JP7149510B2 - Computing system, computing device and program - Google Patents

Description

The present invention relates to an arithmetic system, an arithmetic device and a program.

In recent years, the FDTD method (Finite-Difference Time-Domain method; FDTD method) and other electromagnetic fields using a finite-difference time-domain method that solves Maxwell's equations (hereinafter also referred to as Maxwell's equations) by differentiating them in time and space There is an analysis method (see Patent Document 1, for example). This prior art discloses that a large-scale electromagnetic field analysis is performed by performing parallel calculations using a plurality of arithmetic units.

JP 2009-053075 A

However, according to the conventional technology described above, the results of parallel operations may affect other operations. In such cases, it is necessary to wait for the results of other parallelized operations. There is a problem that simultaneous parallel calculation cannot be performed by the arithmetic unit.

SUMMARY OF THE INVENTION The present invention has been made to solve the above problems, and an object of the present invention is to provide an arithmetic device, an arithmetic management device, and a program capable of simultaneously parallelizing arithmetic operations for electromagnetic field analysis.

In one embodiment of the present invention, the initial time, which is the starting point on the time axis of the calculation of the function of the complex frequency domain for the time-varying electromagnetic field intensity waveform, and the calculation time width from the initial time, are used as calculation conditions. and calculating an initial value, which is a calculation result of the waveform at the initial time acquired by the calculation condition acquisition unit, by discrete time response analysis using an inverse Laplace transform method for the function. a calculation unit for calculating a calculation result of the waveform corresponding to the calculation time width acquired by the calculation condition acquisition unit by sequential calculation along the time axis based on the calculated initial value; an output unit for outputting the calculation result calculated by the calculation unit for each width to the calculation management device ; an arithmetic time width calculation unit that calculates the arithmetic time width from the initial time for each arithmetic unit based on the arithmetic performance of the unit; A calculation condition supplying unit that supplies an initial time and the calculation time width from the initial time as calculation conditions; A computation management device comprising: a computation result acquisition unit that acquires computation results according to the calculation result; and an integration unit that integrates the computation results according to the plurality of initial values acquired by the computation result acquisition unit in order of the initial time is a computing system including

Further, according to an embodiment of the present invention, in the arithmetic system described above, the inverse Laplace transform method is the FILT method.

Further, in one embodiment of the present invention , an initial time, which is the starting point on the time axis for calculation of a complex frequency domain function of a time-varying electromagnetic field intensity waveform, and a calculation time width from the initial time, are calculated. and an initial value, which is a calculation result of the waveform at the initial time obtained by the calculation condition acquisition unit, obtained by the calculation condition acquisition unit by discrete time response analysis using an inverse Laplace transform method for the function. a calculation unit that calculates and calculates a calculation result of the waveform for the calculation time width acquired by the calculation condition acquisition unit by sequential calculation along the time axis based on the calculated initial value; and an output unit configured to output the calculation result calculated by the calculation unit for each calculation time width to the calculation management device.

Further, in one embodiment of the present invention, a computer provided in an arithmetic device is provided with an initial time that is a starting point on the time axis of arithmetic operation on a complex frequency domain function for a waveform of time-varying electromagnetic field intensity, and a calculation condition obtaining step of obtaining a calculation time width as a calculation condition; Calculated by discrete time response analysis, and by sequential calculation along the time axis based on the calculated initial value, the calculation result of the waveform for the calculation time width obtained in the calculation condition obtaining step is obtained. and an output step of outputting the calculation result calculated for each calculation time width in the calculation step to a calculation management device .

According to the present invention, it is possible to provide an arithmetic system, an arithmetic device, and a program capable of simultaneously parallelizing arithmetic operations for electromagnetic field analysis.

It is a figure which shows an example of a structure of the arithmetic unit of this embodiment. It is a figure which shows an example of the calculation result of the calculating|arithmetic apparatus of this embodiment. It is a figure which shows an example of the minute rectangular parallelepiped used for the calculation by the calculating part of this embodiment. FIG. 10 is a diagram showing an example of allocation of temporal positions of electric and magnetic fields; It is a figure which shows an example of the analysis object of this embodiment. It is a figure which shows an example of a structure of the arithmetic system of this embodiment. It is a figure which shows an example of operation|movement of the arithmetic system of this embodiment. It is a figure which shows an example of the calculation result of the parallel calculation by the arithmetic unit of this embodiment. It is a figure which shows the specific example of the response waveform calculated by the several calculating|arithmetic apparatus of this embodiment. It is a figure which shows the specific example of the response waveform calculated by one arithmetic unit by a conventional method.

[Embodiment]
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1 is a diagram showing an example of the configuration of an arithmetic device 10 of this embodiment.

[Configuration of computing device]
The computing device 10 is an information processing device such as a personal computer, performs computation based on supplied information, and outputs computation results.
An example of calculation by the calculation device 10 will be described. The computing device 10 in this example calculates the response waveform fw at a certain position within the analysis area. For example, the computing device 10 uses an antenna that radiates electromagnetic waves as a wave source, an object (for example, a sphere or cylinder) on which the electromagnetic waves radiated from the wave source are incident as a scatterer, and provides an analysis region that includes the wave source and the scatterer. is calculated, a response waveform fw, which is the time change of the electric field strength at a certain position in the analysis area.
In the following description, the response waveform fw is expressed as a graph showing the time change of the electromagnetic field strength, but the response waveform fw may be expressed in any form as long as it is information showing the time change of the electromagnetic field strength. For example, the response waveform fw may be information indicating the spatial distribution of the electromagnetic field or the electromagnetic field in the form of a distribution map in a two-dimensional plane or in a three-dimensional space.
Also, in the following description, a case in which the analysis region includes a scatterer will be described as an example, but the present invention is not limited to this. For example, the analysis region may include an absorber that absorbs radio waves, a radiator that emits radio waves, and the like.

