JP3829191B2 - Method for estimating electromagnetic field of dispersion medium - Google Patents

Description

【００１６】
【数１８】

【００１７】
［ローレンツ媒体］
ここで、ローレンツ分散特性をもったローレンツ媒体については、次の様に計算する。ω_pをｐ番目の分極対の共鳴周波数、Ａ_pをその振幅、δ_pを減衰率、ε_sを静電気的な誘電率、ε_∞を周波数無限大での誘電率、また、Δε＝ε_s−ε_∞とするとき、ｐ対の分極対があるローレンツ媒質の誘電率は周波数座標で次の様になることが知られている。
【００１８】
【数１９】

【００１９】
角周波数ωでは、
【数２０】

とするとき、周波数座標でのアンペアの法則は次の様になる。
【００２０】
【数２１】

ここで、
【００２１】
【数２２】

である。
【００２２】
ここで、数２１あるいは数２２は、逆フーリエ変換をとり、時間についての差分表現にすると、次のようになる。
【００２３】
【数２３】

【００２４】
【数２４】

本発明のＦＤＴＤ法では、数１７から磁場は次の差分漸化式になる。
【００２５】
【数２５】

【００２６】
これらの数２３から数２５を用いてベクトルＥⁿからベクトルＥⁿ⁺¹を求める手順を、図１を用いて説明する。
１）ベクトルＨ^n-1/2とベクトルＥⁿからベクトルＨ^n+1/2を求める。
２）ベクトルＱ_p ^n-1とベクトルＱ_p ⁿとベクトルＥⁿからベクトルＱ_p ⁿ⁺¹を求める。
３）ベクトルＨ^n+1/2とベクトルＥⁿとベクトルＱ_p ⁿ⁺¹とベクトルＱ_p ⁿからベクトルＥⁿ⁺¹を求める。
【００２７】
これに対し、ＬＡＤＥＳ法による従来の方法では、数２１に対応する磁場の差分漸化式を次のようにしている。
【数２６】

また、数２２に対応する電流の差分漸化式は、
【００２８】
【数２７】

である。
完全に時間同期を取ったＦＤＴＤ法では、漸化式は、次のようになる。
【００２９】
【数２８】

電流に関しては、
【００３０】
【数２９】

ここで、
【００３１】
【数３０】

【００３２】
【数３１】

である。
【００３３】
これらの数２３から数２５を用いてベクトルＥⁿからベクトルＥⁿ⁺¹を求める手順を、図６を用いて説明する。
１）ベクトルＨ^n-1/2とベクトルＥⁿからベクトルＨ^n+1/2を求める。
２）ベクトルＨ^n-1/2とベクトルＥⁿとベクトルＥ^n-1とベクトルＪ_p ^n-1とベクトルＪ_p ⁿとからベクトルＥⁿ⁺¹を求める。
３）ベクトルＥⁿ⁺¹とベクトルＥ^n-1とベクトルＪ_p ^n-1とベクトルＪ_p ⁿとからベクトルＪ_p ⁿ⁺¹を求める。
【００３４】
この様に従来のＦＤＴＤ法では８種の変数を用いるが、本発明のＦＤＴＤ法の漸化式では７種の変数を用いることが分かる。
【００３５】
また、数２３と数２７が同等なものであることは次の様にして理解することができる。
数２１と数２６から、次の数３２が導かれる。
【００３６】
【数３２】

また、ＦＴＤＴ法では、次の関係がある。
【００３７】
【数３３】

この数３３と数２９を数２３に代入することにより数２８が得られる。
【００３８】
［デバイ媒体］
次にデバイ分散特性を示すデバイ媒体の場合について説明する。τ_pをｐ番目の分極対の緩和時間とするとき、ｐ対の分極対があるデバイ媒質の誘電率は周波数座標で次の様になることが知られている。
【００３９】
【数３４】

ここで、本発明で用いる数２４に対応する漸化式は、次の様になる。
【００４０】
【数３５】

【００４１】
この式の他に、数２３と数２５を用いて、図２に示す様に処理を進める。
１）ベクトルＨ^n-1/2とベクトルＥⁿからベクトルＨ^n+1/2を求める。
２）ベクトルＱ_p ^n-1とベクトルＱ_p ⁿとベクトルＥⁿからベクトルＱ_p ⁿ⁺¹を求める。
３）ベクトルＨ^n+1/2とベクトルＥⁿとベクトルＱ_p ⁿ⁺¹とベクトルＱ_p ⁿからベクトルＥⁿ⁺¹を求める。
【００４２】
これは、上記のＦＴＤＴの場合と同様であるため、ローレンツ媒体とデバイ媒体との演算処理を同時に進められることがわかる。このため、これらの媒体の混成物についての演算処理を容易に行うことができることも明らかである。
【００４３】
一方文献（）に記載された従来のＤＡＤＥＳ法では、数２８と数２９とに対応する漸化式は、次の様になる。
【００４４】
【数３６】

