, the RAM 25, and the storage medium 26 are connected via the bus 27 and have functions as a computer.

[0014] The input unit 20 is an input device such as a keyboard or a mouse, for example. The output unit 21 is a display device such as a display, for example. The communication unit 22 is a network interface used for wired or wireless communication, for example. The CPU 23 is an integrated circuit capable of executing various programs. The CPU 23 realizes the analysis function of the analysis device 10 described later by executing a program developed in the RAM 25, for example. The ROM 24 is a non-volatile semiconductor memory. The ROM 24 stores programs and control data for controlling the analysis device 10. The RAM 25 is a volatile semiconductor memory, for example. The RAM 25 is used as a working area for the CPU 23. The storage medium 26 is a storage device that stores data non-volatilely. As the storage medium 26, for example, an HDD (Hard Disk Drive) or an SSD (Solid State Drive) is used. The storage medium 26 may be built into the analysis device 10 or externally attached.

[0015] <2-2>Functional Configuration of Analysis Device 10 FIG. 5 is a block diagram showing an example of the functional configuration of the analysis apparatus 10 according to the embodiment. As shown in FIG. 5, the analysis apparatus 10 includes a storage unit 31, a parameter setting unit 32, an array initialization unit 33, an array data reading unit 34, a calculation unit 35, and buses 100 and 102. The storage unit 31 is connected to the parameter setting unit 32, the array initialization unit 33, and the array data reading unit 34 via the bus 100, and is connected to the calculation unit 35 via the bus 102.

[0016] The storage unit 31 is composed of a memory (for example, RAM 25) capable of reading and writing data via the bus 100 and the bus 102. The storage unit 31 has, for example, an analysis space information storage unit 310 and a voxel model storage unit 312. The analysis space information storage unit 310 stores information regarding the analysis region AR. For example, the analysis space information storage unit 310 stores the permittivity of each voxel VX. The voxel model storage unit 312 stores at least one model associated with the analysis region AR. Note that the storage unit 31 may store the processing results of the calculation unit 35 and the like.

[0017] The parameter setting unit 32 sets the analysis space size, the voxel size, the definition of the discrete time interval, and the analysis model (such as an antenna and the conditions of the analysis space) for the analysis region AR. In addition, the parameter setting unit 32 sets the release voxels RVX based on the analysis model and the like. The release voxels RVX are voxels VX that are excluded from the calculation and update of the electromagnetic field described later. Then, the parameter setting unit 32 stores these set values in the storage unit 31. The array initialization unit 33 secures an array of a size necessary for the analysis process and stores the secured array in the storage unit 31. The array data reading unit 34 reads the array data used for the calculation of the electric field and the magnetic field and stores it in the storage unit 31.

[0018] The calculation unit 35 has units for calculating the electric field and the magnetic field. Specifically, the calculation unit 35 includes an electric field component calculation unit 350, an electric field absorption boundary condition calculation unit 352, a magnetic field component calculation unit 354, and a magnetic field absorption boundary condition calculation unit 356.

[0019] The electric field component calculation unit 350 reads out the permittivity for each voxel VX from the analysis space information storage unit 310 and reads out the model from the voxel model storage unit 312. Then, the electric field component calculation unit 350 calculates the electric field components for each voxel VX based on the permittivity and the model for each read voxel VX, and stores the calculation results in the storage unit 31. The electric field absorption boundary condition calculation unit 352 calculates the absorption boundary conditions for the electric field components in the analysis region AR. Then, the electric field absorption boundary condition calculation unit 352 executes a calculation to apply the absorption boundary conditions to the electric field components calculated by the electric field component calculation unit 350, and stores the calculation results in the storage unit 31.

[0020] The magnetic field component calculation unit 354 reads out the permittivity for each voxel VX from the analysis space information storage unit 310 and reads out the model from the voxel model storage unit 312. Then, the magnetic field component calculation unit 354 calculates the magnetic field components for each voxel VX based on the permittivity and the model for each read voxel VX, and stores the calculation results in the storage unit 31. The magnetic field absorption boundary condition calculation unit 356 calculates the absorption boundary conditions for the magnetic field components in the analysis region AR. Then, the magnetic field absorption boundary condition calculation unit 356 executes a calculation to apply the absorption boundary conditions to the magnetic field components calculated by the magnetic field component calculation unit 354, and stores the calculation results in the storage unit 31.