More specifically, the computation target information MDL, the initial time t0, and the computation time width tw are supplied to the computation device 10 as computation conditions OC from a host device (not shown). The calculation device 10 performs calculation to obtain the response waveform fw based on the supplied calculation conditions OC, and outputs the obtained response waveform fw to the host device as the calculation result RS. In this example, the calculation target information MDL includes various information necessary for analyzing the response waveform, such as the electromagnetic field distribution of the electromagnetic wave emitted from the wave source, the shape of the scatterer, the relative position, the dielectric constant, and the magnetic permeability. An example of the calculation result RS by the calculation device 10 will be described with reference to FIG.

FIG. 2 is a diagram showing an example of the calculation result RS of the calculation device 10 of this embodiment. The calculation device 10 outputs the response waveform fw as the calculation result RS. In this example, the response waveform fw is the time change of the electric field intensity at a certain position within the analysis area. In this case, the response waveform fw is indicated by the time (unit: fs (femtosecond)) on the horizontal axis and the electric field strength (unit: V/m) on the vertical axis.
The calculation device 10 calculates a waveform for a certain calculation time width tw (for example, from initial time t0 to time t1) in the response waveform fw. Here, the initial time t0 is the start time of the calculation time width. The value of the response waveform fw (for example, electric field strength) at the initial time t0 is also referred to as the initial value f0.
That is, the arithmetic device 10 calculates the response waveform fw for the arithmetic time width tw from the initial time t0, and outputs the calculated response waveform fw as the arithmetic result RS.

Returning to FIG. 1, the description of the configuration of the arithmetic unit 10 is continued. The calculation device 10 includes a calculation condition acquisition section 110 , a calculation section 120 and an output section 130 .
Calculation condition acquisition unit 110 acquires calculation target information MDL, initial time t0, and calculation time width tw supplied as calculation conditions OC from a host device (not shown).
The computation unit 120 calculates the initial value f0 and the response waveform fw based on the computation condition OC acquired by the computation condition acquisition unit 110 .
The output unit 130 outputs the calculated initial value f0 and the response waveform fw to a host device (not shown).

[Specific example of calculation]
A specific example of the calculation performed by the calculation unit 120 will be described. The calculation unit 120 of the present embodiment uses different calculation methods to calculate the initial value f0 at the initial time t0 and to calculate the response waveform fw after the initial time t0. First, calculation of the response waveform fw after the initial time t0 will be described.

[Calculation example (1) FDTD method]
The calculator 120 calculates the response waveform fw by the FDTD method.

FIG. 3 is a diagram showing an example of a minute rectangular parallelepiped used for calculation by the calculation unit 120 of this embodiment. The calculation unit 120 divides the entire given analysis region into small rectangular parallelepipeds (for example, Yee lattice) shown in the figure. Here, E (slanted) in the figure indicates an electric field, and H (slanted) indicates a magnetic field. The subscripts xyz (both in italics) of the electric field E and the magnetic field H indicate the x-axis direction component, the y-axis direction component, and the z-axis direction component, respectively. The calculation unit 120 applies Maxwell's equations (formulas (1) and (2)) to each of the divided small rectangular parallelepipeds, and performs calculation using the results formulated for each of time and three-dimensional space. . Specifically, it is as follows.

First, find the difference in time. The time differential terms of Faraday's law and Ampere's law shown in Equations (1) and (2) are summarized as Equations (3) and (4).

FIG. 4 is a diagram showing an example of allocation of the time arrangement of the electric field E and the magnetic field H. FIG.
Next, the time arrangement of the electric field E and the magnetic field H as shown in FIG. 4 is assigned to the time axis t, and the central difference is performed. (6) becomes.

Since E ^n−1/2 in equation (6) is not defined here, it is approximated as in equation (7).

Equation (8) is obtained by approximating E ^n−1/2 of equation (6) by equation (7) and substituting it for the first term on the right side of equation (6).

Formulas (5) and (8) are summarized into formulas (9) to (11).

This completes the formulation of time.
Next, we formulate the three-dimensional space. Equations (9) and (10) are divided into six components (electric field Ex, electric field Ey, electric field Ez, magnetic field Hx, magnetic field Hy, magnetic field Hz) and are formulated by applying the spatial arrangement of the electromagnetic field shown in FIG. Then it looks like this: It should be noted that symbols of the electric field E and the magnetic field H are italicized in the following equations (12) to (19).

The calculation unit 120 calculates the response waveform fw after the initial time t0 by applying the calculation formula formulated for time and three-dimensional space as described above to the given initial value f0.

[Calculation example (2) numerical inverse Laplace transform method (FILT method)]
The calculation unit 120 calculates the response waveform fw by a numerical inverse Laplace transform method (FILT method; Fast Inverse Laplace Transform method). The numerical inverse Laplace transform method is also called the NILT method (Numerical Inverse Laplace Transform method).
The complex frequency domain function F(s) can be transformed to the time domain by the numerical inverse Laplace transform method (FILT method). This numerical inverse Laplace transform method (FILT method) is an example of discrete time response analysis by the inverse Laplace transform method. In general, the inverse Laplace transform is defined by the following equation from the Bromwich integral.

In the FILT method, the exponential function of Equation (22) is approximated by Equation (23) below.

ここで、αは近似の精度でありＦＩＬＴ法における有効桁数を示す。式（２３）を式（２２）に代入して、逆ラプラス変換を式（２４）の無限級数で表わす。

Here, α is the accuracy of approximation and indicates the number of significant digits in the FILT method. Substituting equation (23) into equation (22), the inverse Laplace transform is represented by the infinite series of equation (24).

however,

is.
The infinite series of equation (24) is truncated with a finite number of terms for numerical calculation to obtain equation (26).

Here, M (italicized) in Equation (26) is the number of truncated terms in the FILT method. Since Equation (26) is an alternating series, it is transformed into Equation (27) by applying the Euler transformation.

here,

and p (italic) indicates the number of terms of the Euler transformation. Equation (27) can be calculated independently from other observation times at a certain observation time, and the electromagnetic field at each observation time can be easily calculated in parallel.
Also, the error in the FILT method can be expressed by the following equation (29) from the approximation of equation (23).