【００４５】
【数３７】

ここで、
【００４６】
【数３８】

【００４７】
【数３９】

である。
【００４８】
これらの数３６から数３９を用いて演算処理を進めるには、図７に示す次の手順に従う。
１）ベクトルＨ^n-1/2とベクトルＥⁿからベクトルＨ^n+1/2を求める。
２）ベクトルＨ^n+1/2とベクトルＥⁿとベクトルＪ_p ⁿからベクトルＥⁿ⁺¹を求める。
３）ベクトルＥⁿとベクトルＥⁿ⁺¹とベクトルＪ_p ⁿからベクトルＪ_p ⁿ⁺¹を求める。
【００４９】
ちなみに、数２３と数３６とが同等のものであることは、数３７を数３２に代入し、この結果を数２３に代入することによって確認することができる。
【００５０】
さらに本発明の方法として、電流ベクトルＪ_p ⁿ換えて電荷ベクトルＱ_p ⁿを用いることにする。この場合、ＦＴＤＴ法では、数３５は数４０となる。
【００５１】
【数４０】

前記の数４０を数２３に代入して次の漸化式を得る事ができる。
【００５２】
【数４１】

ここで、
【００５３】
【数４２】

【００５４】
【数４３】

である。
【００５５】
これらの数４０から数４３を用いて演算処理を進めるには、図３に示す次の手順に従う。
１）ベクトルＨ^n-1/2とベクトルＥⁿからベクトルＨ^n+1/2を求める。
２）ベクトルＨ^n+1/2とベクトルＥⁿとベクトルＱ_p ⁿからベクトルＥⁿ⁺¹を求める。
３）ベクトルＥⁿとベクトルＥⁿ⁺¹とベクトルＱ_p ⁿからベクトルＱ_p ⁿ⁺¹を求める。この手順は、電流ベクトルＪ_p ⁿを電荷ベクトルＱ_p ⁿと入れ換えただけのものであるので、この場合も、ローレンツ媒体とデバイ媒体との演算処理を同時に行なうことは容易である。
【００５６】
［アルゴリズム］
ここで想定するコンピュータは、入力装置と記憶装置と演算装置と出力装置とを備えた計算装置である。このフローチャートの例を図４、図５に示し、以下に説明する。
Ｆ１）見積もり対象とする領域を微小領域に分割し、その座標を上記の入力装置に入力し記憶装置に保存する。
Ｆ２）各微小領域の誘電率と透磁率を設定し、それらの値を上記の入力装置に入力し記憶装置に保存する。
Ｆ３）入射電磁界の波長を設定し、その値を上記の入力装置に入力し記憶装置に保存する。
Ｆ４）入射電磁界を与える微小領域を設定し、それらの座標と入射電磁界の強度と位相とを上記の入力装置に入力し記憶装置に保存する。
Ｆ５）各微小領域の電界Ｅ、磁界Ｈ、あるいは、演算の途中で用いられる中間変数Ｑ₁からＱ_mまでをリセットし、前記の各微小領域の電界Ｅ、磁界Ｈの座標と入射電磁界の強度と位相とを上記の入力装置に入力し記憶装置に保存する。
Ｆ６）前記の電界Ｅ、磁界Ｈ、あるいは、演算の途中で用いられる中間変数Ｑ₁からＱ_mまでを一時的に保存する変数をそれぞれaＥ、aＨ、aＱ₁〜aＱ_mとし、中間変数Ｑ₁からＱ_mまでを一時的に保存する他の変数をbＱ₁〜bＱ_mとするとき、これらの変数をリセットする。
Ｆ７）その他の変数の初期値を設定する。
【００５７】
Ｆ８）第１の繰り返し演算の指標を当初値に設定する。
Ｆ９）繰り返し演算の第１のフラグを設定し、計算対象とする微小領域を決定する。
Ｆ１０）それぞれの微小領域について、それが入射電界を与える領域かどうかの正否を判断する。
Ｆ１４）この判断が正の場合に、見積り対象となる微小領域の磁界ベクトルＨと電界ベクトルＥに入射電磁界の値を引き渡し、後述の第２のフラグの位置から処理を行う。
Ｆ１１）この判断が否の場合には、各微小領域について、ｐ＝１、２、・・・ｍ、とするとき、以下の処理を行なう。まず、ＨをaＨあるいはaＥから計算する。ここで、aＨあるいはaＥは、時間的に前の磁界ベクトルあるいは電界ベクトルである。より具体的には、数２５を用いて演算する。
Ｆ１２）Ｑ_pをaＥ、aＱ_pあるいはbＱ_pから計算する。ここで、aＱ_pやbＱ_pは、時間的に前の電荷成分である。より具体的には、ローレンツ媒体については数２４、デバイ媒体については数３５あるいは数４０を用いて演算する。
Ｆ１３）ＥをＨ、aＥ、Ｑ₁からＱ_mまで、aＱ₁〜aＱ_mから計算する。より具体的には、数２４、数３５あるいは数４０を用いて演算する。ローレンツ媒体については数２３、デバイ媒体については数４１を用いて演算する。
Ｆ１５）第２のフラグを設定し、aＨをＨに保存する。
Ｆ１６）bＱ_pにaＱ_pを保存する。
Ｆ１７）aＱ_pにＱ_pを保存する。
Ｆ１８）aＥにＥを保存する。
Ｆ１９）全微小領域についての計算が終了したかどうかの正否を判断する。否ならば第１のフラグの位置から再び計算する。
Ｆ２０）正ならば、次の処理を行なう。微小領域におけるＨ、Ｅ、Ｑ₁からＱ_mまでを上記の記憶装置に保存する。
Ｆ２１）すべての計算が終了したかどうかの正否を判断する。
Ｆ２２）否ならば、繰り返し演算の指標を１段階進めて第１のフラグの位置から再び計算する。
Ｆ２３）正ならば、この結果を出力装置に出力する。
Ｆ２４）計算を終了する。
【００５８】
【発明の効果】
本発明では、電界ベクトルの漸化式と磁界ベクトルの漸化式と電荷成分の漸化式とを用いることにより、完全な同期をとりながら使用するメモリ領域を減少させることができ、また、デバイ媒体とローレンツ媒体とを、同じアルゴリズムで取り扱うことができるようになり、これらの媒体の混在した媒体については、これを分割することなく取り扱うことができる。
【図面の簡単な説明】
【図１】本発明においてローレンツ媒体を取り扱う場合の漸次求める変数の流れを示すフローチャートである。
【図２】本発明においてデバイ媒体を取り扱う場合の漸次求める変数の流れを示すフローチャートである。
【図３】本発明においてデバイ媒体を取り扱う第２の場合の漸次求める変数の流れを示すフローチャートである。
【図４】本発明のフローチャートである。
【図５】本発明のフローチャートである。
【図６】従来のローレンツ媒体を取り扱う場合の漸次求める変数の流れを示すフローチャートである。
【図７】従来のデバイ媒体を取り扱う場合の漸次求める変数の流れを示すフローチャートである。[0001]
BACKGROUND OF THE INVENTION
According to the present invention, electromagnetic field distribution or electromagnetic field distribution can be estimated using a computing device including an input device, a storage device, an arithmetic device, and an output device. It is about the estimation method of the field.
[0002]
[Prior art]
As a method of estimating an electromagnetic field by numerical analysis, a time domain finite difference method (FDTD) is well known, which is described in Reference 1 (RJ Luebbers, F. Hunsberger, KS Kunz, RB Standler, and M. Schneider, “A frequency-dependent finite-difference time-domain formulation for dispersivematerials,” IEEE Trans. Electromagn. Compat., Vol. 32, pp. 222-227, Aug. 1990.). Further, as a method for extending the FDTD and handling the dispersion medium, Reference 2 (MD Bui, SS Stuchly, and GI Costache, “Propagation of transients indispersive dielectric media,” IEEE Trans. Microwave Theory Tech., Vol. 39 , pp.1165-1172, July 1991.) and Reference 3 (T. Kashiwa, N. Yoshida, and I. Fukai, “A treatment by the finite”). -difference time-domain method of the dispersive characteristics associated with orientationpolarization, ”Trans. IEICE, vol. E73, no. 8, pp. 1326-1328, 1990.) Auxiliary differential equation (ADE) method, or reference 4 (DM Sullivan, “Frequency-dependent FDTD methods using Z transforms,” IEEE Trans. Antennas Propagat., Vol. 40, pp. 1223-1230, Oct. 1992.) Etc. are known. These are applied to a computer that includes an input device, a storage device, an arithmetic device, and an output device.
[0003]
Among these methods, the RC method uses the least amount of memory, but the accuracy is not as good as the ADE method or the ZT method. However, even in the RC method, reference 5 (DF Kelley and RJ Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antennas Propagat., Vol. 44, pp. 792-797, June 1996. As reported in), by applying a partially linear recursive convolution (PLRC) method, the method can be handled with an accuracy comparable to that of the ADE method or the ZT method. It has become. On the other hand, the memory capacity required for the ADE method and the ZT method is comparable to that of the RC method. As another feature, the ADE method requires different handling when handling different dispersion media (Lorentz media and Debye media), but the RC method and the PLRC method can be estimated by the same handling. Mathematically, it is known that the ADE method is the simplest to handle.
[0004]
