JP2023021711A - Analysis method, analyzer, and analysis program - Google Patents

Abstract

To reduce the calculation time of an electromagnetic field in the FDTD method.SOLUTION: An analysis method of an embodiment performs 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; 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 first parallel processing (S300) including calculation of electric filed components and application of an absorption boundary condition to the electric field components.SELECTED DRAWING: Figure 9

Description

Patent Law Article 30, Paragraph 2 application filed 1. Published at the IEICE General Conference Proceedings on February 23, 2021 2. Presented at the IEICE General Conference Online on March 11, 2021

Embodiments relate to an analysis method, an analysis apparatus, and an analysis program.

2. Description of the Related Art As wireless communication systems become faster, there is an increasing need to appropriately analyze electromagnetic fields generated from devices. As one of the electromagnetic field analysis methods, the FDTD method (Finite-Difference Time-Domain method) is known. The FDTD method is an electromagnetic field analysis technique in which an analysis area is divided into a large number of blocks (hereinafter referred to as voxels), and electric and magnetic fields generated by a wave source within the analysis area are updated over time based on Maxwell's equations.

JP 2014-006851 A JP 2017-011518 A

However, the FDTD method has a large processing load and requires many computer resources. For this reason, the FDTD method has the problem that the calculation time is long when analyzing a large analysis area or when analyzing propagation characteristics targeting high frequency bands such as 5th generation mobile communication. .

SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to provide an analysis method, an analysis apparatus, and an analysis program capable of shortening the calculation time of an electromagnetic field in the FDTD method.

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 an analysis region, updating the time step, and repeatedly executing calculation processing of electromagnetic field components for each of the plurality of voxels. . The computational process includes a first parallel process that includes computing the electric field component and applying an absorbing boundary condition to the electric field component.

The analysis method of the embodiment can shorten the calculation time of the electromagnetic field in the FDTD method.

FIG. 1 is a perspective view showing an example of an analysis region determined by an electromagnetic field analysis process using the FDTD method. FIG. 2 is a perspective view showing an example of setting voxels in an electromagnetic field analysis process 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 the hardware configuration of the analysis device according to the embodiment; FIG. 5 is a block diagram illustrating an example of the functional configuration of the analysis device according to the embodiment; FIG. 6 is a flowchart showing an example of the flow of electromagnetic field analysis processing using the FDTD method. FIG. 7 is a flow chart showing a method of calculating and updating electromagnetic field components in a comparative example. FIG. 8 is a flow chart showing a specific example of a method for calculating electric field components in a comparative example. FIG. 9 is a flow chart showing an example of a method for calculating and updating electromagnetic field components in the embodiment. FIG. 10 is a flow chart showing a specific example of a method for calculating electric field components in the embodiment. FIG. 11 is a bar graph showing the first evaluation result of the processing time of analysis processing. FIG. 12 is a bar graph showing the second evaluation result of the processing time of the analysis processing.

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

<1> Overview of FDTD Method FIG. 1 is a perspective view showing an example of an analysis area AR determined by an electromagnetic field analysis process using the FDTD method. As shown in FIG. 1, the analysis area AR is a three-dimensional area having, for example, a width Lx along the X direction, a depth Ly along the Y direction, and a height Lz along the Z direction. be. Analysis area AR includes, for example, wave source 1 and at least one object 2 . A wave source 1 is a transmission point of radio waves (electromagnetic fields). The radio wave transmitted from the wave source 1 propagates spherically (radially in the electric field intensity contour diagram) around the wave source 1 when the medium constant in the analysis area AR is uniform. Electrical conductivity, magnetic permeability, and the like are used as medium constants. The object 2 has a medium constant different from that of the space within the analysis area AR. Object 2 is, for example, a building. The number of objects 2 set in the analysis area AR, the shape of the objects 2, the medium constant of each object 2, and the like are appropriately set according to the model to be analyzed. Multiple models can be applied to the analysis area AR.