From Equation (29), the calculation error decreases exponentially with respect to approximate parameters. Also, the first term is mainly the calculation error, and the error can be estimated as 10 ^−α .

[Calculation example (3) FDCFD-FILT method]
A general FDFD method (Finite-Difference Frequency-Domain method) solves matrix equations in the frequency domain while using spatial mesh division similar to the above-described FDTD method. The calculation unit 120 of the present embodiment uses the FDCFD method (Finite-Difference Complex Frequency-Domain method), which is an extension of the FDFD method to the complex frequency domain, and the FILT method described above. Maxwell's equations in this complex frequency domain are given by equations (30) and (31).

The formulation of the algorithm of this FDCFD method will be described for a two-dimensional case.
To discretize the computational space, Equations (30) and (31) can be rewritten in the form shown in Equations (32) to (35) below.

To apply a similar procedure to the entire computational space, we use the system of equations in matrix form shown in Equation (36).

Here, as shown in Equation (37), the complex permittivity in the complex frequency s region is expressed by Lorentz-Drude in order to represent the frequency dispersion of metal.

Here, ωp is the plasma frequency, k is the resonance frequency ωj, the medium-specific constant fj, and the number of oscillators having the collision frequency Γj (all symbols in the formula are italicized). By solving the above simultaneous equations, the electromagnetic field in the complex frequency domain can be obtained. The solution x (italics) of equation (36) in the complex frequency domain can be transformed to the time domain by applying the FILT method described above. Here, in the algorithm of this embodiment, the exponential function of Bromwich integral can be approximated by the following equation (38).

where α is an approximation parameter. Substituting equation (38) into the Bromwich integral yields equation (39).

here,

is. The infinite series of Eq. (39) is truncated with a finite number of terms for numerical calculations, and applying the Euler transform yields Eq. (42), which represents the inverse Laplace transform.

ここで、

here,

であり、ｐ（斜体）は、Ｅｕｌｅｒ変換の項数を示す。式（４２）は、ある観測時刻において他の観測時刻とは互いに独立に計算が可能であり、各観測時刻での電磁界を容易に並列計算できる。

and p (italic) indicates the number of terms of the Euler transformation. Equation (42) can be calculated independently from other observation times at a certain observation time, and the electromagnetic field at each observation time can be easily calculated in parallel.

[Calculation example (4) Integral equation method in complex frequency domain]
In this computational example, the scatterer is a PEC (Perfect Electric Conductor) sphere, the thickness of the conductor is zero, and the aperture exists within the range of spherical coordinates (i.e., there is an aperture on a portion of the spherical surface). Assume that An incident wave to this PEC sphere is shown in equation (45).

here,

is. Also, the normalized complex frequency S=s(ε ₀ μ ₀ ) ^1/2 a, the normalized distance R=r/a, a is the radius of the sphere surrounding the scatterer, θin and φin are the angles of incidence, E ₀ ^ (Ezero hat) is the spectrum of the incident wave.
For this example, the electric field integral equation in the complex frequency domain is given by equation (47).

where J(R) is the unknown surface current distribution, t (tee hat) is the unit tangent vector on the surface of the scatterer,

is. The surface of the scatterer is divided into triangular regions and extended using RWG (Rao-Wilton-Glisson) basis functions such as shown in equation (51). That is, the current density J is developed as shown in Equation (50) using RWG basis functions and the like.

where In is the unknown expansion coefficient, N is the number of unknowns,

is. Here, A _n ⁺ and A _n ^- are the areas of triangle T _n ⁺ and triangle T _n ^- , ρ _n ⁺ and ρ _n ^- are the position vectors of the vertices of triangle T _n ⁺ and triangle T _n ^- , l _n is the side length.
Equation (47) is discretized by replacing In with Equation (50) (i.e., J(R) in Equation (50) is replaced with basis function fn(R) in Equation (51) and Equation (50) ) and multiplied by a set of test functions. The surface current is obtained by calculating the inner product in the same manner as the known method of moments. Based on the surface current distribution, the scattered electric field E _θ ^(S) at the observation angle (θ, φ) is given by equation (52).

here,

This complex frequency domain function is numerically transformed to the time domain by applying the FILT method described above.

[Calculation example (5) Complex frequency domain integral equation using static approximation]
FIG. 5 is a diagram showing an example of an object to be analyzed according to this embodiment. In this calculation example, the object to be analyzed is assumed to be an arbitrary-shaped object composed of a uniform metal shown in FIG. Specifically, as shown in the figure, the object to be analyzed is composed of a metal object mt obtained by dividing metal in an arbitrary shape, and the size of the object is set to 0.1 times or less of the incident wavelength.
The dielectric constant of a metal is defined by equation (55) as Lorentz-Drude model.

where s is the complex frequency, ω _p is the plasma frequency, ω _j is the resonance frequency, ν ₀ and ν ₁ are the collision frequencies, A ₀ and A _i are constants specific to the medium, and K is the number of oscillators. (All symbols in the formula are in italics). If the dielectric constant of the object to be analyzed is negative and the size of the object to be analyzed is sufficiently smaller than the incident wavelength, plasmon resonance in which the electromagnetic field in the vicinity of the object to be analyzed is enhanced can be observed.
For formulation, the scattered electromagnetic field and the incident field are represented by equation (56).

Assuming that the object to be analyzed is sufficiently smaller than the incident wavelength, equation (56) is developed into equations (57) and (58) using static approximation.

Here, β=s(ε ₀ μ ₀ ) ^1/2 d, d represents the size of the object to be analyzed. In equations (57) and (58), the 0th order term satisfies the boundary condition of equation (59).

where E ₀ ^± =ε ^−1/2 e ₀ ^± , f _in ^(s) (efin hat s) is the spectrum of the incident wave, and n is the unit normal vector. Also, by this static approximation, the normal direction component of the electric field on the boundary surface of the object to be analyzed can be represented by the following equation (60) using the unknown surface charge density σ̂ (sigma hat).

However, Ω indicates the surface of the object to be analyzed.
Next, from the condition of continuity of the normal component of the electric flux density on the boundary surface, the boundary type integral equation shown in Equation (61) is obtained.