[0021] <3> Operations <3-1> Analysis Processing in the Comparative Example FIG. 6 is a flowchart showing an example of the flow of electromagnetic field analysis processing in the comparative example. Hereinafter, with reference to FIG. 6, an example of the flow of electromagnetic field analysis processing in the comparative example will be described.

[0022] The CPU 23 starts the analysis processing in response to, for example, a user operation (Start).

[0023] First, the CPU 23 reads out the calculation target model (S100). In other words, the model associated with the current calculation target is read out from the voxel model storage unit 312, and the voxel model is generated.

[0024] Next, the CPU 23 determines the analysis region AR (S102). In other words, for example, the parameter setting unit 32 sets the analysis region AR for the calculation target.

[0025] Next, the CPU 23 sets the voxel VX in the analysis region AR (S104). Specifically, for example, the parameter setting unit 32 inputs the three-dimensional (i, j, k) absolute coordinate values set for each voxel VX into the voxel model storage unit 312. "i" corresponds to the x-axis index (i = 1, 2,..., Nx), "j" corresponds to the y-axis index (j = 1, 2,..., Ny), and "k" corresponds to the z-axis index (k = 1, 2,..., Nz).

[0026] Next, the CPU 23 secures an array (S106). Specifically, the array initialization unit 33 secures an area for calculating the three components of the electric field (Ex, Ey, Ez) and the three components of the magnetic field (Ex, Ey, Ez) on the memory (for example, RAM 25).

[0027] Next, the CPU 23 assigns a permittivity to each voxel VX (S108). Specifically, the array data reading unit 34 reads out the permittivity corresponding to each set coordinate value from the voxel model storage unit 312.

[0028] Next, the CPU 23 updates the time step (S110). When the process of S110 is the first time, an initial value (for example, "1") is applied as the number of time steps. When the process of S110 is the second time or later in the analysis process, the number of time steps becomes a numerical value corresponding to the number of times the process of S110 has been executed.

[0029] Next, the CPU 23 calculates the electric field component (S112). In the calculation of the electric field component, the electric field component calculation unit 350 calculates the electric field component in the analysis region AR using the difference equation obtained by expanding Maxwell's equations in the spatial and temporal domains and the voxel model generated in the process of S100.

[0030] Next, the CPU 23 applies an absorption boundary condition to the electric field component (S114). In applying the absorption boundary condition to the electric field component, the electric field absorption boundary condition calculation unit 352 uses the electric field component calculated in the process of S112 and the magnetic field component calculated in the process of S116 described later to calculate the absorption boundary condition of the electric field component so that electromagnetic waves are not reflected at the boundary of the analysis region AR. Note that the electric field absorption boundary condition calculation unit 352 uses, as the magnetic field component when first calculating the absorption boundary condition of the electric field component, for example, a magnetic field component of "0" or a preset initial value.

[0031] Next, the CPU 23 calculates the magnetic field component (S116). Specifically, the magnetic field component calculation unit 354 calculates the magnetic field component in the analysis region AR using the difference equation obtained by expanding Maxwell's equations in the spatial and temporal domains and the voxel model generated in the process of S100.

[0032] Next, the CPU 23 applies an absorption boundary condition to the magnetic field component (S118). Specifically, the magnetic field absorption boundary condition calculation unit 356 uses the electric field component calculated in the process of S112 and the magnetic field component calculated in the process of S116 to calculate the absorption boundary condition of the magnetic field component so that electromagnetic waves are not reflected at the boundary of the analysis region AR. Note that the electric field absorption boundary condition calculation unit 352 uses a magnetic field component of "0" or a preset initial value when first calculating the absorption boundary condition of the electric field component.