Regarding the ADE method, three types of algorithms for multipole Lorentz media and Debye media are described in Reference 6 (M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave. Guided Wave Lett., Vol. 7, pp. 121-123, May 1997.). 1) DADES (Debye ADE Syncronized) method, 2) LADES (Lorentz ADE Syncronized) method, and 3) LADEP (Lorentz ADE Partially Syncronized) method. In the DADE method, complete time synchronization is achieved using a half-negative form in a finite difference expression. In the LADES method, synchronization is performed all over the time, but it is necessary to store the previous electric field component further. In the LEDEP method, it is not necessary to preserve the previous electric field component, but the calculation is less accurate than the LEDES method. This is because the synchronization is partial.
[0005]
In a conventional method for estimating an electromagnetic field by numerical analysis, a recurrence formula corresponding to an electric field vector, a magnetic field vector, and a current vector has been used. On the other hand, in the present invention, by using the recurrence formula corresponding to the electric field vector, the magnetic field vector, and the charge component, the memory area to be used can be reduced while taking complete synchronization. Lorentz media can be handled with the same algorithm.
[0006]
[Problems to be solved by the invention]
In conventional electromagnetic field calculation methods, hybrid media for Lorentz media and Debye media could not be handled with the same algorithm, so separate calculations were necessary and accurate estimation could not be performed.
[0007]
The present invention has been proposed in view of the above, and hybrid media for Lorentz media and Debye media can be handled with the same algorithm, and therefore simultaneous calculation is possible, and the interaction of each media can be taken into account. Therefore, an object of the present invention is to provide a method for estimating the electromagnetic field of a dispersion medium that can be accurately estimated.
[0008]
[Means for Solving the Problems]
In order to achieve the above object, the present invention uses a computing device including an input device, a storage device, an arithmetic device, and an output device to analyze the electromagnetic field distribution or electromagnetic field propagation from a predetermined boundary condition. A method of estimating,
The region to be estimated is divided into minute regions, the coordinates are input to the input device and stored in the storage device, the permittivity and permeability of each minute region are set, and those values are input to the input device. Saving to a storage device, and
Setting the wavelength of the incident electromagnetic field, inputting the value to the input device and storing it in the storage device;
Setting a minute region that gives an incident electromagnetic field, inputting the coordinates and the intensity and phase of the incident electromagnetic field to the input device and storing them in a storage device;
Process including
Using the electric field vector, magnetic field vector, and charge component of the micro area to be estimated,
For each minute region, the Finite Difference Time Domain (FDTD) method is applied to the Maxwell equation of the electromagnetic field,
1) A magnetic field vector is calculated by an arithmetic unit using a temporally previous magnetic field vector and a temporally previous electric field vector,
2) The charge component is calculated by the arithmetic unit using the temporally previous electric field vector and the temporally previous charge component,
3) The electric field vector is obtained by the numerical solution sequentially along the time by the step of calculating by the arithmetic unit using the magnetic field vector, the temporally previous electric field vector, the charge component, and the temporally previous charge component. Basically , the final result is output by an output device.
[0009]
In addition, the present invention is characterized in that the electromagnetic field of the Lorentz medium is estimated and calculated based on the recurrence formulas of Equation 23, Equation 24, and Equation 25 described later.
[0010]
In addition, the present invention is characterized in that the electromagnetic field of the Debye medium is calculated based on the recurrence formulas of Equation 23, Equation 25, and Equation 35 described later.
[0011]
The present invention is also characterized in that the electromagnetic field of the Debye medium is calculated based on the recurrence formulas of Equations 25, 40 and 41 described later.
[0012]
Further, the present invention is a method for estimating an electromagnetic field in the case where a Lorentz medium and a Debye medium are mixed. For the Lorentz medium part, Equations 23, 24 and 25 described later are applied, and The calculation is performed using the recurrence formulas of Equations 23, 25 and 33, or Equations 25, 40 and 41.
[0013]
DETAILED DESCRIPTION OF THE INVENTION
The principle of the present invention will be described below, and then an algorithm when applied to a computer will be described.
[0014]
Assuming that no charge is held inside as follows. The Maxwell equation of this electromagnetic field is as follows.
[0015]
[Expression 17]