ここで、

here,

is.
Next, the unknown charge density is approximated by a basis function j ^ _i (Jay hat eye).

_ai is the unknown expansion coefficient and N is the number of unknowns. Equation (61) is discretized by Equation (62) and trial function _t̂i (tee hat eye) to obtain the simultaneous linear equations of Equation (64).

ただし、

however,

The unknown charge density is obtained by solving the simultaneous linear equations of Equation (64).
When the iterative method is used to solve the simultaneous linear equations, the BIEM (Boundary Integral Equation Method) reduces the calculation time and computer memory to the order of the square of the unknown number N (in italics) O(N^2). proportional (where N^2 denotes N squared). In order to increase the speed by MM (Fast Multipole Method), the object to be analyzed is divided into boxes (see FIG. 5). Here, the Green's function in free space is expressed by the following equation (67).

where r _m and r _m' are distance vectors to the centers of groups m and m',

is. L indicates the number of truncated terms in FMM. Interactions between elements directly compute the matrix elements of equation (64) if they fall within boxes that are close to each other. Otherwise, equation (67) can be used to group the calculations. As a result, the amount of calculation at level 2 where box division is performed twice can be reduced to O(N ^1.5 ), and the amount of calculation can be further reduced to O(N) at the time of multi-level extension where box division is performed.
Also, for eigenmode analysis, Equation (61) is transformed into the following eigenequation.

here,

where k is a mode number and λ _k is an eigenvalue, which are obtained by solving equation (70). Also, the permittivity ε _k at resonance is obtained from the relationship of Equation (71). In order to express the change in surface charge over time, the charge density is developed by the following equation.

Here, a _k (t) indicates expansion coefficients. The following equation is obtained by expanding equation (72) in the complex frequency domain by Laplace transform.

here,

σ _k (r, s) thus obtained is transformed into the time domain by the FILT method.

[Calculation example (6) Exact solution in complex frequency domain]
The case of analyzing the problem of a two-dimensional dielectric cylinder uniform in the z-axis placed in free space will be described. The incident wave is assumed to be an H wave that has a magnetic field component only in the z-axis direction, and exact solutions in the complex frequency domain are obtained for various media that make up the cylinder. Scattered electromagnetic fields Hz(s), Eφ(s) and Er(s) for an incident plane wave Hz(i) can be expressed by equations (76) to (80).

Here, H ₀ (s): incident waveform, A _n : scattering coefficient, I _n (·): first-class modified Bessel function, K _n (·): second-class modified Bessel function, r: observation distance, θ : observation angle, φ: incident angle, ε ₀ : permittivity in vacuum, μ ₀ : magnetic permeability in vacuum, Z ₀ : wave impedance in vacuum (both in italics). The scattering coefficient A _n is obtained as follows by considering the boundary conditions for the medium forming the dielectric cylinder.

1) For a perfect conductor

Here, a is the radius of the cylinder.

2) For dielectrics

Here, ε ₁ : dielectric constant of the cylinder, ε _r : relative dielectric constant of the cylinder, μ ₁ : magnetic permeability of the cylinder, and μ _r : relative magnetic permeability of the cylinder.

3) When dielectric coating is applied to a perfect conductor

Here, b: radius of inner cylinder, a: radius of outer cylinder, ε ₁ : permittivity of outer cylinder, ε _r1 : relative permittivity of outer cylinder, μ ₁ : magnetic permeability of outer cylinder, μ _r1 : outer cylinder is the relative permeability of

4) In the case of two-layer dielectric

Here, ε ₂ : permittivity of inner cylinder, ε _r2 : relative permittivity of inner cylinder, μ ₂ : magnetic permeability of inner cylinder, μ _r2 : relative permeability of inner cylinder.

[Overall Configuration of Computing System]
Next, the overall configuration of the arithmetic system 1 of this embodiment will be described with reference to FIG.
FIG. 6 is a diagram showing an example of the configuration of the arithmetic system 1 of this embodiment. The arithmetic system includes one or more arithmetic devices 10 , an arithmetic management device 20 , and a storage device 30 . In one example of the present embodiment, a case of calculating the response waveform fw using n arithmetic devices 10 from arithmetic device 10-1 to arithmetic device 10-n (n is a natural number) will be described.

The calculation management device 20 supplies the calculation condition OC to the calculation device 10 and acquires the calculation result RS obtained by the calculation device 10 based on the calculation condition OC. The calculation management device 20 causes the plurality of calculation devices 10 to perform parallel calculation of one response waveform fw by supplying different initial times t0 to the plurality of calculation devices 10 and causing them to perform calculations.

The operation management device 20 includes an acquisition unit 210 , an operation time width calculation unit 220 , an operation condition supply unit 230 , an operation result acquisition unit 240 and an integration unit 250 .

The acquisition unit 210 acquires the computation target information MDL and the number of parallel devices NPC from a host device (not shown). Here, the number of parallel devices NPC is the number of parallel processing devices 10 that calculate the response waveform fw.

Based on the number of parallel devices NPC acquired by the acquiring unit 210 and the computing performance CP of each computing device 10, the computing time width calculating unit 220 determines the computing time width tw to be assigned to each computing device 10 for each computing device 10. Calculate to Here, the calculation performance CP may be stored in the storage device 30 in advance, or may be acquired by the calculation management device 20 inquiring of the calculation device 10 . The calculation time width calculation unit 220 calculates the initial time t0 of calculation for each calculation device 10 based on the calculation time width tw calculated for each calculation device 10 .

The calculation condition supply unit 230 supplies the calculation conditions OC to each calculation device 10 . The calculation condition OC includes the initial time t0 calculated by the calculation time width calculator 220 and the calculation time width tw. Specifically, the calculation condition supply unit 230 supplies the calculation condition OC1 including the initial time t0-1 and the calculation time width tw-1 to the calculation device 10-1. Operation condition supply unit 230 supplies operation condition OC2 including initial time t0-2 and operation time width tw-2 to operation device 10-2. Similarly, the calculation condition supply unit 230 supplies the calculation condition OCn including the initial time t0-n and the calculation time width tw-n to the calculation device 10-n.