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

FIG. 3 is a schematic diagram showing an outline of a method for calculating electromagnetic field components using the FDTD method. As shown in FIG. 3, when the calculation of the electromagnetic field component is started in the FDTD method (calculation start), the arrays for the electric field and magnetic field of each voxel VX in the analysis area A are set. This "array" is used for the calculation of the electric and magnetic fields in the analysis area AR and corresponds to the 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 predetermined time intervals for each voxel VX. Ex, Ey, and Ez correspond to the electric field components along the x-, y-, and z-directions, respectively. Hx, Hy, and Hz correspond to magnetic field components along the x-, y-, and z-directions, respectively. When each of the electric field component and the magnetic field component converges, the calculation of the electromagnetic field component ends (completion of calculation). When the electromagnetic field is analyzed using a plurality of models, calculation is performed for each single model, for example. The number of calculations and updates of electromagnetic field components is hereinafter referred to as the number of time steps. For example, when the number of voxels in one model is M and the number of time steps is T, the number of accesses to memory when the model is used is M×T times.

<2> Configuration <2-1> Hardware Configuration of Analysis Apparatus 10 FIG. 4 is a block diagram showing an example of the hardware configuration of the analysis apparatus 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 are provided. 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 a bus 27 and function as a computer.

The input unit 20 is an input device such as a keyboard and a mouse. The output unit 21 is, for example, a display device such as a display. 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 implements an analysis function of the analysis device 10, which will be described later, by executing a program developed in the RAM 25, for example. ROM 24 is a non-volatile semiconductor memory. The ROM 24 stores programs and control data for controlling the analysis device 10 . RAM 25 is, for example, a volatile semiconductor memory. A RAM 25 is used as a work area for the CPU 23 . The storage medium 26 is a storage device that stores data in a nonvolatile manner. As the storage medium 26, for example, an HDD (Hard Disk Drive), an SSD (Solid State Drive), or the like is used. The storage medium 26 may be built in the analysis device 10 or may be externally attached.

<2-2> Functional Configuration of Analysis Apparatus 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 device 10 includes a storage section 31, a parameter setting section 32, an array initialization section 33, an array data reading section 34, a calculation section 35, and buses 100 and 102. FIG. Storage unit 31 is connected to parameter setting unit 32 , array initialization unit 33 , and array data reading unit 34 via bus 100 , and to calculation unit 35 via bus 102 .

The storage unit 31 is composed of a memory (for example, the RAM 25) capable of reading and writing data via the bus 100 and the bus 102. FIG. 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 about 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. Note that the storage unit 31 may store the processing result of the calculation unit 35 or the like.

The parameter setting unit 32 sets the analysis space size, the voxel size, the definition of the discrete time interval, and the analysis model (antenna, analysis space conditions, etc.) for the analysis area AR. Then, the parameter setting unit 32 causes the storage unit 31 to store these setting values. The array initialization unit 33 secures an array of a size required for analysis processing, and stores the secured array in the storage unit 31 . The array data reading unit 34 reads array data used for calculation of the electric field and magnetic field, and stores the data in the storage unit 31 .

The calculator 35 has units for calculating the electric field and the magnetic field. Specifically, the calculator 35 has an electric field component calculator 350 , an electric field absorption boundary condition calculator 352 , a magnetic field component calculator 354 , and a magnetic field absorption boundary condition calculator 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 . Then, the electric field component calculator 350 calculates the electric field component for each voxel VX based on the read medium constant and model for each voxel VX, and stores the calculation result in the storage unit 31 . The electric field absorption boundary condition calculator 352 calculates an absorption boundary condition for the electric field component in the analysis area AR. Then, the electric field absorption boundary condition calculation unit 352 executes calculation for applying the absorption boundary condition to the electric field component calculated by the electric field component calculation unit 350 and causes the storage unit 31 to store the calculation result.

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 . Then, the magnetic field component calculator 354 calculates the magnetic field component for each voxel VX based on the read medium constant and model for each voxel VX, and stores the calculation result in the storage unit 31 . The magnetic field absorbing boundary condition calculator 356 calculates the absorbing boundary condition of the magnetic field component in the analysis area AR. Then, the magnetic field absorbing boundary condition calculation unit 356 executes calculation for applying the absorbing boundary condition to the magnetic field component calculated by the magnetic field component calculation unit 354 and stores the calculation result in the storage unit 31 .

<3> Operation <3-1> Flow of Analysis Processing FIG. 6 is a flowchart showing an example of the flow of analysis processing of an electromagnetic field using the FDTD method. An example of the flow of electromagnetic field analysis processing using the FDTD method will be described below with reference to FIG.

The CPU 23 starts analysis processing (start), for example, in response to a user's operation.