[0033] Next, the CPU 23 determines whether the calculation of the electromagnetic field component has converged (S120). Specifically, for example, the CPU 23 determines whether the calculation of the electromagnetic field component has converged by comparing the respective numerical values of the electric field components (Ex, Ey, Ez) and the magnetic field components (Hx, Hy, Hz) at the current time step with the calculation results of the electromagnetic field components at the previous time step.

[0034] If the calculation of the electromagnetic field component has not converged in the process of S120 (S120, NO), the CPU 23 proceeds to the process of S110. That is, the CPU 23 executes the calculation and update of the electromagnetic field component at the next time step.

[0035] When the calculation of the electromagnetic field components converges in the process of S120 (S120, YES), the CPU 23 ends the series of processes shown in FIG. 6 (END). After that, the analysis device 10 stores the analysis result in, for example, the storage medium 26. Note that the analysis device 10 may display the analysis result on the output unit 21.

[0036] <3-2>Analysis process in the embodiment FIG. 7 is a flowchart showing an example of the flow of the electromagnetic field analysis process in the embodiment. As shown in FIG. 7, the analysis process of the embodiment has a configuration in which S200 and S202 are added between S106 and S108, and S114 is replaced with S204, as compared with the analysis process of the comparative example shown in FIG. 6.

[0037] Specifically, first, when starting the analysis process in the same manner as in the comparative example (START), the CPU 23 reads out the calculation target model (S100), determines the analysis region AR (S102), sets the voxel VX in the analysis region AR (S104), and secures an array (S106).

[0038] Next, the CPU 23 extracts the release voxel RVX from the analysis region AR (S200). As an example of the method for extracting the release voxel RVX, first, the CPU 23 (for example, the parameter setting unit 32) calculates the wavelength λ corresponding to the frequency to be analyzed. Then, the CPU 23 derives a region included in the three-dimensional space inside the building structure such as a building or at a distance greater than several times the wavelength λ from the surface of the building as a deletion region. Then, the CPU 23 sets the voxel VX corresponding to the deletion region as the release voxel RVX. After that, the CPU 23 sets a two-dimensional absorption surface corresponding to each axial direction on the voxel VX at the interface surface in contact with the deletion region (release voxel RVX). Details of the calculation method of this two-dimensional absorption surface will be described later.

[0039] Next, the CPU 23 releases the array corresponding to the release voxel RVX (S202). In other words, the CPU 23 releases the memory area allocated to the voxel VX set in the release voxel RVX. The CPU 23 can use the released memory area for other processes.

[0040] Next, similar to the comparative example, the CPU 23 assigns a medium constant to each voxel VX (S108), updates the time step (S110), and calculates the electric field component (S112). Note that in the analysis process of the embodiment, the calculation of the electric field component for the release voxel RVX is omitted.

[0041] Next, the CPU 23 applies an absorption boundary condition to the electric field component including the region boundary surface of the release voxel RVX (S204). In other words, the CPU 23 applies the absorption boundary condition not only to the region boundary surface between adjacent voxels VX but also to the region boundary surface between the release voxel RVX and the voxel VX.

[0042] Next, similar to the comparative example, the CPU 23 calculates the magnetic field component (S116), applies the absorption boundary condition to the magnetic field component (S118), and determines whether the calculation of the electromagnetic field component has converged (S120). Other operations in the analysis process of the embodiment are the same as those in the analysis process of the comparative example.

[0043] FIG. 8 is a schematic diagram showing an overview of the electromagnetic field analysis process in the embodiment. As shown in FIG. 8, when the calculation of the electromagnetic field components starts in the embodiment (calculation start), arrays for the electric field and magnetic field of each voxel VX in the analysis region AR are set by the processes of S100, S102, S104, and S106. Then, by the processes of S200, S202, and S204, the released voxels RVX are extracted, and the arrays assigned to the released voxels RVX are released. The processes of S110, S112, S206, S116, S118, and S120 are executed, and the three components of the electric field (Ex, Ey, Ez) and the three components of the magnetic field (Hx, Hy, Hz) are updated at a predetermined time interval for each voxel VX. In this calculation, as described with reference to FIG. 7, a two-dimensional absorption surface is set between the released voxels RVX and the voxels VX, and the calculation of the electric field components for the released voxels RVX is omitted. When each of the electric field components and the magnetic field components converges, the calculation of the electromagnetic field components ends (calculation end).