Each arithmetic device 10 calculates the response waveform fw as the arithmetic result RS based on the arithmetic conditions OC supplied from the arithmetic management device 20 . The calculation device 10 supplies the calculated calculation result RS to the calculation management device 20 . Specifically, the calculation device 10-1 supplies the calculation result RS1 to the calculation management device 20. FIG. The calculation device 10-2 supplies the calculation result RS2 to the calculation management device 20. FIG. Similarly, the calculation device 10-n supplies the calculation result RSn to the calculation management device 20. FIG.

The computation result acquisition unit 240 acquires the computation result RS supplied from each computation device 10 . This calculation result RS includes the calculation result of the response waveform fw corresponding to the calculation time width tw assigned to each calculation device 10 .

The integration unit 250 integrates a plurality of computation results RS that the computation result acquisition unit 240 each acquires from the computation device 10 .

[Operation of computing system]
Next, an example of the operation of the computing system 1 will be described with reference to FIG.
FIG. 7 is a diagram showing an example of the operation of the arithmetic system 1 of this embodiment.

(Step S10) The acquisition unit 210 acquires the calculation target information MDL.
(Step S20) The acquisition unit 210 acquires the number of parallel devices NPC. Here, as an example, a case where parallel calculation is performed by four arithmetic units 10 will be described. In this case, the number of parallel devices NPC is "4".
(Step S<b>30 ) The acquisition unit 210 acquires computing performance information from the storage device 30 . This calculation performance information indicates the calculation performance CP of each calculation device 10 . In this example, a case will be described in which the computing performance CP of the four units is the same.

(Step S40) The calculation time width calculation unit 220 calculates the calculation time width tw for each calculation device 10 based on the number of parallel devices NPC obtained in step S20 and the calculation performance information obtained in step S30. . A specific example of the computation time width tw calculated by the computation time width calculator 220 will be described with reference to FIG.

FIG. 8 is a diagram showing an example of a calculation result RS of parallel calculation by the calculation device 10 of this embodiment. In one example of the present embodiment, a case where four arithmetic devices 10 (arithmetic devices 10-1 to 10-4) perform parallel operations will be described. The calculation management device 20 divides the calculation time width tw from the start time ts to the end time te as the calculation target. In this example, the four arithmetic units 10 have the same arithmetic performance CP. Therefore, the computation time width calculator 220 divides the computation time width tw by equally dividing the period from the start time ts to the end time te into four. Specifically, the calculation time width calculator 220 sets the calculation time width tw-1, the calculation time width tw-2, the calculation time width tw-3, and the calculation time width tw-4 from the start time ts to the end time te. Divide into 4 equal parts. Here, the computing time width tw-1 is the computing time width tw assigned to the computing device 10-1. Similarly, the calculation time widths tw-2 to -4 are the calculation time widths tw assigned to the calculation devices 10-2 to -4.

That is, the computation management device 20 includes a computation time width calculator 220 . The calculation time width calculation unit 220 calculates the calculation time width tw from the initial time t0 for each calculation device 10 based on the calculation performance CP of the calculation unit 120 included in each calculation device 10 .

That is, the calculation time width calculator 220 calculates the calculation time width tw based on the calculation performance CP of the calculator 120 . That is, the calculation time width tw is determined based on the calculation performance CP of the calculation unit 120 .

The computation time width calculator 220 arranges the divided computation time widths tw-1 to -4 in time series, and calculates the start time of each computation time width tw as the initial time t0. Specifically, the calculation time width calculation unit 220 sets the start time of the calculation time width tw-1 to the initial time t0-1, sets the start time of the calculation time width tw-2 to the initial time t0-2, and sets the calculation time width The start time of tw-3 is assumed to be initial time t0-3, and the start time of calculation time width tw-4 is assumed to be initial time t0-4.

(Step S50) Returning to FIG. 7, the calculation condition supply unit 230 uses the calculation target information MDL, the calculation time width tw calculated by the calculation time width calculation unit 220 as described above, and the initial time t0 as calculation conditions OC. It is supplied to each computing device 10 . More specifically, the computation time width calculator 220 supplies the computation target information MDL, the computation time width tw-1, and the initial time t0-1 to the computation device 10-1. Similarly, the calculation condition supply unit 230 sends the calculation target information MDL, the calculation time width tw-2, and the initial time t0-2 to the calculation device 10-2, the calculation target information MDL, the calculation time width tw-3, and the initial time t0-2. t0-3 to the arithmetic device 10-3, and the arithmetic target information MDL, the arithmetic time width tw-4 and the initial time t0-4 to the arithmetic device 10-4.

That is, the calculation condition supply unit 230 supplies the initial time t0 that is different for each calculation device 10 as the calculation condition OC to the plurality of calculation devices 10 .

Further, the calculation condition supply unit 230 supplies the calculation time width tw calculated by the calculation time width calculation unit 220 to the calculation device 10 as the calculation condition OC.

Each arithmetic device 10 calculates the response waveform fw as the arithmetic result RS based on the arithmetic conditions OC supplied from the arithmetic management device 20 . The response waveform fw calculated by the arithmetic unit 10 will be described with reference to FIG. 8 again.

The calculation condition obtaining unit 110 of each calculation device 10 obtains the initial time t0. Here, the initial time t0 is the starting point on the time axis for calculation of the time-varying response waveform fw.

Each computing device 10 calculates an initial value f0 at initial time t0. Further, each arithmetic device 10 calculates a response waveform fw corresponding to the arithmetic time width tw based on the calculated initial value f0. More specifically, arithmetic device 10-1 calculates initial value f0-1 at initial time t0-1. Further, the calculation device 10-1 calculates a response waveform fw1 for the calculation time width tw-1 based on the initial value f0-1. Arithmetic devices 10-2 to -4 calculate response waveforms fw-2 to -4 in the same manner as arithmetic device 10-1.