[0016]
[Formula 18]

[0017]
[Lorentz media]
Here, the Lorentz medium having Lorentz dispersion characteristics is calculated as follows. ω _p is the resonance frequency of the p-th polarization pair, A _p is its amplitude, δ _p is the attenuation factor, ε _s is the electrostatic dielectric constant, ε _∞ is the dielectric constant at infinite frequency, and Δε = ε _s when the-epsilon _∞, the dielectric constant of the Lorentz medium has polarization pairs of p pairs are known to be in the following manner in the frequency coordinates.
[0018]
[Equation 19]

[0019]
At angular frequency ω
[Expression 20]

Then, Ampere's law in frequency coordinates is as follows.
[0020]
[Expression 21]

here,
[0021]
[Expression 22]

It is.
[0022]
Here, Equation 21 or Equation 22 takes the inverse Fourier transform and expresses the difference with respect to time as follows.
[0023]
[Expression 23]

[0024]
[Expression 24]

In the FDTD method of the present invention, the magnetic field becomes the following differential recurrence formula from Equation 17.
[0025]
[Expression 25]

[0026]
The procedure from these numbers 23 obtains the vector E ^{n + 1} from the vector E ⁿ using equation 25 will be described with reference to FIG.
1) A vector H ^{n + 1/2} is obtained from the vector H ^{n−1 / 2} and the vector E ⁿ .
2) from the vector Q _p ^n-1 and the vector Q _p ⁿ and the vector E ⁿ seek vector Q _p ^{n + 1.}
3) from the vector H ^{n + 1/2} and the vector E ⁿ and the vector Q _p ^{n + 1} and the vector Q _p ⁿ seek vector E ^{n + 1.}
[0027]
On the other hand, in the conventional method using the LADES method, the difference recurrence formula of the magnetic field corresponding to Equation 21 is as follows.
[Equation 26]

The current difference recurrence formula corresponding to Equation 22 is
[0028]
[Expression 27]

It is.
In the fully time synchronized FDTD method, the recurrence formula is as follows.
[0029]
[Expression 28]

Regarding current,
[0030]
[Expression 29]

here,
[0031]
[30]

[0032]
[31]