[0044] <3-3>Formulation Example for Two-Dimensional Absorption Surface In the analysis method according to the embodiment, the wave equation (Helmholtz equation) regarding the electric field is obtained as follows. First, the wave equations regarding the electric field components Ex, Ey, and Ez are shown in Expressions (1), (2), and (3) respectively. In the following mathematical expressions, "ν p " represents the frequency.

[0045]

Equation

[0046]

Equation

[0047]

Equation

[0048] In the analysis method according to the embodiment, the condition to be satisfied by the two-dimensional absorption surface applied to the region boundary surface of the release voxel RVX can be realized by setting the electric field component reflected by the absorption surface to "0". For example, for a plane wave (Ey and Ez) propagating from x>0 in the yz plane of x = 0, it is sufficient to satisfy equations (4) and (5).

[0049]

Number

[0050]

Number

[0051] Here, equation (6) is also satisfied.

[0052]

Number

[0053] Based on the averaging method, by handling the electric field as follows, sufficient absorption characteristics are realized on the two-dimensional surface. As an example, the formulation of the absorption surface (set on the yz plane, x = 0) for a radio wave propagating in the -x direction is shown. The conditions applied to the electric field components Ey and Ez propagating in the -x direction are given by the following equation (7).

[0054]

Number

[0055] For the electric field component Ez, it is derived by changing the subscript "y" in equation (7) to "z". Also, for the absorption boundary conditions for the electric field components propagating in the y direction and z direction, in each equation, Δx can be set as Δy or Δz, and the position of the absorption surface can be substituted.

[0056] <4>Effects of the Embodiment In the evaluation of outdoor radio wave propagation in the WiFi and mobile phone frequency bands, the main electromagnetic field is the component that propagates through space. The electromagnetic field components that penetrate into relatively large structures such as buildings are absorbed by the structures and do not have a major impact on the propagation characteristic analysis results. However, if the radio waves reflected from the building surface (building boundary surface) and the radio waves that penetrate into and are absorbed by the building are not correctly handled, the accuracy of the analysis results may be significantly degraded. For this reason, in the analysis process of the comparative example, the electromagnetic field calculation is repeatedly performed from the start to the end of the calculation for the area inside the building as well.

[0057] In contrast, the analysis device 10 of the embodiment sets the voxel VX of the space that has a negligible impact on the propagation characteristic evaluation (for example, when evaluating the propagation characteristics of radio waves radiated from a wireless device outdoors in an urban area, the voxel VX where the value of the electromagnetic field component is small, such as inside a building) as the release voxel RVX. Then, before the start of the FDTD calculation, the analysis device 10 releases the array for storing the electromagnetic field components of the release voxel RVX and does not perform iterative calculations. That is, the analysis device 10 extracts in advance the parts that do not have a major impact on the propagation characteristic analysis results, reduces the computer resources, and reduces the main memory used for iterative calculations. As a result, the analysis device 10 according to the embodiment can shorten the calculation time of the electromagnetic field and suppress the memory usage amount. Furthermore, the analysis device 10 applies a two-dimensional absorption region to the boundary surface of the release voxel RVX. Thereby, the analysis device 10 can suppress the generation of unnecessary reflected waves caused by the discontinuity of the voxels and can suppress the degradation of the analysis accuracy caused by the application of the release voxel.

[0058] <5>Others The flowcharts used in the description of the analysis process in the embodiments are merely examples. For each flowchart, as long as the same results as those in the embodiments can be obtained, the processing order may be changed within the possible range, or other processing may be added. The method for extracting the release voxel RVX is not limited to the method described in the embodiments. If the CPU 23 can set a release voxel RVX that has a minimal impact on the analysis results, the release voxel RVX may be extracted by a method other than the method described in the embodiments. In this specification, the analysis device 10 may be referred to as a "server" or a "processing server". The CPU 23 may be referred to as a "processor". Each of the ROM 24, the RAM 25, and the storage medium 26 may be referred to as a "storage circuit" or a "memory".