Here, the calculation unit 120 of the calculation device 10 calculates the initial value f0 by the FDCFD-FILT method described above. That is, the arithmetic unit 10 calculates the initial value f0 by discrete time response analysis using the inverse Laplace transform method. Here, the initial value f0 is the calculation result RS for the response waveform fw (waveform) at the initial time t0 obtained by the calculation condition obtaining unit 110 . Also, the inverse Laplace transform method referred to here is the FILT method.
Also, the output unit 130 of the arithmetic device 10 outputs the initial value f0 calculated by the arithmetic unit 120 .

Further, the calculation unit 120 of the calculation device 10 calculates the response waveform fw for the calculation time width tw after the initial time t0 by the above-described FDTD method. That is, the calculation device 10 calculates the calculation result RS for the predetermined calculation time width tw for the response waveform fw by sequential calculation along the time axis based on the calculated initial value f0.
Further, the output unit 130 of the arithmetic device 10 outputs the arithmetic result RS calculated by the arithmetic unit 120 for each arithmetic time width tw.

(Step S60) Returning to FIG. 7, the calculation result acquisition unit 240 acquires the initial value f0 and the response waveform fw calculated by each calculation device 10, that is, the calculation result RS. Specifically, calculation result obtaining section 240 obtains initial value f0-1 and response waveform fw1 from calculation device 10-1. Similarly, calculation result acquisition section 240 obtains initial value f0-2 and response waveform fw2 from calculation device 10-2 and initial value f0-3 and response waveform fw3 from calculation device 10-3. An initial value f0-4 and a response waveform fw4 are obtained from the device 10-4.

That is, the calculation result obtaining unit 240 obtains the initial value f0 calculated by each of the plurality of calculation devices 10 based on the supplied initial time t0.

(Step S70) The integration unit 250 integrates the divided response waveforms fw (response waveforms fw1 to fw4 in this specific example) obtained from the arithmetic units 10 in step S60 into one response waveform fw. That is, the integration unit 250 integrates the multiple initial values f0 acquired by the calculation result acquisition unit 240 .

[Summary of embodiment]
As described above, when the initial time t0 is given, the arithmetic device 10 calculates the initial value f0 of the response waveform fw at the initial time t0 by discrete time response analysis using the inverse Laplace transform method.

In general, once the initial value f0 of the response waveform fw is obtained, the response waveform fw after the initial time t0 can be obtained by successive calculations along the time axis (for example, the FDTD method described above). However, when obtaining the initial value f0 at a given initial time t0 by the above-described FDTD method, the results of sequential calculations along the time axis before (past) the initial time t0 are required. That is, according to the conventional method, given an arbitrary initial time t0, it is difficult to obtain the value of the response waveform fw at this initial time t0 (that is, the initial value f0).

The arithmetic device 10 of the present embodiment performs discrete time response analysis by inversely transforming the results of arithmetic operations in the s-domain into the t-domain by inverse Laplace transform. Therefore, when an arbitrary initial time t0 is given, the arithmetic device 10 can obtain the value of the response waveform fw at the initial time t0 (that is, the initial value f0) by numerical calculation. That is, the computing device 10 can obtain only a part of the response waveform fw by numerical computation.
Since the calculation device 10 of the present embodiment performs calculation by discrete time response analysis using the inverse Laplace transform method, the initial value f0 can be calculated without referring to calculation results of other calculation devices 10 . Therefore, when a plurality of arithmetic devices 10 of this embodiment are arranged in parallel, each arithmetic device 10 can calculate the initial value f0 in parallel with the other arithmetic devices 10 . That is, according to the arithmetic device 10 of the present embodiment, the calculation of the initial value f0 of the response waveform fw can be parallelized.

Further, the arithmetic unit 10 of the present embodiment employs the FILT method for numerical calculations in the inverse Laplace transform. The inverse Laplace transform is generally a difficult operation, but according to the arithmetic unit 10 of the present embodiment, numerical operations in the inverse Laplace transform can be easily performed.

Further, according to the arithmetic device 10 of the present embodiment, parallelization of the arithmetic device 10 can be facilitated. That is, as described above, if the initial time t0 is given, the arithmetic device 10 of the present embodiment can obtain the initial value f0 (that is, part of the response waveform fw) at the initial time t0 by numerical calculation. . Therefore, by giving different initial times t0 to a plurality of arithmetic devices 10, each arithmetic device 10 can calculate the initial value f0 for this arithmetic device 10. FIG. For example, by giving initial times t0-1 to -4 to four arithmetic devices 10, arithmetic devices 10-1 to -4, arithmetic device 10-1 sets initial value f0-1 to arithmetic device 10-2 calculates the initial value f0-2, the arithmetic unit 10-3 calculates the initial value f0-3, and the arithmetic unit 10-4 calculates the initial value f0-4. Here, each arithmetic unit 10 calculates the initial value f0 independently of the other arithmetic units 10 by discrete time response analysis by the inverse Laplace transform method. That is, the arithmetic device 10 can calculate the initial value f0 without referring to the arithmetic results of other arithmetic devices 10 . Therefore, even if another arithmetic device 10 is in the process of calculating the initial value f0, the arithmetic device 10 can calculate the initial value f0 regardless of the calculation status of the other arithmetic device 10 . In other words, the arithmetic device 10 can individually calculate the initial value f0 (that is, part of the response waveform fw) regardless of the arithmetic conditions of the other arithmetic devices 10, so parallelization of the arithmetic device 10 is easy. can be

Further, the calculation device 10 of the present embodiment calculates the calculation result RS for a predetermined calculation time width tw for the response waveform fw (waveform) by sequential calculation along the time axis based on the calculated initial value f0. . With this configuration, the arithmetic device 10 can calculate not only the initial value f0 but also the response waveform fw of the time width after the initial time t0. In addition, since the arithmetic device 10 calculates the response waveform fw of the time width after the initial time t0 by a conventional method (for example, the FDTD method), existing arithmetic software can be used. Computation software can be configured more easily than when it is not possible.