First, the CPU 23 reads out a calculation target model (S100). In other words, the voxel model storage unit 312 reads the model associated with the current calculation target to generate the voxel model.

Next, the CPU 23 determines an 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 voxels VX in the analysis area 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 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 , corresponding to the z-axis indices (k=1, 2, . . . , Nz).

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

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

Next, the CPU 23 updates the time step (S110). When the process of S110 is performed for 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 or subsequent time in the analysis process, the number of time steps is a numerical value corresponding to the number of times the process of S110 has been executed.

Next, the CPU 23 calculates and updates the electromagnetic field component (S112). The details of how to calculate and update the electromagnetic field components will be described later.

Next, the CPU 23 determines whether or not the calculation of the electromagnetic field component has converged (S114). Specifically, for example, the CPU 23 outputs the numerical values of the electric field components (Ex, Ey, Ez) and the magnetic field components (Hx, Hy, Hz) at the current time step, and the electromagnetic field components at the previous time step. By comparing with the calculation result, it is determined whether or not the calculation of the electromagnetic field component has converged.

When the calculation of the electromagnetic field component has not converged in the process of S114 (S114, NO), the CPU 23 proceeds to the process of S110. That is, the CPU 23 executes calculation and update of the electromagnetic field component in the next time step.

When the calculation of the electromagnetic field component has converged in the process of S114 (S114, YES), the CPU 23 ends the series of processes in FIG. 6 (end). After that, the analysis device 10 stores the analysis result in the storage medium 26, for example. Note that the analysis device 10 may display the analysis result on the output unit 21 .

<3-2> Method of Calculating and Updating Electromagnetic Field Components in Comparative Example FIG. 7 is a flowchart showing a method of calculating and updating electromagnetic field components in a comparative example. A method of calculating and updating electromagnetic field components in the comparative example will be described below with reference to FIG.

In the comparative example, when the calculation and update of the electromagnetic field component is started, the CPU 23 first calculates the electric field component (S200). In the calculation of the electric field component, the electric field component calculation unit 350 uses the difference equation obtained by expanding Maxwell's equations in the space and time domains and the voxel model generated in the processing of S100 to calculate the electric field component in the analysis area AR. calculate.

Next, the CPU 23 applies an absorption boundary condition to the electric field component (S202). 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 S200 and the magnetic field component calculated in the process of S204 described later to calculate the analysis area AR. Calculate the absorbing boundary condition of the electric field component so that the electromagnetic waves are not reflected at the boundary. The electric field absorption boundary condition calculator 352 uses, for example, "0" or a preset initial value of the magnetic field component as the magnetic field component when first calculating the absorption boundary condition of the electric field component.

Next, the CPU 23 calculates magnetic field components (S204). Specifically, the magnetic field component calculation unit 354 calculates the magnetic field component in the analysis area AR using the difference equation obtained by expanding Maxwell's equations in the space and time domains and the voxel model generated in the process of S100. do.

Next, the CPU 23 applies an absorbing boundary condition to the magnetic field component (S206). Specifically, the magnetic field absorption boundary condition calculation unit 356 uses the electric field component calculated in the process of S200 and the magnetic field component calculated in the process of S204 to prevent the electromagnetic wave from being reflected at the boundary of the analysis area AR. Then, we calculate the absorbing boundary condition of the magnetic field component. Note that the electric field absorption boundary condition calculator 352 uses the magnetic field component of “0” or a preset initial value when first calculating the absorption boundary condition of the electric field component. When the processing of S206 is completed, the CPU 23 terminates the series of processing in FIG. 8 (return).

(Specific example of calculation method of electric field component in comparative example)
FIG. 8 is a flowchart showing a specific example of a method of calculating electric field components in the comparative example, and shows an example of a method of calculating electric field components Ex of each voxel VX set in the analysis area AR. A specific example of the electric field component updating method in the comparative example will be described below with reference to FIG. 8 . In this calculation method, the CPU 23 defines variables "i", "j", "j1", "k" and "k1". The variables i, j, and k are associated with x, y, and z coordinates, respectively.

After starting the process of S112 at a certain time step, the CPU 23 starts (starts) the calculation of the electric field component Ex in the process of S200.

First, the CPU 23 executes the process of "k=2" (S210). That is, in the process of S210, "2" is substituted for the variable k.

