JP7699354B2 - Analysis method, analysis device, and analysis program - Google Patents

Description

The embodiments relate to an analysis method, an analysis device, and an analysis program.

As wireless communication systems become faster, there is an increasing need to properly analyze the electromagnetic fields generated by the devices. One method of analyzing electromagnetic fields is the finite-difference time-domain method (FDTD method). The FDTD method is an electromagnetic field analysis technique that divides the analysis domain into many blocks (hereafter called voxels) and updates the electric and magnetic fields generated by wave sources within the analysis domain over time based on Maxwell's equations.

JP 2014-006851 A JP 2017-011518 A

However, the FDTD method requires the allocation of memory to hold the electric field, magnetic field, and medium constants for each voxel in the analysis domain from the start (time 0) of the repeated calculations to reproduce the passage of time until the set end time, and requires calculation of update equations for the electric field, magnetic field, and absorbing boundary. For this reason, when analyzing a large analysis domain or when analyzing propagation characteristics targeting high frequency bands such as 5th generation mobile communications, the FDTD method requires the allocation of a large amount of memory, which results in long calculation times.

The present invention aims to provide an analysis method, an analysis device, and an analysis program that can shorten the calculation time for electromagnetic fields in the FDTD method and reduce memory usage.

The analysis method of the embodiment is an analysis method that performs 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 an analysis domain, setting at least one of the plurality of voxels as a free voxel based on a model of the analysis domain, and repeatedly updating the time step and performing calculation processing of the electromagnetic field components for each of the plurality of voxels. The calculation processing includes calculation of the electric field components for the plurality of voxels and application of an absorbing boundary condition to the electric field components. In the calculation processing, the calculation of the electric field components for at least one free voxel is omitted.

The analysis method of the embodiment can reduce the calculation time of the electromagnetic field in the FDTD method and reduce memory usage.

FIG. 1 is a perspective view showing an example of an analysis domain determined by an analysis process of an electromagnetic field using the FDTD method. FIG. 2 is a perspective view showing an example of voxel setting in the analysis process of an electromagnetic field using the FDTD method. FIG. 3 is a schematic diagram showing an outline of a method for calculating electromagnetic field components using the FDTD method. FIG. 4 is a block diagram illustrating an example of a hardware configuration of the analysis device according to the embodiment. FIG. 5 is a block diagram illustrating an example of a functional configuration of the analysis device according to the embodiment. FIG. 6 is a flowchart showing an example of the flow of an electromagnetic field analysis process in the comparative example. FIG. 7 is a flowchart showing an example of the flow of an electromagnetic field analysis process in the embodiment. FIG. 8 is a schematic diagram showing an overview of the analysis process of the electromagnetic field in the embodiment.

The following describes embodiments with reference to the drawings. The embodiments illustrate devices and methods for embodying the technical ideas of the invention. The drawings are schematic or conceptual. In the following description, components having substantially the same functions and configurations are given the same reference numerals. The X, Y, and Z directions correspond to directions that intersect with each other.

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

Figure 2 is a perspective view showing an example of voxel setting in the analysis of an electromagnetic field using the FDTD method. As shown in Figure 2, in the analysis of an electromagnetic field using the FDTD method, the analysis area AR is divided into a plurality of blocks (voxels VX) arranged three-dimensionally. The voxels VX are set to an arbitrary size. Coordinate values (x coordinate, y coordinate, z coordinate) are set for each voxel VX, and the medium constants of the object 2 corresponding to the coordinate values are associated with each voxel. The analysis area AR is an analysis target with an absorbing boundary condition set around it, and the number of voxels VX is finite. In the FDTD method, when updating the electric field and magnetic field over time, the electric field and magnetic field calculated in the previous time step and the medium constants for each voxel VX are used. Therefore, in order to calculate an electromagnetic field using the FDTD method, a memory is required to hold the electric field, magnetic field, and medium constants according to the number of voxels VX.

Figure 3 is a schematic diagram showing an overview of a method for calculating electromagnetic field components using the FDTD method. As shown in Figure 3, when the calculation of electromagnetic field components begins in the FDTD method (calculation start), an array for the electric field and magnetic field of each voxel VX in the analysis area AR is set. This "array" is used to calculate the electric field and magnetic field in the analysis area AR, and corresponds to a memory area allocated for 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 at a predetermined time interval for each voxel VX. 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 converge, the calculation of the electromagnetic field components ends (calculation end). Note that when the electromagnetic field is analyzed using multiple models, the calculation is performed for each single model, for example. Hereinafter, the number of calculations and updates of the electromagnetic field components will be referred to as the number of time steps. For example, if a model has M voxels and T time steps, the number of memory accesses when that model is used will be M x T.

<2> Configuration <2-1> Hardware configuration of analysis device 10 Fig. 4 is a block diagram showing an example of a 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 a function as a computer.