Further, in the arithmetic device 10 of the present embodiment, the arithmetic time width tw is determined based on the arithmetic performance CP of the arithmetic unit 120 . Therefore, when the calculation of the response waveform fw is parallelized, a larger computation time width tw is allocated to the computation device 10 with relatively high performance, and a smaller computation time width tw is allocated to the computation device 10 with relatively low performance. can be assigned. Here, the high-performance arithmetic unit 10 has a relatively high arithmetic speed, and the low-performance arithmetic unit 10 has a relatively low arithmetic speed. Each arithmetic unit 10 takes charge of the arithmetic time width tw based on the arithmetic performance CP, so that, for example, a large arithmetic time width tw is allocated to the arithmetic unit 10 with low performance, resulting in an increase in the arithmetic time. Problems can be reduced.

Further, the calculation management device 20 of this embodiment includes a calculation condition supply section 230 , a calculation result acquisition section 240 and an integration section 250 . The calculation condition supply unit 230 supplies the initial time t0 that is different for each calculation device 10 as the calculation condition OC to the plurality of calculation devices 10 . The calculation result obtaining unit 240 obtains the initial value f0 calculated by each of the plurality of calculation devices 10 based on the supplied initial time t0. The integration unit 250 integrates a plurality of initial values f0 (that is, part of the response waveform fw) computed by each computing device 10 into one response waveform fw. According to the operation management device 20 of this embodiment, parallelization of the operation device 10 can be facilitated.

Further, the computation management device 20 of this embodiment includes a computation time width calculator 220 . The computation time width calculator 220 calculates the computation time width tw from the initial time t0 for each computation device 10 based on the computation performance CP of the computation unit 120 included in each computation device 10 . By providing this calculation time width calculation unit 220, when the calculation of the response waveform fw is parallelized by a plurality of calculation devices 10, a larger calculation time width tw is assigned to the calculation device 10 with relatively high performance, A smaller computation time width tw can be assigned to a computation device 10 with relatively low performance. In this way, the calculation management device 20 calculates the calculation time width tw to be assigned to each calculation device 10 by the calculation time width calculation unit 220 for each calculation device 10 , thereby calculating the calculation time by each calculation device 10 for each calculation device 10 . can be adjusted to For example, the operation management device 20 allocates a small operation time width tw to the low-performance operation device 10 and allocates a large operation time width tw to the high-performance operation device 10, so that each operation device 10 The time from the start of calculation to the end of calculation (that is, calculation processing time) can be made uniform.

As described above, according to the arithmetic device 10 and the arithmetic management device 20 of the present embodiment, it is possible to simultaneously perform the arithmetic operation for obtaining the response waveform fw by a plurality of arithmetic devices 10, and one arithmetic device Compared to the case where 10 obtains the response waveform fw, it is possible to reduce the computational load per computing device 10 . Therefore, according to the arithmetic device 10 and the arithmetic management device 20 of the present embodiment, the response waveform fw can be calculated in a reasonable arithmetic processing time without using an extremely high-performance arithmetic device 10 such as a supercomputer. .

[Example of calculation result]
A specific example of the response waveform fw calculated by a plurality of parallel arithmetic units 10 will be described with reference to FIG.
FIG. 9 is a diagram showing a specific example of response waveforms fw calculated by the plurality of arithmetic units 10 of this embodiment. In this example, the response waveform fw is calculated by parallel calculation of six arithmetic units 10, ie, arithmetic units 10-11 to -16 (none of which are shown). The calculation device 10-11 calculates the response waveform fw11 for the calculation time width tw11 (time t1 to time t2). The calculation device 10-12 calculates the response waveform fw12 for the calculation time width tw12 (time t2 to time t3). Similarly, the computing devices 10-13 to -16 calculate the response waveforms fw13 to fw16, respectively.
The integration unit 250 of the calculation management device 20 integrates the calculated response waveforms fw11 to fw16 as a response waveform fw.

[Example of comparison with conventional calculation results]
FIG. 10 is a diagram showing a concrete example of the response waveform wo calculated by one computing device according to the conventional method. The response waveform wo in FIG. 10 is calculated by a single computing device through sequential computation along the time axis according to a conventional method (for example, the FDTD method). In the case of the example shown in FIG. 10, the same calculation object information MDL as the calculation object information MDL given when obtaining the response waveform fw of FIG. 9 is given to one arithmetic unit. In other words, the response waveform fw in FIG. 9 and the response waveform wo in FIG. 10 are the result of computation for the same computation target information MDL. It is shown that the response waveform fw, which is the result of parallel computation by the plurality of computing devices 10 shown in FIG. 9, and the response waveform wo by one computing device are in good agreement. In other words, according to the arithmetic device 10 and the arithmetic management device 20 of the present embodiment, even if a plurality of arithmetic devices 10 perform simultaneous parallel arithmetic, the same arithmetic result as the conventional method performed by a single arithmetic device can be obtained. can get.

Further, it took 90 minutes for one arithmetic unit to calculate the response waveform wo by sequential arithmetic along the time axis according to the conventional method (for example, the FDTD method). On the other hand, the experimental results of the computation method of the present embodiment when using the computation device 10 with the same computation performance CP are as follows. For example, when calculating the response waveform fw by parallel calculation by four arithmetic units 10, the arithmetic processing time for one arithmetic unit 10 to calculate the initial value f0 is 5 minutes, and the arithmetic processing time is tw. The arithmetic processing time for calculating the response waveform fw was 28 minutes. That is, according to the calculation method of the present embodiment, the calculation processing time required for one calculation device to calculate 10 initial values f0 and to calculate the response waveform fw for the calculation time width tw was 32 minutes. Since the arithmetic unit 10 of this embodiment is parallelized, the entire response waveform fw can be calculated in 32 minutes. Therefore, in the case of this example, it was shown that the calculation method of the present embodiment can calculate the response waveform fw in about 35% of the calculation processing time of the conventional method.