Next, the CPU 23 executes the processing of "k1=k-1" (S212). That is, in the process of S212, the calculation result of "k-1" is substituted for the variable k1.

Next, the CPU 23 executes the process of "j=2" (S214). That is, in the process of S214, "2" is substituted for the variable j.

Next, the CPU 23 executes the processing of "j1=j-1" (S216). That is, in the process of S216, the calculation result of "j-1" is substituted for the variable j1.

Next, the CPU 23 executes the process of "i=1" (S218). That is, in the process of S218, "1" is substituted for the variable i.

Next, the CPU 23 calculates the electric field component Ex (x, y, z) (S220). Specifically, the function (1) shown below, for example, is used to calculate the electric field component Ex(x, y, z).
ex(i,j,k) = cax(i,j,k) * ex(i,j,k) + cbx(i,j,k) * ((hz(i,j,k)-hz(i ,j1,k)) * kedy(j) - (hy(i,j,k) - hy(i,j,k1)) * kedz(k)) …(1)
"ex(i,j,k)" corresponds to the calculated electric field component Ex of the voxel VX associated with the coordinates (i,j,k). "cax(i,j,k)" corresponds to the coefficients on the electric field based on permittivity and conductivity. "cbx(i,j,k)" corresponds to the coefficients on the magnetic field based on permittivity and conductivity. "hy(i,j,k)" corresponds to the calculated magnetic field component Hy of the voxel VX associated with the coordinates (i,j,k). "hz(i,j,k)" corresponds to the calculated magnetic field component Hz of the voxel VX associated with the coordinates (i,j,k). "kedy" corresponds to a factor based on the reciprocal of the voxel dimension along the y-axis. "kedz" corresponds to a factor based on the reciprocal of the voxel dimension along the z-axis.

Next, the CPU 23 determines whether or not "i=mkx" is satisfied (S222). "mkx" is a constant corresponding to the largest numerical value among the x-coordinates assigned to the analysis area AR. That is, in the process of S222, the CPU 23 determines whether or not the loop process in which the x-coordinate is changed has been completed.

When it is determined in the process of S222 that "i=mkx" is not satisfied (S220, NO), the CPU 23 executes the process of "i=i+1" (S224). That is, in the process of S224, the variable i is incremented. After completing the process of S224, the CPU 23 proceeds to the process of S220. That is, the CPU 23 executes calculation processing of the electric field component Ex corresponding to the next x-coordinate voxel VX.

When determining that "i=mkx" is satisfied in the process of S222, the CPU 23 determines whether "j=mky" is satisfied (S226). "mky" is a constant corresponding to the largest numerical value among the y-coordinates assigned to the analysis area AR. That is, in the process of S226, the CPU 23 determines whether or not the loop process in which the y-coordinate is changed has been completed.

When it is determined in the process of S226 that "j=mky" is not satisfied (S226, NO), the CPU 23 executes the process of "j=j+1" (S228). That is, in the process of S228, the variable j is incremented. When the process of S228 is completed, the CPU 23 proceeds to the process of S216. That is, the CPU 23 executes calculation processing of the electric field component Ex corresponding to the next y-coordinate voxel VX.

When determining that "j=mky" is satisfied in the process of S226 (S226, YES), the CPU 23 determines whether "k=mkz" is satisfied (S230). “mkz” is a constant corresponding to the largest numerical value among the z-coordinates assigned to the analysis area AR. That is, in the process of S230, the CPU 23 determines whether or not the loop process in which the z-coordinate is changed has been completed.

When it is determined in the process of S230 that "k=mkz" is not satisfied (S230, NO), the CPU 23 executes the process of "k=k+1" (S232). That is, in the process of S232, the variable k is incremented. When the process of S232 is completed, the CPU 23 proceeds to the process of S212. That is, the CPU 23 executes calculation processing of the electric field component Ex corresponding to the next z-coordinate voxel VX.

When determining that "k=mkz" is satisfied in the process of S230 (S230, YES), the CPU 23 terminates the series of processes in FIG. 8 (end).