[0059] The hardware configuration of the analysis device 10 described in the embodiments may be other configurations. For example, instead of the CPU 23, an MPU (Micro Processing Unit), an ASIC (Application Specific Integrated Circuit), or an FPGA (field-programmable gate array) may be used. Some or all of the functions of the analysis device 10 may be realized by dedicated hardware, or may be configured as a program executed by a processor such as the CPU 23. That is, each function of the analysis device 10 can be realized using a computer and a program, and the program may be recorded on a storage medium or provided via a network.

[0060] Note that the present invention is not limited to the above-described embodiments, and various modifications can be made without departing from the gist thereof at the implementation stage. Also, the respective embodiments may be implemented in appropriate combination, and in that case, the combined effects can be obtained. Furthermore, the above-described embodiments include various inventions, and various inventions can be extracted by combinations selected from a plurality of disclosed constituent elements. For example, even if some constituent elements are deleted from all the constituent elements shown in the embodiments, if the problem can be solved and the effects can be obtained, the configuration from which these constituent elements are deleted can be extracted as an invention.

Explanation of Reference Numerals

[0061] 1…Wave source 2…Object 10…Analysis device 20…Input unit 21…Output unit 22…Communication unit 23…CPU 24…ROM 25…RAM 26…Storage medium 27, 100, 102…Bus 31…Storage unit 32…Parameter setting unit 33…Array initialization unit 34…Array data reading unit 35…Calculation unit 310…Analysis space information storage unit 312…Voxel model storage unit 350…Electric field component calculation unit 352…Electric field absorption boundary condition calculation unit 354…Magnetic field component calculation unit 356…Magnetic field absorption boundary condition calculation unit

Claims

1. An analysis device that performs electromagnetic field analysis using the Finite-Difference Time-Domain (FDTD) method, comprising: setting a plurality of voxels in an analysis region; setting at least one of the plurality of voxels as a free voxel based on a model of the analysis region; and a processor that repeatedly executes updating of a time step and calculation processing of electromagnetic field components for each of the plurality of voxels, wherein the calculation processing includes calculation of an electric field component for the plurality of voxels, application of an absorption boundary condition to the electric field component, and application of an absorption boundary condition to a region boundary surface between the at least one free voxel and an adjacent voxel, and in the calculation processing, calculation of an electric field component for the at least one free voxel is omitted, Analysis device.

2. Further comprising a memory, wherein the processor allocates a memory area used for calculation of the plurality of voxels to the memory and releases a portion corresponding to the voxel set as the at least one free voxel among the memory areas, The analysis device according to claim 1.

3. In the calculation processing, the processor calculates so that an electric field component reflected by the region boundary surface becomes zero, The analysis device according to claim 1.

4. An analysis program for performing electromagnetic field analysis using the Finite-Difference Time-Domain (FDTD) method, causing a computer to set a plurality of voxels in an analysis region; set at least one of the plurality of voxels as a free voxel based on a model of the analysis region; repeatedly execute updating of a time step and calculation processing of electromagnetic field components for each of the plurality of voxels, wherein the calculation processing includes calculation of an electric field component for the plurality of voxels, application of an absorption boundary condition to the electric field component, and application of an absorption boundary condition to a region boundary surface between the at least one free voxel and an adjacent voxel, and in the calculation processing, calculation of an electric field component for the at least one free voxel is omitted, Analysis program.

5. Causing a computer to allocate a memory area used for calculation of the plurality of voxels to a memory, Further causing to execute releasing a portion corresponding to a voxel set in at least one of the release voxels in the memory area. The analysis program according to claim 4. **Claim 6** A computer, In the calculation process, further causing to execute calculating so that an electric field component reflected by the region boundary surface becomes zero. The analysis program according to claim 4.

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