It is.
[0033]
The procedure from these numbers 23 obtains the vector E ^{n + 1} from the vector E ⁿ using equation 25 will be described with reference to FIG.
1) A vector H ^{n + 1/2} is obtained from the vector H ^{n−1 / 2} and the vector E ⁿ .
2) From the vector H ^n-1/2 and the vector E ⁿ and the vector E ^n-1 and the vector J _p ^n-1 and the vector J _p ⁿ seek vector E ^{n + 1.}
3) and a vector E ^{n + 1} and the vector E ^n-1 and the vector J _p ^n-1 and the vector J _p ⁿ seek vector J _p ^{n + 1.}
[0034]
Thus, it can be seen that the conventional FDTD method uses 8 types of variables, but the recurrence formula of the FDTD method of the present invention uses 7 types of variables.
[0035]
Further, it can be understood that the expressions 23 and 27 are equivalent as follows.
From the equations 21 and 26, the following equation 32 is derived.
[0036]
[Expression 32]

The FTDT method has the following relationship.
[0037]
[Expression 33]

By substituting Equations 33 and 29 into Equation 23, Equation 28 is obtained.
[0038]
[Debye Media]
Next, a case of a Debye medium exhibiting Debye dispersion characteristics will be described. When τ _p is the relaxation time of the p-th polarization pair, it is known that the dielectric constant of a Debye medium with a p-pair polarization pair is as follows in frequency coordinates.
[0039]
[Expression 34]

Here, the recurrence formula corresponding to Expression 24 used in the present invention is as follows.
[0040]
[Expression 35]

[0041]
In addition to this equation, the processing proceeds as shown in FIG.
1) A vector H ^{n + 1/2} is obtained from the vector H ^{n−1 / 2} and the vector E ⁿ .
2) from the vector Q _p ^n-1 and the vector Q _p ⁿ and the vector E ⁿ seek vector Q _p ^{n + 1.}
3) from the vector H ^{n + 1/2} and the vector E ⁿ and the vector Q _p ^{n + 1} and the vector Q _p ⁿ seek vector E ^{n + 1.}
[0042]
Since this is the same as in the case of FTDT, it can be seen that the arithmetic processing of the Lorentz medium and the Debye medium can proceed simultaneously. For this reason, it is clear that the arithmetic processing about the hybrid of these media can be performed easily.
[0043]
On the other hand, in the conventional DADE method described in the literature (), the recurrence formulas corresponding to Equations 28 and 29 are as follows.
[0044]
[Expression 36]

[0045]
[Expression 37]

here,
[0046]
[Formula 38]

[0047]
[39]

It is.
[0048]
In order to advance the arithmetic processing using these equations 36 to 39, the following procedure shown in FIG. 7 is followed.
1) A vector H ^{n + 1/2} is obtained from the vector H ^{n−1 / 2} and the vector E ⁿ .
2) from the vector H ^{n + 1/2} and the vector E ⁿ and the vector J _p ⁿ seek vector E ^{n + 1.}
3) from the vector E ⁿ and the vector E ^{n + 1} and the vector J _p ⁿ seek vector J _p ^{n + 1.}
[0049]
Incidentally, it can be confirmed that Expressions 23 and 36 are equivalent by substituting Expression 37 into Expression 32 and substituting the result into Expression 23.
[0050]
As a further method of the present invention, instead of the current vector J _p ⁿ to the use of charge vector Q _p ^n. In this case, in the FTDT method, Equation 35 becomes Equation 40.
[0051]
[Formula 40]

The following recurrence formula can be obtained by substituting Equation 40 into Equation 23.
[0052]
[Expression 41]

here,
[0053]
[Expression 42]

[0054]
[Equation 43]