Calculations of the electric field components Ey and Ez are performed in the same order as the electric field component Ex, for example, and a calculation method similar to that of the electric field component Ex is applied. For example, the calculation of the electric field component Ey(x,y,z) (i.e., the calculation of ey(i,j,k)) uses the function (2) shown below and the electric field component Ez(x, y,z) (ie updating ez(i,j,k)) uses function (3) shown below.

ey(i,j,k) = cay(i,j,k) * ey(i,j,k) + cby(i,j,k) * ((hx(i,j,k)-hx(i ,j,k1)) * kedz(k) - (hz(i,j,k) - hz(i1,j,k)) * kedx(i)) …（2）
ez(i,j,k) = caz(i,j,k) * ez(i,j,k) + cbz(i,j,k) * ((hy(i,j,k)-hy(i1 ,j,k)) * kedx(i) - (hx(i,j,k) - hx(i,j1,k)) * kedy(j)) …（3）
Also, each of the magnetic field components Hx, Hy and Hz is calculated based on Maxwell's equations. Each of the magnetic field components Hx, Hy and Hz of each voxel VX within the analysis area AR can be calculated in the same order as the electric field components, for example.

<3-3> Electromagnetic Field Component Calculation and Updating Method in Embodiment FIG. 9 is a flow chart showing an example of an electromagnetic field component calculation and updating method in the embodiment. As shown in FIG. 9, in the embodiment, when the calculation and updating of the electromagnetic field component is started, the CPU 23 first executes parallel processing of calculation of the electric field component and application of the absorbing boundary condition to the electric field component (S300). Then, the CPU 23 executes parallel processing of calculation of the magnetic field component and application of the absorbing boundary condition to the magnetic field component (S302). When the processing of S302 is completed, the CPU 23 terminates the series of processing in FIG. 9 (return). In this way, the parallel processing of S300 (electric field component) and the parallel processing of S302 (magnetic field component) are executed by different loop processes. The details of how to apply the absorbing boundary condition to are the same as in the comparative example.

(Specific example of method for calculating electric field component in the embodiment)
FIG. 10 is a flowchart showing a specific example of a method of calculating electric field components in the embodiment, and shows an example of a method of calculating three electric field components of each voxel VX set in the analysis area AR. A specific example of the electric field component updating method according to the embodiment will be described below with reference to FIG. 10 . In this calculation method, the CPU 23 defines variables "j", "j1", "k" and "k1". The variables j and k are associated with the y and z coordinates respectively.

When the process of S112 is started at a certain time step, the CPU 23 starts the process of S300 (start).

First, the CPU 23 executes the process of "k=1" (S310). That is, in the process of S310, "1" is substituted for the variable k.

Next, the CPU 23 executes the process of "j=1" (S312). That is, in the process of S312, "1" is substituted for the variable j.

Next, the CPU 23 executes the processing of "k1=k-1" (S314). That is, in the process of S314, the calculation result of "k-1" is substituted for the variable k1.

Next, the CPU 23 executes the processing of "j1=j-1" (S316). That is, in the process of S316, the calculation result of "j-1" is substituted for the variable j1.

Next, the CPU 23 calculates electric field components Ex (x, y, z), Ey (x, y, z), and Ez (x, y, z) (S318). In the process of S318, each of the electric field components Ex(x, y, z), Ey(x, y, z), and Ez(x, y, z) is converted to the electric field described with reference to FIG. It is calculated by the same calculation method as the calculation method of the component.

Next, the CPU 23 applies an absorbing boundary condition to the electric field components Ex(x, y, z), Ey(x, y, z), and Ez(x, y, z) (S320). The application of absorbing boundary conditions to each of the electric field components Ex(x, y, z), Ey(x, y, z), and Ez(x, y, z) in the processing of S320, see, for example, FIG. is performed in a manner similar to that described in .

Next, the CPU 23 determines whether or not "j=mky" is satisfied (S322). That is, in the processing of S322, the CPU 23 determines whether or not the loop processing in which the y-coordinate is changed has been completed.

When it is determined in the process of S322 that "j=mky" is not satisfied (S322, NO), the CPU 23 executes the process of "j=j+1" (S324). That is, in the process of S324, the variable j is incremented. When the process of S324 is completed, the CPU 23 proceeds to the process of S314. That is, the CPU 23 executes the calculation of the three components of the electric field corresponding to the next y-coordinate voxel VX and the application of the absorbing boundary condition.

When determining that "j=mky" is satisfied in the process of S322 (S322, YES), the CPU 23 determines whether "k=mkz" is satisfied (S326). That is, in the process of S326, the CPU 23 determines whether or not the loop process in which the z-coordinate is changed has been completed.