The input unit 20 is an input device such as a keyboard or a mouse. The output unit 21 is a display device such as a display. The communication unit 22 is a network interface used for wired or wireless communication. The CPU 23 is an integrated circuit capable of executing various programs. The CPU 23 executes a program deployed in the RAM 25, for example, to realize the analysis function of the analysis device 10 described later. 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 in a non-volatile manner. For example, a hard disk drive (HDD) or a solid state drive (SSD) is used as the storage medium 26. The storage medium 26 may be built into the analysis device 10 or may be attached externally.

<2-2> Functional configuration of analysis device 10 Fig. 5 is a block diagram showing an example of the functional configuration of analysis device 10 according to an embodiment. As shown in Fig. 5, analysis device 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. Storage unit 31 is connected to each of parameter setting unit 32, array initialization unit 33, and array data reading unit 34 via bus 100, and is connected to calculation unit 35 via bus 102.

The storage unit 31 is composed of a memory (e.g., 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 related to the analysis area AR. For example, the analysis space information storage unit 310 stores the medium constant of each voxel VX. The voxel model storage unit 312 stores at least one model associated with the analysis area AR. The storage unit 31 may also store the processing results of the calculation unit 35 and the like.

The parameter setting unit 32 sets the analysis space size, voxel size, definition of discrete time intervals, and analysis model (antenna and analysis space conditions, etc.) for the analysis region AR. The parameter setting unit 32 also sets free voxels RVX based on the analysis model, etc. Free voxels RVX are voxels VX that are not subject to the calculation and updating of the electromagnetic field described below. The parameter setting unit 32 then stores these set values in the memory unit 31. The array initialization unit 33 secures an array of a size required for the analysis process, and stores the secured array in the memory unit 31. The array data reading unit 34 reads out array data used in the calculation of the electric field and magnetic field, and stores it in the memory unit 31.

The calculation unit 35 has various units for calculating the electric field and the magnetic field. Specifically, the calculation unit 35 has 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.

The electric field component calculation unit 350 reads the medium constant for each voxel VX from the analysis space information storage unit 310, and reads the model from the voxel model storage unit 312. The electric field component calculation unit 350 then calculates the electric field component for each voxel VX based on the medium constant and model for each voxel VX that have been read, and stores the calculation results in the storage unit 31. The electric field absorption boundary condition calculation unit 352 calculates the absorption boundary condition for the electric field component in the analysis region AR. The electric field absorption boundary condition calculation unit 352 then performs a calculation to apply the absorption boundary condition to the electric field component calculated by the electric field component calculation unit 350, and stores the calculation results in the storage unit 31.

The magnetic field component calculation unit 354 reads the medium constant for each voxel VX from the analysis space information storage unit 310, and reads the model from the voxel model storage unit 312. The magnetic field component calculation unit 354 then calculates the magnetic field component for each voxel VX based on the medium constant and model for each voxel VX that it has read, and stores the calculation results in the storage unit 31. The magnetic field absorbing boundary condition calculation unit 356 calculates the absorbing boundary conditions for the magnetic field components in the analysis region AR. The magnetic field absorbing boundary condition calculation unit 356 then performs a calculation to apply the absorbing 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.

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

The CPU 23 starts the analysis process (starts), for example, in response to a user operation.

First, the CPU 23 reads the calculation target model (S100). In other words, the model associated with the current calculation target is read into the voxel model storage unit 312, and a voxel model is generated.

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

Next, the CPU 23 sets the voxel VX in the analysis region AR (S104). Specifically, for example, the three-dimensional (i, j, k) absolute coordinate values set by the parameter setting unit 32 for each voxel VX are input to 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).

Next, the CPU 23 secures an array (S106). Specifically, the array initialization unit 33 secures an area in a memory (e.g., the RAM 25) to be used for calculating the three components of the electric field (Ex, Ey, Ez) and the three components of the magnetic field (Ex, Ey, Ez).

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

Next, the CPU 23 updates the time steps (S110). If the process of S110 is the first time, an initial value (e.g., "1") is applied as the number of time steps. If the process of S110 is the second or subsequent time in the analysis process, the number of time steps becomes a value according to the number of times the process of S110 has been executed.

Next, the CPU 23 calculates the electric field components (S112). In calculating the electric field components, the electric field component calculation unit 350 calculates the electric field components in the analysis area AR using a difference equation that expands Maxwell's equations in the spatial and temporal domains and the voxel model generated in the processing of S100.

Next, the CPU 23 applies the absorbing boundary condition to the electric field component (S114). In applying the absorbing boundary condition to the electric field component, the electric field absorbing 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 below to calculate the absorbing boundary condition of the electric field component so that the electromagnetic wave is not reflected at the boundary of the analysis area AR. Note that the electric field absorbing boundary condition calculation unit 352 uses, for example, "0" or a magnetic field component with a preset initial value as the magnetic field component when first calculating the absorbing boundary condition of the electric field component.