It is.
[0055]
In order to advance the arithmetic processing using these equations 40 to 43, the following procedure shown in FIG. 3 is followed.
1) A vector H ^{n + 1/2} is obtained from the vector H ^{n−1 / 2} and the vector E ⁿ .
2) from the vector H ^{n + 1/2} and the vector E ⁿ and the vector Q _p ⁿ seek vector E ^{n + 1.}
3) from the vector E ⁿ and the vector E ^{n + 1} and the vector Q _p ⁿ seek vector Q _p ^{n + 1.} This procedure, since those of the current vector J _p ⁿ only interchanged and the charge vectors Q _p ^n, in this case also, it is easy to carry out arithmetic processing of Lorentz medium and Device media simultaneously.
[0056]
[algorithm]
The computer assumed here is a computing device including an input device, a storage device, an arithmetic device, and an output device. Examples of this flowchart are shown in FIGS. 4 and 5 and will be described below.
F1) The area to be estimated is divided into minute areas, and the coordinates are input to the input device and stored in the storage device.
F2) A dielectric constant and a magnetic permeability of each minute region are set, and those values are input to the input device and stored in the storage device.
F3) Set the wavelength of the incident electromagnetic field, input the value to the input device, and save it in the storage device.
F4) A minute region to which an incident electromagnetic field is applied is set, and the coordinates and the intensity and phase of the incident electromagnetic field are input to the input device and stored in the storage device.
F5) electric field E of each minute region, the magnetic field H or, from intermediate variables Q ₁ used during the operation to reset the up Q _m, wherein the electric field E of each minute region, the magnetic field H coordinates with the incident electromagnetic field The intensity and phase are input to the input device and stored in the storage device.
F6) The electric field E, the magnetic field H or, from intermediate variables Q ₁ used in the course of operation aE variable for temporarily storing up to Q _m, respectively, aH, and aQ ₁ ~aQ _m, intermediate variable Q ₁ when temporarily the other variables to store the bQ ₁ ~bQ _m up to Q _m from reset these variables.
F7) Set initial values of other variables.
[0057]
F8) The index of the first iterative calculation is set to the initial value.
F9) The first flag of the repetitive calculation is set, and a minute area to be calculated is determined.
F10) For each minute region, it is determined whether or not it is a region that provides an incident electric field.
F14) When this determination is positive, the value of the incident electromagnetic field is transferred to the magnetic field vector H and the electric field vector E of the minute region to be estimated, and processing is performed from the position of the second flag described later.
F11) If this determination is negative, the following processing is performed when p = 1, 2,... First, H is calculated from aH or aE. Here, aH or aE is the previous magnetic field vector or electric field vector in time. More specifically, the calculation is performed using Equation 25.
F12) to calculate the Q _p aE, from aQ _p or bQ _p. Here, aQ _p and bQ _p are temporally previous charge components. More specifically, the calculation is performed using Equation 24 for the Lorentz medium and Equation 35 or 40 for the Debye medium.
F13) E is calculated from aQ _{1 to} aQ _m from H, aE, Q ₁ to Q _m . More specifically, the calculation is performed using Expression 24, Expression 35, or Expression 40. The calculation is performed using Equation 23 for the Lorentz medium and Equation 41 for the Debye medium.
F15) Set the second flag and save aH to H.
F16) Store aQ _p in bQ _p .
F17) Store Q _p in aQ _p .
F18) E is stored in aE.
F19) It is determined whether or not the calculation for all the minute regions is complete. If not, the calculation starts again from the position of the first flag.
F20) If positive, the following processing is performed. H, E, and Q ₁ to Q _m in the minute area are stored in the storage device.
F21) It is determined whether or not all calculations have been completed.
F22) If not, the index of the repetitive calculation is advanced by one step and recalculated from the position of the first flag.
F23) If positive, output this result to the output device.
F24) The calculation is terminated.
[0058]
【The invention's effect】
In the present invention, by using the recurrence formula of the electric field vector, the recurrence formula of the magnetic field vector, and the recurrence formula of the charge component, it is possible to reduce the memory area to be used while maintaining perfect synchronization. The medium and the Lorentz medium can be handled by the same algorithm, and a medium in which these media are mixed can be handled without being divided.
[Brief description of the drawings]
FIG. 1 is a flowchart illustrating a flow of variables that are gradually obtained when a Lorentz medium is handled in the present invention.
FIG. 2 is a flowchart showing a flow of variables to be gradually obtained when dealing with a Debye medium in the present invention.
FIG. 3 is a flowchart showing a flow of variables that are gradually obtained in the second case of handling a Debye medium in the present invention.
FIG. 4 is a flowchart of the present invention.
FIG. 5 is a flowchart of the present invention.
FIG. 6 is a flowchart showing a flow of variables that are gradually obtained when a conventional Lorentz medium is handled.
FIG. 7 is a flowchart showing a flow of variables that are gradually obtained when a conventional Debye medium is handled.

Claims (4)

A method of estimating an electromagnetic field distribution or electromagnetic field propagation from a preliminarily given boundary condition using a computing device including an input device, a storage device, an arithmetic device, and an output device,
Dividing the region to be estimated into minute regions, inputting the coordinates to the input device and storing them in a storage device;
Setting the dielectric constant and permeability of each minute region, inputting those values into the input device and storing them in a storage device;
Setting the wavelength of the incident electromagnetic field, inputting the value to the input device and storing it in the storage device;
Setting a minute region that gives an incident electromagnetic field, inputting the coordinates and the intensity and phase of the incident electromagnetic field to the input device and storing them in a storage device;
When the polarization pair is p = 1, 2,..., M, the electric field E, the magnetic field H, or intermediate variables Q ₁ to Q _m used in the middle of the calculation are reset, Performing a process including: inputting the electric field E, the coordinates of the magnetic field H, and the intensity and phase of the incident electromagnetic field of each minute region in the input region to the input device and storing them in a storage device;
Further, for some function F (t), a predetermined interval of t is divided into N minute intervals of width Δt, and in order from the end, 1, 2,... N,. And the value of the function F in the nth section is represented by F ⁿ , and for some function G, G ^{n + 1/2} = (G ^{n + 1} + G ⁿ ) / 2, G ^{n− When 1/2} = (G ⁿ + G ^n-1 ) / 2,
setting an index of a first iterative operation for n to an initial value and setting a first flag for the iterative operation;
Determining a micro area to be calculated;
For each minute region, determining whether it is a region that provides an incident electric field,
If this determination is positive, passing the value of the incident electromagnetic field to the magnetic field vector H and electric field vector E of the micro area to be estimated, and performing processing from the position of the second flag described later;
If this is not the case,
In each minute region, when the polarization pair is p = 1, 2,..., M, ω _p is the resonance frequency of the p-th polarization pair, A _p is its amplitude, δ _p is the attenuation factor, ε _s Is an electrostatic permittivity, ε _∞ is a dielectric constant at an infinite frequency, and Δε = ε _s −ε _∞ ,
1) A recurrence formula for the next time using the electric field vector E and the magnetic field vector H for the magnetic field vector H;