When it is determined in the process of S326 that "k=mkz" is not satisfied (S326, NO), the CPU 23 executes the process of "k=k+1" (S328). That is, in the process of S328, the variable k is incremented. When the process of S328 is completed, the CPU 23 proceeds to the process of S312. That is, the CPU 23 executes calculation of the three components of the electric field corresponding to the next z-coordinate voxel VX and application of the absorbing boundary condition.

When determining that "k=mkz" is satisfied in the process of S326 (S326, YES), the CPU 23 ends the series of processes in FIG. 10 (end).

The processing described with reference to FIG. 10 is executed by fixing the x-coordinate of the voxel VX to be calculated and changing the y-coordinate and z-coordinate. Calculation and updating of the electric field components Ex, Ey and Ez of different x-coordinates can be calculated and updated by parallel processing of the CPU 23 . Further, each of the magnetic field components Hx, Hy and Hz can be calculated in the same manner as the electric field components Ex, Ey and Ez. For example, the calculation and update of the magnetic field component (S302) may be performed in the flow chart shown in FIG. )”, S319 is replaced with “Applying absorbing boundary conditions to Hx (x, y, z), Hy (x, y, z), Hz (x, y, z)”, loop processing It has a configuration in which the processing of variables used in is changed as appropriate.

<4> Effect of the Embodiment The process that requires the most time in the FDTD calculation is the process of updating the electromagnetic field component and the process of applying the absorbing boundary condition. Therefore, these time-step processes (eg, S110, S112, and S114) are preferably parallelized and vectorized. Updating the electromagnetic field components and applying the absorbing boundary condition are triple loops of spatial coordinates (x, y, z), and thread parallelization of the processing of these multiple loops can speed up the analysis processing.

The program used in the method of calculating and updating the electromagnetic field components in the comparative example described with reference to FIG. and applying absorbing boundary conditions to the components. If automatic parallelization by a program compiler is applied to the calculation method of the comparative example, cache reusability may be lacking and sufficient speed improvement may not be expected.

In contrast, the program used in the electromagnetic field component calculation and update method in the embodiment described with reference to FIG. ing. Then, loop processing is executed for each component of the electromagnetic field so as to increase the continuous access of the memory and the amount of calculation per instruction. As described above, the analysis method according to the embodiment performs parallel thread processing for triple loop calculations, and is optimized in consideration of vectorization, so parallel FDTD calculations can be speeded up. As a result, the analysis method according to the embodiment can improve cache reusability and load balance, and can shorten the electromagnetic field calculation time in the FDTD method.

Below, the results of performing analysis processing by applying similar FDTD analysis parameters to each of the embodiment and the comparative example are shown.
(FDTD analysis parameters)
Voxel dimensions [mm] | Δx, Δy, Δz = 20 mm
Analysis area (x, y, z) [m] | (760, 700, 28)
Absorbing boundary condition | CPML (10Layer)
Analysis frequency [GHz] | 1.298
Tx-antenna (λ/2 dipole) | Polarization: vertical, installation height [m]: 12.5
Main memory capacity | 134 (334 GB x 400 nodes)
(calculation time)
Before program optimization (comparative example): about 280 hours After program optimization (embodiment): about 167 hours That is, the analysis device 10 according to the embodiment can perform calculations about 40% faster than the comparative example. Therefore, the analysis device 10 according to the embodiment can reduce the calculation cost by about 40% compared to the comparative example.

Furthermore, the analysis method according to the embodiment preferably uses single-precision real numbers as the numeric data type handled by the calculator. By using single-precision real numbers for analysis processing, the analysis device 10 according to the embodiment can improve data waiting caused by an imbalance between cache lines and arithmetic units, increase the amount of data transfer, and improve continuous memory access and It is possible to increase the amount of calculation per statement. In other words, the analysis method according to the embodiment can significantly speed up the analysis process by modifying the program using single-precision real numbers.

FIG. 11 is a bar graph showing the first evaluation result of the processing time of analysis processing. FIG. 11 shows the difference in calculation speed when loop division (comparative analysis processing) is applied to analysis processing and automatic parallelization of processing is applied. As shown in FIG. 11, assuming that the calculation speed when double-precision real numbers are used as the standard for the speed-up ratio in this evaluation result is "1.0", single-precision real numbers were used. The calculation speed in this case was "1.6". That is, the analysis processing using single-precision real numbers can be calculated 1.6 times faster than the analysis processing using double-precision real numbers.