[Modification]
Note that the calculation device 10 has been described so far as calculating the initial value f0 and the response waveform fw, but the present invention is not limited to this. The arithmetic device 10 may calculate only the initial value f0. When the calculation target information MDL and the initial time t0 are given, the calculation device 10 can calculate the initial value f0 by discrete time response analysis using the inverse Laplace transform method. Here, the number of arithmetic units 10 that perform parallel arithmetic corresponds to the number of initial values f0. The response waveform fw can also be obtained by calculating the initial values f0-1 to -n using n arithmetic units 10 and plotting the calculated initial values f0-1 to -n. If the response waveform fw is obtained by plotting the initial values f0-1 to -n, the response waveform fw can be obtained without the calculation device 10 calculating the response waveform fw. That is, if the arithmetic unit 10 calculates the initial value f0 by discrete time response analysis using the above-described inverse Laplace transform method, the arithmetic unit 10 can respond without performing sequential arithmetic along the time axis based on the calculated initial value f0. A waveform fw can be obtained.
For example, if tens of thousands of arithmetic units 10 are parallelized, tens of thousands of calculated initial values f0 can be plotted as a response waveform fw.

Although the embodiment of the present invention has been described in detail with reference to the drawings, the specific configuration is not limited to this embodiment, and modifications can be made as appropriate without departing from the scope of the present invention. . You may combine the structure as described in embodiment mentioned above.

Note that each unit included in the arithmetic device 10 and the arithmetic management device 20 in the above embodiment may be realized by dedicated hardware, or may be realized by a memory and a microprocessor. .

In addition, each unit provided in the arithmetic unit 10 and the arithmetic management unit 20 is configured by a memory and a CPU (central processing unit), and a program for realizing the function of each unit provided in the arithmetic unit 10 and the arithmetic management unit 20 is loaded into the memory. The function may be realized by executing the

Also, a program for realizing the function of each part provided in the arithmetic device 10 and the arithmetic management device 20 is recorded in a computer-readable recording medium, and the program recorded in this recording medium is read by the computer system and executed. Accordingly, processing may be performed by each unit included in the control unit. It should be noted that the "computer system" referred to here includes hardware such as an OS and peripheral devices.

The "computer system" also includes the home page providing environment (or display environment) if the WWW system is used.
The term "computer-readable recording medium" refers to portable media such as flexible discs, magneto-optical discs, ROMs and CD-ROMs, and storage devices such as hard discs incorporated in computer systems. Furthermore, "computer-readable recording medium" means a medium that dynamically retains a program for a short period of time, like a communication line when transmitting a program via a network such as the Internet or a communication line such as a telephone line. It also includes those that hold programs for a certain period of time, such as volatile memories inside computer systems that serve as servers and clients in that case. Further, the program may be for realizing part of the functions described above, or may be capable of realizing the functions described above in combination with a program already recorded in the computer system.

Reference Signs List 1 operation system 10 operation device 110 operation condition acquisition unit 120 operation unit 130 output unit 20 operation management device 210 acquisition unit 220 operation time width calculation unit 230 operation conditions Supply unit 240 Calculation result acquisition unit 250 Integrating unit 30 Storage device MDL Calculation target information tw Calculation time width f0 Initial value t0 Initial time fw Response waveform

Claims (4)

change over timeof the electromagnetic field strengthabout the waveformfor complex frequency domain functionsan initial time that is the starting point on the time axis of the operation;The calculation time width from the initial time is used as the calculation conditiongetCalculation conditionan acquisition unit;
SaidCalculation conditionAn initial value, which is a calculation result of the waveform at the initial time acquired by the acquisition unit,for the functionCalculated by discrete time response analysis using the inverse Laplace transform methodand calculating a calculation result of the waveform corresponding to the calculation time width obtained by the calculation condition obtaining unit by performing sequential calculation along the time axis based on the calculated initial value.a computing unit;
Sending the calculation result calculated by the calculation unit for each calculation time width to the calculation management device an output unit for output;
a computing device comprising
an arithmetic time width calculation unit that calculates the arithmetic time width from the initial time for each arithmetic unit based on the arithmetic performance of the arithmetic unit for each arithmetic unit obtained by inquiring of each arithmetic unit;
an arithmetic condition supply unit that supplies, as arithmetic conditions, the initial time and the arithmetic time width from the initial time, which are different for each of the arithmetic devices, to the plurality of arithmetic devices;
a calculation result obtaining unit that obtains a calculation result corresponding to the initial value calculated by each of the plurality of calculation devices based on the supplied initial time;
an integration unit that integrates the operation results corresponding to the plurality of initial values acquired by the operation result acquisition unit in order of the initial time;
an arithmetic management unit comprising
Computing system including The arithmetic system according to claim 1, wherein the inverse Laplace transform method is the FILT method. a calculation condition obtaining unit that obtains, as calculation conditions, an initial time, which is the starting point on the time axis of calculation for a complex frequency domain function of a time-varying electromagnetic field intensity waveform, and a calculation time width from the initial time;
calculating an initial value, which is a calculation result of the waveform at the initial time obtained by the calculation condition obtaining unit, by discrete time response analysis using an inverse Laplace transform method for the function, and calculating the calculated initial value; a calculation unit that calculates the calculation result of the waveform for the calculation time width acquired by the calculation condition acquisition unit by sequential calculation along the time axis based on
an output unit that outputs the calculation result calculated by the calculation unit for each calculation time width to a calculation management device;
A computing device comprising In the computer equipped with the arithmetic unit,
a calculation condition acquisition step of obtaining, as calculation conditions, an initial time, which is the starting point on the time axis of calculation for a function of the complex frequency domain for the time-varying electromagnetic field intensity waveform, and a calculation time width from the initial time ;
calculating an initial value, which is a calculation result of the waveform at the initial time obtained in the calculation condition obtaining step, by discrete time response analysis using an inverse Laplace transform method for the function , and calculating the calculated initial value; a calculation step of calculating the calculation result of the waveform for the calculation time width obtained in the calculation condition acquisition step, by sequential calculation along the time axis based on
an output step of outputting the calculation result calculated for each calculation time width in the calculation step to a calculation management device ;
program to run the

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