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

Next, the CPU 23 applies the absorbing boundary condition to the magnetic field component (S118). Specifically, the magnetic field absorbing 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 absorbing boundary condition of the magnetic field component so that the electromagnetic wave is not reflected at the boundary of the analysis area AR. Note that when initially calculating the absorbing boundary condition of the electric field component, the electric field absorbing boundary condition calculation unit 352 uses a magnetic field component of "0" or a preset initial value.

Next, the CPU 23 determines whether the calculation of the electromagnetic field components has converged (S120). Specifically, for example, the CPU 23 determines whether the calculation of the electromagnetic field components has converged by comparing the 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.

If the calculation of the electromagnetic field components has not converged in the process of S120 (S120, NO), the CPU 23 proceeds to the process of S110. In other words, the CPU 23 executes the calculation and update of the electromagnetic field components in the next time step.

If the calculation of the electromagnetic field components has converged in the process of S120 (S120, YES), the CPU 23 ends the series of processes in FIG. 6 (END). After that, the analysis device 10 stores the analysis results in, for example, the storage medium 26. The analysis device 10 may also display the analysis results on the output unit 21.

<3-2> Analysis process in the embodiment Fig. 7 is a flowchart showing an example of the flow of the analysis process of the electromagnetic field 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, compared to the analysis process of the comparative example shown in Fig. 6.

Specifically, as in the comparative example, when the CPU 23 starts the analysis process (START), it reads the model to be calculated (S100), determines the analysis area AR (S102), sets the voxel VX in the analysis area AR (S104), and secures the array (S106).

Next, the CPU 23 extracts free voxels RVX from the analysis area AR (S200). As an example of a method for extracting free voxels RVX, first, the CPU 23 (for example, the parameter setting unit 32) calculates a wavelength λ corresponding to the frequency of the analysis target. The CPU 23 then derives, as the deletion area, an area included in the interior of a building structure such as a building, or an inner three-dimensional space that is a distance from the surface of the building that is greater than several times the wavelength λ. The CPU 23 then sets the voxels VX that correspond to the deletion area as free voxels RVX. After that, the CPU 23 sets two-dimensional absorption surfaces corresponding to each axis direction to the voxels VX of the boundary surface that contacts the deletion area (free voxels RVX). The calculation method of this two-dimensional absorption surface will be described in detail later.

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

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

Next, the CPU 23 applies an absorbing boundary condition to the electric field components including the domain boundary surface of the released voxel RVX (S204). In other words, the CPU 23 applies an absorbing boundary condition not only to the domain boundary surface between adjacent voxels VX, but also to the domain boundary surface between the released voxel RVX and the voxel VX.

Next, the CPU 23 calculates the magnetic field components (S116), applies an absorbing boundary condition to the magnetic field components (S118), and determines whether the calculation of the electromagnetic field components has converged (S120), as in the comparative example. The other operations of the analysis process of the embodiment are the same as those of the comparative example.

Figure 8 is a schematic diagram showing an overview of the electromagnetic field analysis process in the embodiment. As shown in Figure 8, when the calculation of the electromagnetic field components starts in the embodiment (calculation start), the processes of S100, S102, S104, and S106 set the arrays for the electric field and magnetic field of each voxel VX in the analysis area AR. Then, the processes of S200, S202, and S204 extract the released voxel RVX, and release the arrays assigned to the released voxel RVX. 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 for each voxel VX at a predetermined time interval. In this calculation, as explained with reference to FIG. 7, a two-dimensional absorbing surface is set between the released voxel RVX and the voxel VX, and the calculation of the electric field component for the released voxel RVX is omitted. When the electric field component and the magnetic field component each converge, the calculation of the electromagnetic field component ends (end of calculation).

<3-3> Example of formulation for two-dimensional absorbing surface In the analysis method according to the embodiment, the wave equation (Helmholtz equation) for the electric field is calculated as follows. First, the wave equations for the electric field components Ex, Ey, and Ez are shown in equations (1), (2), and (3), respectively. In the following equations, "ν _p " represents the frequency.

...(1)

... (2)

...(3)

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

...(4)

...(5)

Here, equation (6) is also satisfied.

...(6)

By treating the electric field as follows based on the averaging method, sufficient absorption characteristics can be achieved on a two-dimensional surface. As an example, the formulation of an absorption surface (set on the yz plane, x = 0) for radio waves propagating in the -x direction is shown below. The condition applied to the electric field components Ey and Ez propagating in the -x direction is given by the following equation (7).

...(7)

The electric field component Ez is derived by changing the subscript "y" to "z" in equation (7). The absorbing boundary conditions for the electric field components propagating in the y and z directions can be determined by substituting the position of the absorbing surface for Δx in each equation, either Δy or Δz.