FIG. 12 is a bar graph showing the second evaluation result of the processing time of the analysis processing. FIG. 12 applies loop splitting (analysis processing of the comparative example) or loop fusion (analysis processing of the embodiment) to the analysis processing, and automatic parallelization of processing or OMP parallelization (parallelization of processing using OpenMP directives). ) is applied. As shown in FIG. 12, assuming that the calculation speed when loop division and automatic parallelization are applied is "1.0" as a standard for the speed-up ratio in this evaluation result, loop division and OMP The calculation speed was "1.3" when parallelization was applied, and the calculation speed was "1.6" when loop fusion and OMP parallelization were applied. In this way, the analysis processing in which OMP parallelization is applied to a loop fusion-applied program can be calculated 1.6 times faster than the analysis processing in which loop division and automatic parallelization are applied. That is, in the analysis method according to the embodiment, parallelization using the OMP directive is more effective than automatic parallelization, and cache reusability can be improved by using loop fusion.

<5> Others The flowchart used to explain the analysis process in the embodiment is merely an example. In each flowchart, the order of processing may be changed within a possible range, and other processing may be added, as long as the same result as in the embodiment can be obtained. In this specification, the analysis device 10 may be called a "server" or a "processing server". The CPU 23 may also be called a "processor". Each of the ROM 24, RAM 25 and storage medium 26 may be called a "storage circuit".

The hardware configuration of the analysis device 10 described in the embodiment may be another configuration. 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. Each function of the analysis device 10 may be partially or wholly 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 apparatus 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.

It should be noted that the present invention is not limited to the above-described embodiments, and various modifications can be made in the implementation stage without departing from the scope of the invention. In addition, each embodiment may be implemented in combination as appropriate, in which case the combined effect can be obtained. Furthermore, various inventions are included in the above embodiments, 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 effects can be obtained, the configuration with the constituent elements deleted can be extracted as an invention.

DESCRIPTION OF SYMBOLS 1... Wave source 2... Object 10... Analysis apparatus 20... Input part 21... Output part 22... Communication part 23... CPU
24 ROM
25 RAM
26 storage media 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 section 352 ... electric field absorption boundary condition calculation section 354 ... magnetic field component calculation section 356 ... magnetic field absorption boundary condition calculation section

Claims (7)

An analysis method for performing electromagnetic field analysis using the FDTD method (Finite-Difference Time-Domain method),
setting a plurality of voxels in the analysis area;
Updating the time step and repeatedly executing the calculation process of the electromagnetic field component for each of the plurality of voxels,
wherein the computational process includes a first parallel process including computation of an electric field component and application of an absorbing boundary condition to the electric field component;
analysis method. The calculation process includes a second parallel process including calculation of a magnetic field component and application of an absorbing boundary condition to the magnetic field component, wherein the first parallel process and the second parallel process are loop processes different from each other. executed by
The analysis method according to claim 1. A single-precision real number is used for the calculation process,
The analysis method according to claim 1 or 2. An analysis device that performs electromagnetic field analysis using the FDTD method (Finite-Difference Time-Domain method),
A processor that repeatedly executes setting a plurality of voxels in an analysis region, updating time steps, and calculating electromagnetic field components for each of the plurality of voxels,
the computational process includes a first parallel process that includes calculating an electric field component and applying an absorbing boundary condition to the electric field component;
analysis equipment. The computing process includes a second parallel process including calculation of a magnetic field component and application of an absorbing boundary condition to the magnetic field component, and the processor mutually interconnects the first parallel process and the second parallel process. run through different loops,
The analysis device according to claim 4. The processor utilizes single-precision real numbers for the calculation process.
The analysis device according to claim 4 or 5. An analysis program for performing electromagnetic field analysis using the FDTD method (Finite-Difference Time-Domain method),
to the computer,
setting a plurality of voxels in the analysis area;
updating the time step and repeatedly executing the calculation process of the electromagnetic field component for each of the plurality of voxels;
the computational process includes a first parallel process that includes calculating an electric field component and applying an absorbing boundary condition to the electric field component;
Analysis program.

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