According to
2) the charge component Q _p, the recurrence formula for the next time using the electric field vector E of the charge component Q _p;

According to
3) A recurrence formula for the electric field vector E for the next time using the magnetic field vector H, the electric field vector E, and the charge component Q _p ;

Sequentially calculating with an arithmetic device according to
Setting a second flag;
A step of determining whether or not the calculation for all the micro regions has been completed;
If not, calculating again from the position of the first flag;
If positive, storing the magnetic field vector H, the electric field vector E, and the charge component Q _p in the minute region in the storage device;
Determining whether all calculations have been completed,
If not, a step of calculating the index of the repetitive calculation by one step and calculating again from the position of the first flag;
If it is positive, a calculation process is terminated, and a process including outputting the result to an output device is performed. A method of estimating an electromagnetic field distribution or electromagnetic field propagation from a preliminarily given boundary condition using a computing device including an input device, a storage device, an arithmetic device, and an output device,
Dividing the region to be estimated into minute regions, inputting the coordinates to the input device and storing them in a storage device;
Setting the dielectric constant and permeability of each minute region, inputting those values into the input device and storing them in a storage device;
Setting the wavelength of the incident electromagnetic field, inputting the value to the input device and storing it in the storage device;
Setting a minute region that gives an incident electromagnetic field, inputting the coordinates and the intensity and phase of the incident electromagnetic field to the input device and storing them in a storage device;
In each minute region, the polarization pairs, p = 1, 2, when · · · m, that the electric field E of each minute region, the magnetic field H or, from intermediate variables Q ₁ used during the operation to Q _m And inputting the electric field E and the coordinates of the magnetic field H and the intensity and phase of the incident electromagnetic field into each of the input devices and storing them in a storage device.
Further, for some function F (t), a predetermined interval of t is divided into N minute intervals of width Δt, and in order from the end, 1, 2,... N,. And the value of the function F in the nth section is represented by F ⁿ , and for some function G, G ^{n + 1/2} = (G ^{n + 1} + G ⁿ ) / 2, G ^{n− When 1/2} = (G ⁿ + G ^n-1 ) / 2,
setting an index of a first iterative operation for n to an initial value and setting a first flag for the iterative operation;
Determining a micro area to be calculated;
For each minute region, determining whether it is a region that provides an incident electric field,
If this determination is positive, passing the value of the incident electromagnetic field to the magnetic field vector H and electric field vector E of the micro area to be estimated, and performing processing from the position of the second flag described later;
If this is not the case,
ω _p is the resonance frequency of the p-th polarization pair, A _p is its amplitude, δ _p is the attenuation factor, ε _s is the electrostatic dielectric constant, ε _∞ is the dielectric constant at infinite frequency, and Δε = ε _s −ε _∞, and for each minute region,
1) A recurrence formula for the next time using the electric field vector E and the magnetic field vector H for the magnetic field vector H;

According to
2) the charge component Q _p, the recurrence formula for the next time using the electric field vector E of the charge component Q _p;

According to
3) A recurrence formula for the electric field vector E for the next time using the magnetic field vector H, the electric field vector E, and the charge component Q _p ;

Sequentially calculating with an arithmetic device according to
Setting a second flag;
A step of determining whether or not the calculation for all the micro regions has been completed;
If not, calculating again from the position of the first flag;
If positive, storing the magnetic field vector H, the electric field vector E, and the charge component Q _p in the minute region in the storage device;
Determining whether all calculations have been completed,
If not, a step of calculating the index of the repetitive calculation by one step and calculating again from the position of the first flag;
If it is positive, a calculation process is terminated, and a process including outputting the result to an output device is performed. A method of estimating an electromagnetic field distribution or electromagnetic field propagation from a preliminarily given boundary condition using a computing device including an input device, a storage device, an arithmetic device, and an output device,
Dividing the region to be estimated into minute regions, inputting the coordinates to the input device and storing them in a storage device;
Setting the dielectric constant and permeability of each minute region, inputting those values into the input device and storing them in a storage device;
Setting the wavelength of the incident electromagnetic field, inputting the value to the input device and storing it in the storage device;
Setting a minute region that gives an incident electromagnetic field, inputting the coordinates and the intensity and phase of the incident electromagnetic field to the input device and storing them in a storage device;
In each minute region, the polarization pairs, p = 1, 2, when · · · m, that the electric field E of each minute region, the magnetic field H or, from intermediate variables Q ₁ used during the operation to Q _m And inputting the electric field E and the coordinates of the magnetic field H and the intensity and phase of the incident electromagnetic field into each of the input devices and storing them in a storage device.
Further, for some function F (t), a predetermined interval of t is divided into N minute intervals of width Δt , and in order from the end, 1, 2,... N,. And the value of the function F in the nth section is represented by F ⁿ , and for some function G, G ^{n + 1/2} = (G ^{n + 1} + G ⁿ ) / 2, G ^{n− When 1/2} = (G ⁿ + G ^n-1 ) / 2,
setting an index of a first iterative operation for n to an initial value and setting a first flag for the iterative operation;
Determining a micro area to be calculated;
For each minute region, determining whether it is a region that provides an incident electric field,
If this determination is positive, passing the value of the incident electromagnetic field to the magnetic field vector H and electric field vector E of the micro area to be estimated, and performing processing from the position of the second flag described later;
If this is not the case,
ω _p is the resonance frequency of the p-th polarization pair, A _p is its amplitude, δ _p is the attenuation factor, ε _s is the electrostatic dielectric constant, ε _∞ is the dielectric constant at infinite frequency, and Δε = ε _s and -ε _∞,
1) A recurrence formula for the next time using the electric field vector E and the magnetic field vector H for the magnetic field vector H;