<4> Effects of the embodiment In the evaluation of outdoor radio wave propagation of WiFi and mobile phone frequency bands, the main electromagnetic field is a component propagating through space. The electromagnetic field components that penetrate into a relatively large structure such as a building are absorbed by the structure and do not have a major effect on the propagation characteristic analysis results. However, if the radio waves reflected by the building surface (building boundary surface) and the radio waves that penetrate and are absorbed inside the building are not properly 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 repeated from the start to the end of the calculation for the area inside the building.

In contrast, the analysis device 10 of the embodiment sets voxels VX in a space that has a small effect on the propagation characteristic evaluation (for example, voxels VX in which the value of the electromagnetic field component is small, such as inside a building, when performing a propagation characteristic evaluation of radio waves emitted from a wireless device outdoors, such as in an urban area) as released voxels RVX. Then, before starting the FDTD calculation, the analysis device 10 releases the array for storing the electromagnetic field components of the released voxels RVX, and does not perform repeated calculations. In other words, the analysis device 10 extracts in advance parts that do not have a major effect on the propagation characteristic analysis results, reduces computer resources, and reduces the main memory used for repeated calculations. As a result, the analysis device 10 of the embodiment can shorten the calculation time of the electromagnetic field and suppress memory usage. Furthermore, the analysis device 10 applies a two-dimensional absorbing region to the boundary surface of the released voxels RVX. This allows the analysis device 10 to suppress the generation of unnecessary reflected waves caused by discontinuous voxels, and suppresses the deterioration of analysis accuracy caused by the application of open voxels.

<5> Others The flowcharts used in the description of the analysis process in the embodiment are merely examples. As long as the same results as those in the embodiment can be obtained, the order of processing may be changed as much as possible, or other processing may be added. The method of extracting the released voxels RVX is not limited to the method described in the embodiment. If it is possible to set the released voxels RVX that have a small effect on the analysis result, the CPU 23 may extract the released voxels RVX by a method other than the method described in the embodiment. In this specification, the analysis device 10 may be called a "server" or a "processing server". The CPU 23 may be called a "processor". Each of the ROM 24, the RAM 25, and the storage medium 26 may be called a "storage circuit" or a "memory".

The hardware configuration of the analysis device 10 described in the embodiment 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. In other words, 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 the program may be provided via a network.

The present invention is not limited to the above-described embodiment, and various modifications can be made in the implementation stage without departing from the gist of the invention. The embodiments may be implemented in appropriate combination, in which case the combined effects can be obtained. Furthermore, the above-described embodiment includes various inventions, and various inventions can be extracted by combinations selected from the multiple constituent elements disclosed. For example, if the problem can be solved and an effect can be obtained even if some constituent elements are deleted from all the constituent elements shown in the embodiment, the configuration from which these constituent elements are deleted can be extracted as an invention.

Reference Signs List 1: Wave source 2: Object 10: Analysis device 20: Input section 21: Output section 22: Communication section 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 (6)

An analysis device that performs electromagnetic field analysis using a finite-difference time-domain method (FDTD method),
a processor that repeatedly executes the steps of: setting a plurality of voxels in an analysis domain; setting at least one of the plurality of voxels as a released voxel based on a model of the analysis domain; updating a time step; and calculating an electromagnetic field component for each of the plurality of voxels;
the calculation process includes calculating an electric field component for the plurality of voxels, applying an absorbing boundary condition to the electric field component, and applying an absorbing boundary condition to a domain boundary surface between the at least one released voxel and an adjacent voxel, and in the calculation process, the calculation of the electric field component for the at least one released voxel is omitted.
Analysis device. Further comprising a memory;
the processor allocates a memory area to be used for calculation of the plurality of voxels in the memory, and releases a portion of the memory area corresponding to the voxel set as the at least one released voxel;
The analysis device according to claim 1 . The processor performs calculations in the calculation process so that the electric field component reflected at the region boundary surface becomes zero.
The analysis device according to claim 1 . An analysis program for performing electromagnetic field analysis using the finite-difference time-domain method (FDTD method),
On the computer,
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;
repeatedly updating the time step and calculating the electromagnetic field components for each of the plurality of voxels;
the calculation process includes calculating an electric field component for the plurality of voxels, applying an absorbing boundary condition to the electric field component, and applying an absorbing boundary condition to a domain boundary surface between the at least one released voxel and an adjacent voxel, and in the calculation process, the calculation of the electric field component for the at least one released voxel is omitted.
Analysis program. On the computer,
allocating a memory area in a memory for use in computing the plurality of voxels;
and freeing a portion of the memory area corresponding to the voxel set as the at least one free voxel.
The analysis program according to claim 4 . On the computer,
The calculation process further includes calculating so that the electric field component reflected at the region boundary surface becomes zero.
The analysis program according to claim 4.