According to
2) the charge component Q _p, the recurrence formula for the next time using the electric field vector E of the charge component Q _p;

According to
3) A recurrence formula for the electric field vector E for the next time using the magnetic field vector H, the electric field vector E, and the charge component Q _p ;

Sequentially calculating with an arithmetic device according to
Setting a second flag;
A step of determining whether or not the calculation for all the micro regions has been completed;
If not, calculating again from the position of the first flag;
If positive, storing the magnetic field vector H, the electric field vector E, and the charge component Q _p in the minute region in the storage device;
Determining whether all calculations have been completed,
If not, a step of calculating the index of the repetitive calculation by one step and calculating again from the position of the first flag;
If it is positive, a calculation process is terminated, and a process including outputting the result to an output device is performed. A method of estimating an electromagnetic field distribution or electromagnetic field propagation from a preliminarily given boundary condition using a computing device including an input device, a storage device, an arithmetic device, and an output device,
Dividing the region to be estimated into minute regions, inputting the coordinates to the input device and storing them in a storage device;
Setting the dielectric constant and permeability of each minute region, inputting those values into the input device and storing them in a storage device;
Setting the wavelength of the incident electromagnetic field, inputting the value to the input device and storing it in the storage device;
Setting a minute region that gives an incident electromagnetic field, inputting the coordinates and the intensity and phase of the incident electromagnetic field to the input device and storing them in a storage device;
In each minute region, the polarization pairs, p = 1, 2, when · · · m, that the electric field E of each minute region, the magnetic field H or, from intermediate variables Q ₁ used during the operation to Q _m And inputting the electric field E and the coordinates of the magnetic field H and the intensity and phase of the incident electromagnetic field into each of the input devices and storing them in a storage device.
Further, for some function F (t), a predetermined interval of t is divided into N minute intervals of width Δt, and in order from the end, 1, 2,... N,. And the value of the function F in the nth section is represented by F ⁿ , and for some function G, G ^{n + 1/2} = (G ^{n + 1} + G ⁿ ) / 2, G ^{n− When 1/2} = (G ⁿ + G ^n-1 ) / 2,
setting an index of a first iterative operation for n to an initial value and setting a first flag for the iterative operation;
Determining a micro area to be calculated;
For each minute region, determining whether it is a region that provides an incident electric field,
If this determination is positive, passing the value of the incident electromagnetic field to the magnetic field vector H and electric field vector E of the micro area to be estimated, and performing processing from the position of the second flag described later;
If this is not the case,
ω _p is the resonance frequency of the p-th polarization pair, A _p is its amplitude, δ _p is the attenuation factor, ε _s is the electrostatic dielectric constant, ε _∞ is the dielectric constant at infinite frequency, and Δε = ε _s and -ε _∞,
1) A recurrence formula for the next time using the electric field vector E and the magnetic field vector H for the magnetic field vector H;

According to
For Lorenz media part,
2-1) The charge component Q _p, the recurrence formula for the next time using the electric field vector E of the charge component Q _p;

According to
3-1) A recurrence formula of the electric field vector E for the next time using the magnetic field vector H, the electric field vector E, and the charge component Q _p ;

Sequentially calculating with an arithmetic device according to
For the Debye media part,
2-2) The charge component Q _p, the recurrence formula for the next time using the electric field vector E of the charge component Q _p;

According to
3-2) A recurrence formula of the electric field vector E for the next time using the magnetic field vector H, the electric field vector E, and the charge component Q _p ;

Sequentially calculating with an arithmetic device according to
Or, for the Debye media part,
2-3) The charge component Q _p, the recurrence formula for the next time using the electric field vector E of the charge component Q _p;

According to
3-3) A recurrence formula for electric field vector E for the next time using magnetic field vector H, electric field vector E, and charge component Q _p ;

Sequentially calculating with an arithmetic device according to
Setting a second flag;
A step of determining whether or not the calculation for all the micro regions has been completed;
If not, calculating again from the position of the first flag;
If positive, storing the magnetic field vector H, the electric field vector E, and the charge component Q _p in the minute region in the storage device;
Determining whether all calculations have been completed,
If not, a step of calculating the index of the repetitive calculation by one step and calculating again from the position of the first flag;
If it is positive, a calculation process is terminated, and a process including outputting the result to an output device is performed.

Images